VOLATILITY DYNAMICS OF NYMEX NATURAL GAS FUTURES PRICES

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "VOLATILITY DYNAMICS OF NYMEX NATURAL GAS FUTURES PRICES"

Transcription

1 VOLATILITY DYNAMICS OF NYMEX NATURAL GAS FUTURES PRICES Hiroaki Suenaga Reearch Fellow School of Economic and Finance Curin Buine School Curin Univeriy of Technology Aaron Smih Aian Profeor Deparmen of Agriculural and Reource Economic Univeriy of California Davi and Member Giannini Foundaion Jeffrey William Daniel Baron DeLoach Profeor Deparmen of Agriculural and Reource Economic Univeriy of California Davi and Member Giannini Foundaion Correpondence o: Hiroaki Suenaga School of Economic and Finance Curin Buine School Curin Univeriy of Technology GPO Box U987 Perh WA 6845 Auralia. e mail: Phone: Fax:

2 VOLATILITY DYNAMICS OF NYMEX NATURAL GAS FUTURES PRICES ABSTRACT We examine he volailiy dynamic of daily naural ga fuure raded on he NYMEX via he parially overlapping ime erie POTS model of Smih 005 Journal of Applied Economeric. We how ha aide from a ime o mauriy effec volailiy exhibi wo imporan feaure ha are cloely relaed o he eaonal cycle of US naural ga demand and orage. Fir volailiy i greaer in he winer han in he ummer. Second he perience of price hock and hence he correlaion among concurrenly raded conrac diplay ubanial eaonal and cro ecional variaion in a way conien wih he heory of orage. We demonrae ha by ignoring he eaonaliy in he volailiy dynamic of naural ga fuure price previou udie have uggeed ubopimal hedging raegie.

3 . INTRODUCTION Naural ga demand in he US peak beween December and March due o reidenial heaing during he winer. Alhough hi unremarkable fac implie higher average price in winer ineremporal arbirage miigae he price effec; he winer price equal he off peak pring and ummer price plu he co of carry. Thi paern i implied by he heory of orage which aer ha he equilibrium conellaion of po and fuure price repreen he price a which he marginal benefi of curren conumpion equal he expeced marginal benefi of oring a commodiy for fuure conumpion William and Wrigh 99. Thi relaionhip doe no hold beween wo conrac price if invenory i effecively zero a any poin beween heir mauriy dae. The ypical eaonaliy in he conellaion of naural ga price i illuraed in Figure which diplay all 7 NYMEX fuure price on April 003. Thoe conrac alhough reching ix year ino he fuure are aligned in Figure o he convenional April March year in naural ga. Thi alignmen reveal he rong increae in price during he fall and early winer preciely when ock are peaking. Unlike for mo commodiie orage faciliie for naural ga can reach collecive capaciy during hi period which lead o price relaionhip ha imply ignifican eaonaliy in he marginal co of orage. Srong eaonaliy in demand and orage alo implie highly nonlinear volailiy dynamic. Volailiy i naurally high in he winer conrac becaue he high marginal co of naural ga producion and he inelaic winer demand mean ha hock of even a mall magniude can caue a large price wing. A he ame ime he high naural ga invenory inended for all winer monh reduce volailiy of he early winer conrac becaue hock can be accommodaed albei parially by releaing or aborbing invenory. Such flexibiliy i ineviably

4 lower laer in he winer. The eaonal orage paern alo implie ha price of winer conrac ar flucuaing a early a he preceding off peak demand period during which informaion arrive abou he fuure availabiliy of ored ga. In conra price of pring and ummer conrac hould no exhibi ubanial movemen unil he end of he preceding peak demand eaon becaue lile invenory i carried over from winer o pring in a normal year. In hi paper we examine he volailiy dynamic of he NYMEX naural ga fuure price uing he parially overlapping ime erie POTS model of Smih 005. Unlike convenional model of commodiy price dynamic he POTS model rea he daily price on a given conrac a a ingle ime erie. A ime proceed ome conrac reach delivery and ceae o exi while oher are born and begin rading. In hi ene a e of conrac coniue a e of parially overlapping ime erie. Each of hee ime erie behave a a maringale proce which allow he model o be applied direcly o he fir difference of he commodiy fuure price and herefore o avoid mi pecifying he price level dynamic. To accoun for he volailiy dynamic he POTS model ue nonparameric funcion. Thi flexible pecificaion capure he ime o mauriy effec eaonal volailiy and oher nonlinear volailiy dynamic reuling from he peculiariie of naural ga a a commodiy. To illurae he pracical imporance of hee feaure of he POTS model we apply our analyi of he volailiy dynamic of naural ga fuure price o he andard opimal hedging raegy. We illurae ha eaonal and cro ecional variaion in he degree of perience of he price hock ogeher wih he eaonaliy in he arrival of informaion imply ha he December and ummer June hrough Augu conrac are more effecive han oher conrac in minimizing he variance of porfolio reurn. We conra hi reul wih he reul from previou udie which ignore eaonal and cro ecional variaion in volailiy of naural ga price and which recommend he ue of he adjacen delivery conrac for hedging.

5 Much of he previou reearch on naural ga no o menion oher energy fuure ha no accouned for complex volailiy dynamic reuling from he peculiariie of hee commodiie. One common approach in previou udie of energy fuure price ha been o pecify he po price a a funcion of underlying ae variable following ipulaed ochaic procee. The uggeed model i hen ued o derive he valuaion formula of fuure and oher derivaive conrac any difference from he oberved fuure price being inerpreed a repreening a rik premium. Example of hi approach are Schwarz 997 for he NYMEX crude oil and Lucia and Schwarz 00 for he Nordpool wholeale elecriciy marke. For naural ga Manoliu and Tompaidi 00 have applied one and wo facor model o NYMEX fuure price and repor ha he eimaed model exhibi rong eaonal variaion while deviaion from hi eaonal mean rever o zero. A econd common approach ha been o examine direcly he relaionhip beween he po and fuure price wihou ipulaing he ochaic procee of he oberved price erie. Two queion are commonly addreed in uch udie: i if he fuure price i unbiaed in forecaing ubequenly realized po price and ii if he po price and he price of concurrenly raded fuure conrac exhibi long run relaionhip and if o how quickly hey rever o he long run relaionhip afer deviaing from i. The fir queion i uually addreed by examining he aiical ignificance of he difference beween he po or nearby fuure and he fuure price oberved much earlier. Several udie have repored ha he NYMEX naural ga fuure price are downward biaed in forecaing he ubequenly realized po price and inerpreed hi bia a repreening a rik premium Wall 995; Modjahedi and Movaagh 005; Movaagh and Modjahedi 005. For he econd queion Roo and Lien 003 and Lien and Roo 999 ue variou coinegraion mehod o examine he long run relaionhip beween he po price and he price of concurrenly raded fuure conrac. 3

6 They conclude ha hee price hare a common ochaic rend and repond o deviaion from heir long run relaionhip in uch a way ha he difference beween he price converge o zero. Thi reul implie ha imulaneouly raded fuure price are in one o one relaionhip and herefore have zero bai in he long run. Improper or incomplee underanding of volailiy dynamic can lead uch udie o erroneou concluion abou he marke rik premium or more generally he efficiency of exiing fuure marke. William and Wrigh 99 how ha he equilibrium fuure price derived from a dynamic raional expecaion model of a eaonal orable commodiy are highly nonlinear and non mooh which i o ay ha hey canno be expreed in a reduced form. Clearly pecified eaonal price cycle can only approximae he rue price dynamic. Srong eaonaliy in orage implie ha he difference beween he po price and price of concurrenly raded fuure conrac or he bai repreening he co of carry varie acro conrac delivery monh. Previou udie on po fuure relaionhip have no incorporaed uch eaonal variaion in he bai. In conra he POTS model avoid uch mipecificaion by differencing ou he price level dynamic. Aide from hee modeling iue mo previou udie have uilized only a ube of price daa available from organized exchange where muliple conrac wih differen mauriy dae are concurrenly raded. One pracice i o conruc a monhly daa erie by acking he fuure price from ome paricular day of he monh. Thi pracice i paricularly common o e of bia in fuure price for mo energy fuure conrac are defined in monhly block. Anoher pracice i o conruc a daily erie by plicing ogeher he nearby fuure conrac. Eiher pracice no only dicard much informaion bu alo dior he emporal dynamic of he oberved price erie due o wiching from one delivery monh o anoher. 4

7 . Parially Overlapping Time Serie Model The parially overlapping ime erie POTS model of Smih 005 i a laen facor model of daily fuure price change. The laen facor repreen he fac ha conemporaneou fuure price are ied ogeher by ineremporal arbirage. In a ingle facor eing he model ake he following form ΔF = ε + λ u where ΔF i an n vecor of daily fuure price change wih n repreening he number of conrac raded on day. I comprie ΔFm = Fm Fm where he wo ubcrip repreen he mauriy and rading dae repecively. The wo ubcrip implicily define he number of day o mauriy a d = m. The calar ε i a laen facor and i n vecor of facor loading. The n vecor u denoe he idioyncraic error wih u ~ N0 I n and λ ignifie an n n diagonal marix ha deermine he variance of he idioyncraic error. The componen of he marice and λ are pecified a funcion of mauriy dae and ime o mauriy of conrac. Tha i m = d m λm = λd m For idenificaion we pecify E[ε ] = E[ε um] = 0 for all m and and E[ΔF I ] = 0 where I denoe he informaion e available a. Thee aumpion aer ha a erie of daily fuure price change follow a maringale difference equence which implie a zero rik premium. Following Smih 005 we pecify he condiional variance of ε by he GARCH proce 5

8 3 E[ε I ] = h = ω + β h + α E[ε I ] Becaue he uncondiional variance of ε equal uniy we have ω = α β. The la erm in 3 i E[ε I ] = ε + P where ε = E[ε I ] and P = E[ε ε I ] which are obained hrough he Kalman filer Hamilon 994. The POTS model a defined in hrough 3 i economerically imilar o facor model of commodiy price dynamic uch a Schwarz 997 and Manoliu and Tompaidi 00 a applied o naural ga. Among he major difference i ha he POTS model view he daily price on a given conrac a a ingle ime erie and pecifie he dynamic of daily price change. In conra convenional facor model pecify he dynamic of daily price level and no price change. By modeling daily price change which are a maringale difference equence he POTS model avoid pecifying eaonal or any oher deerminiic variaion in he underlying po price level and hence i free of approximaion bia. Thi bia could be ofen large in commodiy price model epecially for commodiie ha exhibi uch a rong eaonal paern a naural ga Suenaga 005. The POTS model alo employ flexible funcional form in pecifying he facor loading m and he variance of he idioyncraic error λm. In conra convenional facor model e.g. Schwarz 997 pecify a ochaic proce of he po price dynamic wih a mall number of parameer hereby impoing a paricular rucure on he facor loading in he fuure pricing equaion. Even he mo complex of hee model including an increaed number of facor and/or pecifying dynamic of each facor by more complex ochaic proce ill pecify a imple variance erm for he idioyncraic error wih a mo cro ecional variaion acro 6

9 conrac delivery monh. In conra he flexible funcional form employed in he POTS model inend o capure ime o mauriy effec and eaonal volailiy a well a oher nonlinear volailiy dynamic of naural ga fuure price reuling from peculiariie of he commodiy. 3. DATA AND ESTIMATION RESULTS 3. Daa We eimae he model in and uing daily elemen price daa from he NYMEX naural ga fuure marke. The NYMEX ared rading naural ga fuure conrac in April 990. Conrac raded in hi marke are defined in monhly block wih each conrac providing for he delivery of 0000 million Briih Thermal uni BTu of naural ga a he Henry Hub locaed in Louiiana. The marke iniially raded conrac a far a year before he fir calendar day of he delivery monh bu ha gradually exended hi horizon o 6 year. Conrac were iniially raded unil even buine day prior o he fir calendar day of he delivery monh bu rading wa laer exended o 3 buine day prior o he delivery monh. We analyze he daily change in he logarihm of elemen price and our ample pan January 99 o December Becaue dian delivery conrac are no alway acively raded we drop conrac of more han monh o mauriy. Excluding hee obervaion we have a ample of 4068 price among 75 conrac. 3. Eimaion Reul In applying he POTS model o he NYMEX naural ga fuure price daa we pecify he facor loading and he variance of idioyncraic error in by he following rigonomeric funcion 7

10 5 m m m = = + + m d a0 a d a j= λ m m = λ d = b m 0 + b m d + πjd + m πjd in + a j co dmax d m j max πjd + 5 m m b + j in b j co j= dmax dmax πjd where dmax = 365. To capure eaonaliy we eimae one uch funcion for each conrac monh i.e. for all m =. Specified a in he wo funcion become more flexible a he number of rigonomeric erm increae. Alhough hi exra flexibiliy allow he model o fi he oberved daa beer i alo make he coefficien eimae more eniive o exreme obervaion. By uing only five rigonomeric erm we allow ufficien flexibiliy o capure eaonaliy and ime o delivery effec bu we avoid exce eniiviy o oulier. We eimae he model by he mehod of Maximum Likelihood wih he iniial value obained by he ieraive approximae EM mehod of Smih Table ummarize he coefficien eimae of he GARCH parameer. In he able he coefficien eimae of α and β are 0.09 and The um of he wo coefficien 0.90 i le han uniy indicaing ha he condiional volailiy of he common underlying facor i highly perien ye i aionary. Figure plo he uncondiional variance of daily price change of each of conrac which we compue a + λ for d ranging from 0 o 365 day o mauriy uing he eimaed m m d m md facor loading m and he variance of he idioyncraic error λm. The figure exhibi a lea four inereing feaure. Fir on any given dae he volailiy of conrac ha are cloer o mauriy exceed ha of more dian conrac. Thi feaure ofen called he Samuelon effec indicae ha hock o po price are expeced o diipae omewha over ime. Second volailiy of cloe o mauriy conrac i ubanially higher for winer conrac han for lae pring or ummer conrac. Third during he period from early May o lae Sepember 8

11 volailiy increae for all conrac mauring before he end of he following peak eaon. Finally during he early winer early November o mid January volailiy rie for all conrac alhough he January o April conrac diplay much larger increae han he oher conrac. The la hree feaure follow naurally from eaonaliy in he demand for naural ga. Nearby winer conrac exhibi high price volailiy becaue demand reache conemporaneou upply capaciy in winer. Even hough high winer invenory allow price hock of ome magniude o be aborbed he high winer volailiy depiced in Figure indicae ha uch price buffering i only limied. Summer conrac exhibi low nearby volailiy becaue low demand relaive o upply mean ha demand hock can be aborbed by alering he amoun injeced ino orage. The gradual volailiy increae in he lae pring and ummer May o lae Sepember reflec he arrival of imporan marke informaion. During hi period invenory coninuouly change a exce naural ga producion i ored for ue in he ubequen peak demand eaon. Ga ored in hi period will no be carried over o he following off peak demand eaon unle ga demand in he coming peak demand eaon i unuually low. Such informaion will no be revealed unil acual demand and/or upply condiion are realized. Hence price volailiy increae during he May o lae Sepember rading period bu only for he conrac deliverable o he coming peak demand eaon and earlier. During early winer new informaion provide rong ignal abou he imminen peak eaon a well a he likely amoun invenory carryover from he curren peak demand eaon o ubequen monh. Nonehele he amoun of ga carried over from he peak o he ubequen off peak eaon i very mall relaive o he amoun ored over he off peak eaon in a normal year. Thu nearby conrac exhibi high volailiy during hi early winer period 9

12 bu volailiy alo increae albei only marginally for conrac ha maure in he ummer. By mid January mo of he informaion abou he curren peak eaon ha arrived and price volailiy begin o decline. Thee eaonal paern in price variance correpond o he eaonal paern in ga orage. Temporal arbirage induce a fair amoun of naural ga o be carried over from he off peak demand eaon April hrough June o he peak demand eaon December o March o ha he price difference beween hee eaon i on average equal o he co of carry. Figure 3 illurae hi orage paern. In he figure he US naionwide working ga orage i he lowe in March afer which i gradually increae hroughou pring and ummer unil i reache an annual high in Ocober or November. A rapid decreae of invenory from November hrough he following February indicae ha a large amoun of ored ga i wihdrawn o mee wih a high demand for heaing energy. Table ummarize he proporion of he variance explained by he common facor ε. I indicae ha he model explain on average abou 83% of daily price variaion. In general pring and ummer conrac are more cloely relaed o he common facor han winer conrac. Figure 4 illurae for each of he mauriie how he proporion of oal price variance explained by he common facor change over he ime ahead of expiraion. We meaure hi proporion by / + λ. For all conrac hi proporion drop m m d m md m md ubanially below 00 percen in he la few monh before mauriy. Thi paern indicae ha a delivery approache he fuure price increaingly reflec local condiion a he Henry Hub and le condiion in naural ga marke in he re of Norh America. Such a paern i no urpriing for naural ga. Becaue he fuure conrac for naural ga repreen a monhlong flow hrough he Henry Hub raher han he more radiional warehoue receip for he commodiy in ore local congeion in pipeline can diconnec nearby fuure from marke 0

13 elewhere. For he ame reaon of nework congeion hoe local marke elewhere omeime have po or nearby forward price eiher a eep dicoun or eep premium o he average hroughou he nework. Figure 4 alo how ha for conrac ha deliver beween Ocober and March he hare explained by he common facor drop ubanially around he middle o he end of Augu and keep decreaing aferward. Tha i much of he po Augu price variaion in hee conrac emanae from informaion of a hor erm naure ha doe no affec he amoun of carryover o he following off peak eaon. Coupled wih he high volailiy of hee conac in hi period ee Figure hi obervaion implie ha he high invenory accumulaed by lae ummer allow only limied buffering of curren marke hock. Thi lack of abiliy o aborb hock likely arie from he high marginal co of invenory adjumen which increae wih he invenory level becaue injecing ga back ino underground orage require he ga o be a ever higher preure. In hi ame po Augu period conrac ha deliver afer he end of he following peak eaon exhibi low oal volailiy ee Figure bu a high proporion of heir variaion i capured by he common facor ee Figure 4. Thu he common facor repreen informaion abou marke condiion in he following off peak eaon bu relaively lile uch informaion arrive in hi period. The fac ha he Ocober o March conrac are weakly relaed o he facor in hi period i conien wih he mall invenory carryover from he peak eaon o he following off peak eaon. Thi lack of carryover reduce he poenial for arbirage acro hee wo period and herefore i weaken he link beween he price of conrac ha deliver before he end of he peak eaon and hoe ha deliver afer he end of he peak eaon. In um he eimaed POTS model reveal ha he volailiy of naural ga fuure price exhibi boh he Samuelon effec and rong eaonaliy. Volailiy i higher for winer conrac

14 han for oher conrac. Volailiy alo increae from early May o Sepember for all conrac mauring by he end of he following peak demand eaon and from early November hrough mid January for he January o April conrac. The correlaion beween he daily price change of concurrenly raded conrac end o be highe during hee wo period. Overall our model illuminae he complex dynamic of naural ga price volailiy which previou udie were unable o dicern becaue heir economeric model preumed a volailiy pecificaion ha i oo imple. 4 OPTIMAL HEDGING STRATEGY In hi ecion we exend our analyi of he volailiy dynamic of naural ga fuure price o inveigae he implicaion for hedging. We conider a imple hedging raegy in which a hedger ha a po poiion Q a ime and imulaneouly ake a hor poiion in X fuure conrac for delivery a τ >. A + k < τ he hedger clear i poiion by elling Q uni in he po marke and buying X fuure conrac for delivery a τ. The hedger change in wealh from o + k ignoring he inere rae i 4 W = S S Q F F X = ΔS F Q + k + k + k τ τ + k η Δ + k τ where Si i he po price a i η = X/Q i he hedge raio. The variance of W + k i F i τ i he period i price of he fuure conrac for delivery a τ and 5 V[ W ] = V[ ΔS ] + V[ ΔF ] η cov[ ΔS F ] Q + k + k η + k τ + k Δ + k τ which i minimized by * 6 η τ = cov[ ΔS + k ΔF + k ]/ V[ ΔF + k ] τ τ

15 Subiuing 6 ino 5 yield he minimized variance * 7 V[ W ] = V[ ΔS ] ρ Q + k η τ + k + k τ where ρ k τ + i he correlaion beween po and fuure conrac for delivery τ in heir price change over period o + k. Alernaively for a hedger minimizing he variance of he porfolio reurn r = rs η r rf he opimal hedge raio and he aociaed minimum variance are r* 8 ητ = cov[ Δ lns + k Δ lnf + k ]/ V[ Δ lnf + k ] τ τ + k η τ + k + k τ r* r 9 V[ r ] = V[ Δ lns ] ρ Q where r ρ k τ + repreen he correlaion beween he log po price and log price of fuure conrac for delivery a τ over he period o + k. Three remark hould be made abou hee hedging raegie. Fir many organized exchange concurrenly rade muliple conrac wih differen mauriy dae. Thu alhough he fuure conrac o be included ino he porfolio τ i exogenou o he above raegy i hould be a deciion variable for he hedger. The expreion 6 and 8 indicae ha given he ime of enry and hedging horizon k he hedger hould include ino i porfolio he fuure conrac for which he price change ha he highe correlaion wih he po price change. Becaue only a finie number of conrac are raded on any given day one need o calculae he opimal hedge raio only for he fuure conrac wih he highe correlaion o he po price. Second he ime of enry and hedging horizon k hould be alo endogenou o he hedger deciion. The choice of and k i imporan paricularly for commodiy wih rong eaonaliy in mean price. Given a priori knowledge of uch a eaonal paern a hedger hould 3

16 no hold a po poiion from he peak o he off peak demand eaon for uch pracice would yield a lea on average a negaive reurn. The hedge raio in 6 and 8 are opimal only given ha he deciion o carry over from o + k i predeermined. In pracice a poiion hould be held only if he expeced wealh E[W+k] exceed he value of rik aociaed wih he minimum variance of porfolio reurn. Finally he expreion 6 hrough 9 indicae ha boh he opimal hedge raio and he fuure conrac included ino he porfolio depend on wo aribue: i he covariance of po and fuure price and ii he variance of fuure price change. Specificaion on he volailiy dynamic of po and fuure price play key role in deermining empirical eimae of hee aiic and hence he opimal hedging raegy. The POTS model by allowing eaonal and cro ecional variaion in he facor loading and he variance of idioyncraic error yield an opimal hedge raio ha varie by τ and k. In conra convenional model of commodiy price dynamic deermine facor loading by he ime o mauriy of he conrac and a mall number of parameer defining he ochaic procee of he underlying facor. Due o hi rericive pecificaion he opimal hedge raio implied by hee model doe no vary by conrac delivery dae. In paricular a imple one facor mean reverion model conidered by Schwarz 997 and he wo facor model by Manoliu and Tompaid 00 boh imply ha he opimal porfolio alway include he nearby conrac. In oher word he pecificaion choice for he ochaic procee of he underlying facor deermine he opimal hedging raegy. The andard regreion model conidered for he analyi of he po fuure price relaionhip are imilarly incapable of implying cro ecional and eaonal variaion in he opimal hedge raio due o a imple variance rucure aumed for he diurbance erm. 4

17 4. Opimal Hedging Sraegy Implied by he POTS Model We evaluae he opimal hedge raio baed on he uncondiional variance of daily price change implied by he eimaed POTS model. 4 In doing o we ue he nearby fuure price a a proxy for he po price. Baed on our dicuion in Secion 3. a delivery approache he fuure price increaingly reflec condiion a he Henry Hub. In hi ene he nearby conrac approximae a po price again which marke paricipan may wan o hedge. We conider he cae where and k are predeermined and he hedger deciion i o chooe he fuure conrac o be included ino he porfolio τ and he hedge raio. We find he opimal oluion for he wo cae wih differen holding period: i a hedger who carrie a hor poiion only for a ingle day k = and ii a hedger who carrie a hor poiion for one monh aring a he fir day of each calendar monh and ending a he la day of he ame monh. We conider hee wo cae o deermine wheher very hor holding period are le eniive o he modeling of price dynamic. From he POTS model he uncondiional variance of daily fuure price change i given a 0 E[ΔFΔF ] = + λ λ Wih he aumpion ud iid ~ N0 he diagonal and off diagonal elemen are E[ Δ ] = d m + λd m F m E m [ Δ F ΔF ] = d m δ for m > and m. where d = m and δ =. Uing he expreion he correlaion beween daily price change of wo fuure conrac for delivery and i 5

18 6 δ λ δ δ λ δ δ δ ρ + + = = π π where δi = i and i π = + i i i i i i δ λ δ δ i he quare roo of he hare of he oal variance of conrac i explained by he common facor. Equaion indicae ha he variance of he porfolio reurn i minimized when he porfolio include he fuure conrac for which he large hare of price change i accouned for by he common facor. For a day long holding period he opimal hedge raio and he minimized variance are 3 * η = δ λ δ δ δ + 4 V[ * W η + ] = Q ρ δ λ δ + For he hedging raegy wih he monh long holding period over o we need he expreion for he uncondiional variance of daily fuure price change which wih he maringale propery aumed in he model i imply he um of he daily price change over hi period 5 = + = Δ Δ ʹ ʹ ] ʹ [ E λ λ F F wih i elemen 6 = + = Δ ] E[ m m m m m F λ = = Δ Δ ] [ E m m m F F for m > m. The correlaion beween he wo conrac over he horizon o i

19 7 7 ρ = + + = = = λ λ The opimal hedge raio and he aociaed minimum variance are 8 * η = = = + λ 9 ] V[ * W η = Q ρ λ + = Equaion 3 and 8 indicae ha he opimal hedge raio i a funcion of he ime of enry he hedging horizon k and he delivery period of he fuure conrac in he porfolio. I paricular he opimal hedge raio increae wih he variance of he nearby fuure price ha i aribuable o he common facor and/or he proporion of he fuure price variance explained by he common facor. In oher word a hedger hould ake a large hor poiion when he nearby fuure price i very volaile and i i rongly relaed o he fuure price of ubequen delivery. Even when he nearby fuure price i very volaile a hedger poiion i mall if i price movemen i no cloely relaed o he oher concurrenly raded conrac. 4. Opimal Hedging Sraegy for Naural Ga Figure 5 hrough 7 illurae he fuure conrac included ino he opimal porfolio he opimal hedging raio and he minimum variance aained by he opimal porfolio for each of he wo hedging horizon. Fir for a daily hedging raegy he opimal porfolio frequenly include four conrac: he December conrac for he period beween mid May and mid Augu and

20 eiher he June July or Augu conrac for he period beween mid Sepember and mid April in he following year. Thee conrac are ofen ued becaue hey exhibi he highe hare of heir price volailiy explained by he common facor in relevan period. Oher conrac are rarely included ino he porfolio. Becaue hor daed conrac exhibi ubanial idioyncraic volailiy he opimal porfolio never include hee conrac. The hree monh ahead conrac i he hore horizon and i ued only in he fir half of April and he fir half of Augu where he variance minimizing conrac wiche gradually from he Augu o winer and from he December o ummer conrac repecively. The predominance of he June July Augu and December conrac i conien wih our previou dicuion relaing eaonaliy of price volailiy o ha of naural ga demand and orage. From he beginning of he year he opimal porfolio include he July conrac and hen i wiche o he Augu conrac. Conrac for earlier mauriy are no ued due o heir high idioyncraic volailiy. Thi high idioyncraic volailiy repreen he Samuelon effec for he March conrac wherea i i due o low ga orage for he April o June conrac price movemen of hee conrac in repone o demand upply and oher marke hock are no linked o one anoher hrough available orage. In he middle of April he opimal conrac for hedging purpoe wiche from he Augu o dian conrac a he Augu conrac become ubjec o he mauriy effec. Thi raniion i raher quick wih he Augu conrac replaced by he December conrac by mid May. The Sepember hrough November conrac are ued only for a hor duraion becaue of heir high idioyncraic variance. The nex raniion ake place in he middle of Augu when he opimal porfolio wiche o he March conrac a idioyncraic variance of he December conrac increae rapidly. The January and February conrac are no ued in hi raniion becaue a large hare of heir price variaion i conrac pecific. The March and April conrac are opimal 8

21 only for a hor period becaue price movemen of hee wo conrac are conrac pecific due o he low invenory applicable during hoe wo monh. Figure 6a plo he opimal hedge raio a a funcion of he dae wihin he ga year. A hown in 3 he opimal hedge raio i imply he raio of he covariance beween he nearby and he fuure conrac o he variance of he fuure conrac included in he porfolio. In he figure he opimal hedge raio i alway above one indicaing ha he covariance alway exceed he variance of he fuure conrac. Thi i becaue he fuure conrac included ino he opimal porfolio are a lea hree monh away from delivery and hence diplay lile variaion a dominan hare of which reflec he common facor. Wheher a hedge raio above uniy make ene i a queion for he whole heory of opimal hedging. The opimal hedge raio i paricularly high in December and January during which he price variance of he nearby conrac i largely aribuable o he common facor yielding large covariance. Even hough he nearby fuure conrac exhibi high price volailiy from Sepember o November he opimal hedge raio i only moderae in hee monh becaue much of he price variaion i conrac pecific and hence ha low covariance. Figure 6b plo he opimal hedge raio for he porfolio including he econd poiion conrac which i he opimal oluion according o he one and wo facor model conidered by Manoliu and Tompade Two obervaion become clear wih hi comparion of he wo hedging raegie. Fir he opimal hedge raio i ubanially lower for he porfolio including he econd poiion han for he opimal porfolio implied by he POTS model. Thi i imply becaue he hare of he price variance explained by he common facor i maller for he econd poiion han for more dian conrac. Second he opimal hedge raio decreae a he conrac approache mauriy. Thi i again becaue he hare of he price variance explained by he common facor decreae due o he Samuelon effec. Thee reul are peculiar o he mean 9

22 reverion proce aumed for he underlying facor in he model of Manoliu and Tompade 00. Thi paricular ochaic proce aure ha he facor loading increae monoonically a he conrac approache i mauriy dae wherea he variance of he idioyncraic error by pecificaion i conan over he enire horizon. Conequenly he price correlaion mu alway be he highe for he wo conrac wih he minimum diance in heir mauriy dae. Figure 7a illurae he variance of he opimal porfolio relaive o he variance of he unhedged porfolio i.e. he oal variance of he nearby fuure price. The figure how ha he opimal hedging raegy implied by he eimaed POTS model reduce price rik ubanially. The variance i reduced o le han 40% of he variance of he nearby fuure excep ha i i above 40% in Ocober November and February. The magniude of variance reducion i mall in hee hree monh a he nearby fuure price he November December and March conrac are inherenly very volaile and heir price volailiy i conrac pecific. Quie noiceably he variance of he opimal porfolio i below 35% of he variance of he nearby fuure price for December and January during which he nearby fuure January and February conrac price are very volaile. For each of he monh he minimum variance aained by he opimal porfolio i higher oward he end of each monh imply becaue he Samuelon effec raie he conrac pecific volailiy of he nearby fuure. Figure 7b compare he opimal hedging raegy implied by he POTS model wih he raighforward raegy of uilizing he econd poiion conrac. The figure indicae ha he raegy baed on he POTS model aain he porfolio variance ha i abou 5 o 45 percen below he variance of he porfolio uilizing he econd poiion conrac. Thi i becaue he fuure conrac included in he former raegy i le ubjec o conrac pecific variaion han in he econd poiion conrac. 0

23 The opimal hedging raegie for a monhly horizon yield eenially he ame reul a hoe for a daily horizon. Three ummer conrac June July and Augu and he December conrac are he mo commonly included ino he opimal porfolio wherea he re of he fuure conrac are le common wih he Ocober and November conrac ued in April and May repecively and he January and April conrac in Augu and Sepember. The opimal hedging raio and he minimum variance aained by he opimal conac are alo imilar o hoe for daily hedging raegy. They are almo idenical o he monhly average of heir correponding value for daily hedging horizon price rik i reduced o half he ize of price variance of he nearby conrac and he hedge raio range beween. and lighly above.0 due o a mall variance of he fuure conrac included in he porfolio. 5. CONCLUSION We examine he volailiy dynamic of NYMEX naural ga fuure price uing he parially overlapping ime erie POTS model of Smih 005. The eimaed POTS model reveal ha he NYMEX naural ga fuure price exhibi ime o mauriy effec and rong eaonal variaion in heir price volailiy volailiy rapidly increae in he la hree monh of rading period and i higher for winer conrac han for pring and ummer conrac. In addiion our analyi reveal ha he perience of price hock and hence he correlaion beween daily price change in concurrenly raded conrac exhibi ubanial eaonal and cro ecional variaion. Specifically price volailiy i relaively high in wo rading period: early November o mid January for he January o April conrac and early May o Sepember for all conrac mauring before he following March. Such volailiy dynamic are cloely relaed o he eaonal paern of he US naural ga orage in a way conien wih he heory of orage.

24 The depiced porrai of naural ga price volailiy dynamic implie ha a rader in need of hedging price rik hould cro hedge wih a fuure conrac of a lea hree monh o mauriy o avoid high conrac pecific volailiy in nearby conrac. In addiion hey hould include in heir porfolio he December conrac o hedge again po price rik during pring and ummer monh and eiher of he June July and Augu conrac in winer monh. The opimal hedge raio i high ranging from. o lighly above.0 becaue he price of he fuure conrac exhibi much maller movemen han he nearby conrac while hey hare much informaion regarding underlying marke condiion. Thee reul ugge ha he previou udie of he po fuure price relaionhip and he dynamic of naural ga fuure price are ubjec o mipecificaion bia in he variance rucure of he diurbance erm in heir regreion model. In paricular model of commodiy dynamic hould allow more flexible pecificaion in paricular eaonal and cro ecional variaion in he facor loading and he variance of he idioyncraic error. Alo he analyi of po fuure price relaionhip hould allow eaonal and cro ecional variaion in he variance of he diurbance erm. The aumpion of a conan more pecifically zero bai i clearly inappropriae for he co of carry i no conan for a orable commodiy wih rong eaonaliy in demand and/or upply. The opimal hedging raegie implied by hee mipecified model are noiceably ineffecive wih he variance of he porfolio reurn 8 o 80% higher han he minimum variance aained by he hedging raegy uggeed by he eimaed POTS model.

25 ENDNOTE Suenaga 005 illurae ha hi difference in he level of complexiy of he ipulaed variance rucure of he laen facor and idioyncraic error ha a ubanial impac on he oher model parameer epecially he rik premium. We alo eimaed he model allowing for a nonzero mean in he log price change. The eimae of hi mean parameer i very mall in value and our main reul are unaffeced. 3 Thi approximae EM mehod involve ieraion of he following hree ep: obain he prediced value of he laen facor and GARCH condiional variance hrough Kalman Filer maximize he expeced complee daa likelihood wih repec o he pline parameer condiional on he prediced value of laen facor and GARCH condiional variance from he fir ep and 3 eimae he GARCH parameer holding he pline parameer a he value from he ep. 4 One can alo evaluae he opimal hedge raio uing he model implied condiional variance. Unlike he uncondiional variance ued in he main ex he condiional variance depend on he hiorical movemen of he naural ga fuure price. We only preen evaluaion baed on he uncondiional variance becaue our objecive here i o draw a general implicaion abou he need o model eaonaliy. 5 See Table 4 and 5 on page 38 and 39 of Manoliu and Tompaid 00. Number in Figure 6b were calculaed by uing he volailiy eimae of he POTS model in 3. 3

26 BIBLIOGRAPHY Hamilon J. D Sae Space Model in Engle R. F. and McFadden D. L. ed. Handbook of Economeric Vol. 4. Elevier Amerdam. Lien D. and Roo T. H Convergence o he long run equilibrium: The cae of naural ga marke Energy Economic : Lucia J. J. and Schwarz E. S. 00. Elecriciy price and power derivaive: Evidence from he Nordic Power Exchange Review of Derivaive Reearch 5: Manoliu M. and Tompaidi S. 00. Energy fuure price: Term rucure model wih Kalman filer eimaion Applied Mahemaical Finance 9: 43. Movaagh N. and Modjahedi B Bia in backwardaion in naural ga fuure price Journal of Fuure Marke 5: Modjahedi B. and Movaagh N Naural ga fuure: Bia predicive performance and he heory of orage Energy Economic 7: Roo T. H. and Lien D Can modeling he naural ga fuure marke a a hrehold coinegraed yem improve hedging and forecaing performance? Inernaional Review of Financial Analyi : 7 3. Schwarz E. S The ochaic behavior of commodiy price: Implicaion for valuaion and hedging Journal of Finance 5:

27 Smih A Parially overlapping ime erie model: A new model for volailiy dynamic in commodiy fuure Journal of Applied Economeric 0: Suenaga H Analyi of po forward price relaionhip in he rerucured elecriciy marke Ph.D. Dieraion Univeriy of California Davi California. Wall W. D An economeric analyi of he marke for naural ga fuure Energy Journal 6: William J. C. and Wrigh B. D. 99. Sorage and Commodiy Marke. Cambridge Univeriy Pre New York. 5

28 Table. Maximum Likelihood Eimae of GARCH Parameer Coefficien SE raio GARCH Parameer Wih repec o 0 Wih repec o α α + β Log Likelihood BIC.8E

29 Table. Proporion of he Variance Explained by a Common Facor Overall By conrac

30 Figure. NYMEX naural ga elemen price a of April Price $/MBT Delivery Monh 8

31 Figure. Variance of daily log price change implied by he eimaed POTS model Trading dae monh 9

32 Figure 3. US naural ga underground orage Monhly average of working ga for Monhly Average Working Ga Sorage Billion c Monh 30

33 Figure 4. Share of price variaion explained by he common facor 00% 90% 80% 70% 60% 50% % 30% 3 0% 0% 0% Trading dae monh 3

34 Figure 5. Delivery monh of he fuure conrac included in he opimal porfolio Monhly Daily Time of Enry Monh 3

35 Figure 6. Opimal hedge raio a Porfolio uggeed by he eimaed POTS model Monhly Daily Time of Enry Monh b Porfolio including he econd poiion conrac Monhly Daily Time of Enry Monh 33

36 Figure 7. Minimum variance aained by he opimal porfolio a Relaive o he variance of unhedged porfolio Monhly Daily 00% 90% 80% 70% 60% 50% 40% 30% 0% 0% 0% Time of Enry Monh b Relaive o he variance of porfolio including he econd poiion conrac Monhly Daily 00% 90% 80% 70% 60% 50% 40% 30% 0% 0% 0% Time of Enry Monh 34

6.003 Homework #4 Solutions

6.003 Homework #4 Solutions 6.3 Homewk #4 Soluion Problem. Laplace Tranfm Deermine he Laplace ranfm (including he region of convergence) of each of he following ignal: a. x () = e 2(3) u( 3) X = e 3 2 ROC: Re() > 2 X () = x ()e d

More information

How has globalisation affected inflation dynamics in the United Kingdom?

How has globalisation affected inflation dynamics in the United Kingdom? 292 Quarerly Bullein 2008 Q3 How ha globaliaion affeced inflaion dynamic in he Unied Kingdom? By Jennifer Greenlade and Sephen Millard of he Bank Srucural Economic Analyi Diviion and Chri Peacock of he

More information

YTM is positively related to default risk. YTM is positively related to liquidity risk. YTM is negatively related to special tax treatment.

YTM is positively related to default risk. YTM is positively related to liquidity risk. YTM is negatively related to special tax treatment. . Two quesions for oday. A. Why do bonds wih he same ime o mauriy have differen YTM s? B. Why do bonds wih differen imes o mauriy have differen YTM s? 2. To answer he firs quesion les look a he risk srucure

More information

Fortified financial forecasting models: non-linear searching approaches

Fortified financial forecasting models: non-linear searching approaches 0 Inernaional Conference on Economic and inance Reearch IPEDR vol.4 (0 (0 IACSIT Pre, Singapore orified financial forecaing model: non-linear earching approache Mohammad R. Hamidizadeh, Ph.D. Profeor,

More information

2.4 Network flows. Many direct and indirect applications telecommunication transportation (public, freight, railway, air, ) logistics

2.4 Network flows. Many direct and indirect applications telecommunication transportation (public, freight, railway, air, ) logistics .4 Nework flow Problem involving he diribuion of a given produc (e.g., waer, ga, daa, ) from a e of producion locaion o a e of uer o a o opimize a given objecive funcion (e.g., amoun of produc, co,...).

More information

A Comparative Study of Linear and Nonlinear Models for Aggregate Retail Sales Forecasting

A Comparative Study of Linear and Nonlinear Models for Aggregate Retail Sales Forecasting A Comparaive Sudy of Linear and Nonlinear Model for Aggregae Reail Sale Forecaing G. Peer Zhang Deparmen of Managemen Georgia Sae Univeriy Alana GA 30066 (404) 651-4065 Abrac: The purpoe of hi paper i

More information

Long Term Spread Option Valuation and Hedging

Long Term Spread Option Valuation and Hedging Long Term Spread Opion Valuaion and Hedging M.A.H. Demper, Elena Medova and Ke Tang Cenre for Financial Reearch, Judge Buine School, Univeriy of Cambridge, Trumpingon Sree, Cambridge CB 1AG & Cambridge

More information

Calculation of variable annuity market sensitivities using a pathwise methodology

Calculation of variable annuity market sensitivities using a pathwise methodology cuing edge Variable annuiie Calculaion of variable annuiy marke eniiviie uing a pahwie mehodology Under radiional finie difference mehod, he calculaion of variable annuiy eniiviie can involve muliple Mone

More information

Topic: Applications of Network Flow Date: 9/14/2007

Topic: Applications of Network Flow Date: 9/14/2007 CS787: Advanced Algorihm Scribe: Daniel Wong and Priyananda Shenoy Lecurer: Shuchi Chawla Topic: Applicaion of Nework Flow Dae: 9/4/2007 5. Inroducion and Recap In he la lecure, we analyzed he problem

More information

4. International Parity Conditions

4. International Parity Conditions 4. Inernaional ariy ondiions 4.1 urchasing ower ariy he urchasing ower ariy ( heory is one of he early heories of exchange rae deerminaion. his heory is based on he concep ha he demand for a counry's currency

More information

Equity Valuation Using Multiples. Jing Liu. Anderson Graduate School of Management. University of California at Los Angeles (310) 206-5861

Equity Valuation Using Multiples. Jing Liu. Anderson Graduate School of Management. University of California at Los Angeles (310) 206-5861 Equiy Valuaion Uing Muliple Jing Liu Anderon Graduae School of Managemen Univeriy of California a Lo Angele (310) 206-5861 jing.liu@anderon.ucla.edu Doron Niim Columbia Univeriy Graduae School of Buine

More information

Subsistence Consumption and Rising Saving Rate

Subsistence Consumption and Rising Saving Rate Subience Conumpion and Riing Saving Rae Kenneh S. Lin a, Hiu-Yun Lee b * a Deparmen of Economic, Naional Taiwan Univeriy, Taipei, 00, Taiwan. b Deparmen of Economic, Naional Chung Cheng Univeriy, Chia-Yi,

More information

New Evidence on Mutual Fund Performance: A Comparison of Alternative Bootstrap Methods. David Blake* Tristan Caulfield** Christos Ioannidis*** and

New Evidence on Mutual Fund Performance: A Comparison of Alternative Bootstrap Methods. David Blake* Tristan Caulfield** Christos Ioannidis*** and New Evidence on Muual Fund Performance: A Comparion of Alernaive Boorap Mehod David Blake* Trian Caulfield** Chrio Ioannidi*** and Ian Tonk**** June 2014 Abrac Thi paper compare he wo boorap mehod of Koowki

More information

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements Inroducion Chaper 14: Dynamic D-S dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuing-edge

More information

Vector Autoregressions (VARs): Operational Perspectives

Vector Autoregressions (VARs): Operational Perspectives Vecor Auoregressions (VARs): Operaional Perspecives Primary Source: Sock, James H., and Mark W. Wason, Vecor Auoregressions, Journal of Economic Perspecives, Vol. 15 No. 4 (Fall 2001), 101-115. Macroeconomericians

More information

Usefulness of the Forward Curve in Forecasting Oil Prices

Usefulness of the Forward Curve in Forecasting Oil Prices Usefulness of he Forward Curve in Forecasing Oil Prices Akira Yanagisawa Leader Energy Demand, Supply and Forecas Analysis Group The Energy Daa and Modelling Cener Summary When people analyse oil prices,

More information

Chapter 7. Response of First-Order RL and RC Circuits

Chapter 7. Response of First-Order RL and RC Circuits Chaper 7. esponse of Firs-Order L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural

More information

A Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation

A Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation A Noe on Using he Svensson procedure o esimae he risk free rae in corporae valuaion By Sven Arnold, Alexander Lahmann and Bernhard Schwezler Ocober 2011 1. The risk free ineres rae in corporae valuaion

More information

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART TWO

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART TWO Profi Tes Modelling in Life Assurance Using Spreadshees, par wo PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART TWO Erik Alm Peer Millingon Profi Tes Modelling in Life Assurance Using Spreadshees,

More information

Hedging with Forwards and Futures

Hedging with Forwards and Futures Hedging wih orwards and uures Hedging in mos cases is sraighforward. You plan o buy 10,000 barrels of oil in six monhs and you wish o eliminae he price risk. If you ake he buy-side of a forward/fuures

More information

CHAPTER 11 NONPARAMETRIC REGRESSION WITH COMPLEX SURVEY DATA. R. L. Chambers Department of Social Statistics University of Southampton

CHAPTER 11 NONPARAMETRIC REGRESSION WITH COMPLEX SURVEY DATA. R. L. Chambers Department of Social Statistics University of Southampton CHAPTER 11 NONPARAMETRIC REGRESSION WITH COMPLEX SURVEY DATA R. L. Chamber Deparmen of Social Saiic Univeriy of Souhampon A.H. Dorfman Office of Survey Mehod Reearch Bureau of Labor Saiic M.Yu. Sverchkov

More information

Revisions to Nonfarm Payroll Employment: 1964 to 2011

Revisions to Nonfarm Payroll Employment: 1964 to 2011 Revisions o Nonfarm Payroll Employmen: 1964 o 2011 Tom Sark December 2011 Summary Over recen monhs, he Bureau of Labor Saisics (BLS) has revised upward is iniial esimaes of he monhly change in nonfarm

More information

Newton's second law in action

Newton's second law in action Newon's second law in acion In many cases, he naure of he force acing on a body is known I migh depend on ime, posiion, velociy, or some combinaion of hese, bu is dependence is known from experimen In

More information

Morningstar Investor Return

Morningstar Investor Return Morningsar Invesor Reurn Morningsar Mehodology Paper Augus 31, 2010 2010 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion

More information

Why Do Real and Nominal. Inventory-Sales Ratios Have Different Trends?

Why Do Real and Nominal. Inventory-Sales Ratios Have Different Trends? Why Do Real and Nominal Invenory-Sales Raios Have Differen Trends? By Valerie A. Ramey Professor of Economics Deparmen of Economics Universiy of California, San Diego and Research Associae Naional Bureau

More information

Cointegration: The Engle and Granger approach

Cointegration: The Engle and Granger approach Coinegraion: The Engle and Granger approach Inroducion Generally one would find mos of he economic variables o be non-saionary I(1) variables. Hence, any equilibrium heories ha involve hese variables require

More information

4.8 Exponential Growth and Decay; Newton s Law; Logistic Growth and Decay

4.8 Exponential Growth and Decay; Newton s Law; Logistic Growth and Decay 324 CHAPTER 4 Exponenial and Logarihmic Funcions 4.8 Exponenial Growh and Decay; Newon s Law; Logisic Growh and Decay OBJECTIVES 1 Find Equaions of Populaions Tha Obey he Law of Uninhibied Growh 2 Find

More information

Heat demand forecasting for concrete district heating system

Heat demand forecasting for concrete district heating system Hea demand forecaing for concree diric heaing yem Bronilav Chramcov Abrac Thi paper preen he reul of an inveigaion of a model for hor-erm hea demand forecaing. Foreca of hi hea demand coure i ignifican

More information

SAMPLE LESSON PLAN with Commentary from ReadingQuest.org

SAMPLE LESSON PLAN with Commentary from ReadingQuest.org Lesson Plan: Energy Resources ubject: Earth cience Grade: 9 Purpose: students will learn about the energy resources, explore the differences between renewable and nonrenewable resources, evaluate the environmental

More information

Graphing the Von Bertalanffy Growth Equation

Graphing the Von Bertalanffy Growth Equation file: d:\b173-2013\von_beralanffy.wpd dae: Sepember 23, 2013 Inroducion Graphing he Von Beralanffy Growh Equaion Previously, we calculaed regressions of TL on SL for fish size daa and ploed he daa and

More information

How Much Can Taxes Help Selfish Routing?

How Much Can Taxes Help Selfish Routing? How Much Can Taxe Help Selfih Rouing? Tim Roughgarden (Cornell) Join wih Richard Cole (NYU) and Yevgeniy Dodi (NYU) Selfih Rouing a direced graph G = (V,E) a ource and a deinaion one uni of raffic from

More information

Forecasting Malaysian Gold Using. GARCH Model

Forecasting Malaysian Gold Using. GARCH Model Applied Mahemaical Sciences, Vol. 7, 2013, no. 58, 2879-2884 HIKARI Ld, www.m-hikari.com Forecasing Malaysian Gold Using GARCH Model Pung Yean Ping 1, Nor Hamizah Miswan 2 and Maizah Hura Ahmad 3 Deparmen

More information

Two-Group Designs Independent samples t-test & paired samples t-test. Chapter 10

Two-Group Designs Independent samples t-test & paired samples t-test. Chapter 10 Two-Group Deign Independen ample -e & paired ample -e Chaper 0 Previou e (Ch 7 and 8) Z-e z M N -e (one-ample) M N M = andard error of he mean p. 98-9 Remember: = variance M = eimaed andard error p. -

More information

Fair games, and the Martingale (or "Random walk") model of stock prices

Fair games, and the Martingale (or Random walk) model of stock prices Economics 236 Spring 2000 Professor Craine Problem Se 2: Fair games, and he Maringale (or "Random walk") model of sock prices Sephen F LeRoy, 989. Efficien Capial Markes and Maringales, J of Economic Lieraure,27,

More information

Chapter 8 Student Lecture Notes 8-1

Chapter 8 Student Lecture Notes 8-1 Chaper Suden Lecure Noes - Chaper Goals QM: Business Saisics Chaper Analyzing and Forecasing -Series Daa Afer compleing his chaper, you should be able o: Idenify he componens presen in a ime series Develop

More information

Regime Switching in Dynamics of Risk Premium: Evidence from SHIBOR ABSTRACT

Regime Switching in Dynamics of Risk Premium: Evidence from SHIBOR ABSTRACT Regime Swiching in Dynamic of Rik Premium: Evidence from SHIBOR Baochen Yang College of Managemen and Economic, Tianjin Univeriy Tianjin 372, China bchyang@ju.edu.cn Tel: 86-22-8789859, 86-39249878 Yunpeng

More information

The International Investment Position of Jamaica: An Estimation Approach

The International Investment Position of Jamaica: An Estimation Approach WP/04 The Inernaional Invemen Poiion of Jamaica: An Eimaion Approach Dane Docor* Economic Informaion & Publicaion Deparmen Bank of Jamaica Ocober 2004 Abrac Thi paper eek o inroduce he inernaional invemen

More information

Economics 140A Hypothesis Testing in Regression Models

Economics 140A Hypothesis Testing in Regression Models Economics 140A Hypohesis Tesing in Regression Models While i is algebraically simple o work wih a populaion model wih a single varying regressor, mos populaion models have muliple varying regressors 1

More information

A Brief Introduction to the Consumption Based Asset Pricing Model (CCAPM)

A Brief Introduction to the Consumption Based Asset Pricing Model (CCAPM) A Brief Inroducion o he Consumpion Based Asse Pricing Model (CCAPM We have seen ha CAPM idenifies he risk of any securiy as he covariance beween he securiy's rae of reurn and he rae of reurn on he marke

More information

Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613.

Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613. Graduae School of Business Adminisraion Universiy of Virginia UVA-F-38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised

More information

Price-to-Earnings Ratios: Growth and Discount Rates

Price-to-Earnings Ratios: Growth and Discount Rates Price-o-Earnings Raios: Growh and Discoun Raes Andrew Ang Ann F. Kaplan Professor of Business Columbia Universiy Xiaoyan Zhang Associae Professor of Finance Kranner School of Managemen, Purdue Universiy

More information

Machine Learning in Pairs Trading Strategies

Machine Learning in Pairs Trading Strategies Machine Learning in Pairs Trading Sraegies Yuxing Chen (Joseph) Deparmen of Saisics Sanford Universiy Email: osephc5@sanford.edu Weiluo Ren (David) Deparmen of Mahemaics Sanford Universiy Email: weiluo@sanford.edu

More information

Derivatives. Forwards and Futures. Forward. Futures. Options. Initial Cost

Derivatives. Forwards and Futures. Forward. Futures. Options. Initial Cost Derivaives Forwards and Fuures A derivaive securiy is a securiy whose value depends on he values of oher more basic underlying variables. Forward The mos common derivaive securiies are forward, fuures

More information

CHARGE AND DISCHARGE OF A CAPACITOR

CHARGE AND DISCHARGE OF A CAPACITOR REFERENCES RC Circuis: Elecrical Insrumens: Mos Inroducory Physics exs (e.g. A. Halliday and Resnick, Physics ; M. Sernheim and J. Kane, General Physics.) This Laboraory Manual: Commonly Used Insrumens:

More information

The naive method discussed in Lecture 1 uses the most recent observations to forecast future values. That is, Y ˆ t + 1

The naive method discussed in Lecture 1 uses the most recent observations to forecast future values. That is, Y ˆ t + 1 Business Condiions & Forecasing Exponenial Smoohing LECTURE 2 MOVING AVERAGES AND EXPONENTIAL SMOOTHING OVERVIEW This lecure inroduces ime-series smoohing forecasing mehods. Various models are discussed,

More information

Chapter 8: Regression with Lagged Explanatory Variables

Chapter 8: Regression with Lagged Explanatory Variables Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One

More information

Data Analysis Toolkit #7: Hypothesis testing, significance, and power Page 1

Data Analysis Toolkit #7: Hypothesis testing, significance, and power Page 1 Daa Analyi Toolki #7: Hypohei eing, ignificance, and power Page 1 The ame baic logic underlie all aiical hypohei eing. Thi oolki illurae he baic concep uing he mo common e, - e for difference beween mean.

More information

CVA calculation for CDS on super senior ABS CDO

CVA calculation for CDS on super senior ABS CDO MPRA Munich Personal RePEc Archive CVA calculaion for CDS on super senior AS CDO Hui Li Augus 28 Online a hp://mpra.ub.uni-muenchen.de/17945/ MPRA Paper No. 17945, posed 19. Ocober 29 13:33 UC CVA calculaion

More information

A Further Examination of Insurance Pricing and Underwriting Cycles

A Further Examination of Insurance Pricing and Underwriting Cycles A Furher Examinaion of Insurance ricing and Underwriing Cycles AFIR Conference, Sepember 2005, Zurich, Swizerland Chris K. Madsen, GE Insurance Soluions, Copenhagen, Denmark Svend Haasrup, GE Insurance

More information

CSE202 Greedy algorithms

CSE202 Greedy algorithms CSE0 Greedy algorihm . Shore Pah in a Graph hore pah from Princeon CS deparmen o Einein' houe . Shore Pah in a Graph hore pah from Princeon CS deparmen o Einein' houe Tree wih a mo edge G i a ree on n

More information

Technical Description of S&P 500 Buy-Write Monthly Index Composition

Technical Description of S&P 500 Buy-Write Monthly Index Composition Technical Descripion of S&P 500 Buy-Wrie Monhly Index Composiion The S&P 500 Buy-Wrie Monhly (BWM) index is a oal reurn index based on wriing he nearby a-he-money S&P 500 call opion agains he S&P 500 index

More information

CBOE VIX PREMIUM STRATEGY INDEX (VPD SM ) CAPPED VIX PREMIUM STRATEGY INDEX (VPN SM )

CBOE VIX PREMIUM STRATEGY INDEX (VPD SM ) CAPPED VIX PREMIUM STRATEGY INDEX (VPN SM ) CBOE VIX PREIU STRATEGY INDEX (VPD S ) CAPPED VIX PREIU STRATEGY INDEX (VPN S ) The seady growh of CBOE s volailiy complex provides a unique opporuniy for invesors inen on capuring he volailiy premium.

More information

Supply Chain Management Using Simulation Optimization By Miheer Kulkarni

Supply Chain Management Using Simulation Optimization By Miheer Kulkarni Supply Chain Managemen Using Simulaion Opimizaion By Miheer Kulkarni This problem was inspired by he paper by Jung, Blau, Pekny, Reklaii and Eversdyk which deals wih supply chain managemen for he chemical

More information

Java Semantics. The Stack and Heap. Primitive Types. Semantics and Specifying Procedures. David Evans

Java Semantics. The Stack and Heap. Primitive Types. Semantics and Specifying Procedures. David Evans univeriy of virginia fall 2006 Semanic and Specifying Procedure Java Semanic David Evan www.c.virginia.edu/c205 2 The Sack and Heap Sring = new Sring (); Sring i a ype in he Java API for repreening equence

More information

What is a swap? A swap is a contract between two counter-parties who agree to exchange a stream of payments over an agreed period of several years.

What is a swap? A swap is a contract between two counter-parties who agree to exchange a stream of payments over an agreed period of several years. Currency swaps Wha is a swap? A swap is a conrac beween wo couner-paries who agree o exchange a sream of paymens over an agreed period of several years. Types of swap equiy swaps (or equiy-index-linked

More information

PROFITS AND POSITION CONTROL: A WEEK OF FX DEALING

PROFITS AND POSITION CONTROL: A WEEK OF FX DEALING PROFITS AND POSITION CONTROL: A WEEK OF FX DEALING Richard K. Lyon U.C. Berkeley and NBER Thi verion: June 1997 Abrac Thi paper examine foreign exchange rading a he dealer level. The dealer we rack average

More information

Term Structure of Commodities Futures. Forecasting and Pricing.

Term Structure of Commodities Futures. Forecasting and Pricing. erm Srucure of Commodiies Fuures. Forecasing and Pricing. Marcos Escobar, Nicolás Hernández, Luis Seco RiskLab, Universiy of orono Absrac he developmen of risk managemen mehodologies for non-gaussian markes

More information

THE PERFORMANCE OF OPTION PRICING MODELS ON HEDGING EXOTIC OPTIONS

THE PERFORMANCE OF OPTION PRICING MODELS ON HEDGING EXOTIC OPTIONS HE PERFORMANE OF OPION PRIING MODEL ON HEDGING EXOI OPION Firs Draf: May 5 003 his Version Oc. 30 003 ommens are welcome Absrac his paper examines he empirical performance of various opion pricing models

More information

YEN FUTURES: EXAMINING HEDGING EFFECTIVENESS BIAS AND CROSS-CURRENCY HEDGING RESULTS ROBERT T. DAIGLER FLORIDA INTERNATIONAL UNIVERSITY SUBMITTED FOR

YEN FUTURES: EXAMINING HEDGING EFFECTIVENESS BIAS AND CROSS-CURRENCY HEDGING RESULTS ROBERT T. DAIGLER FLORIDA INTERNATIONAL UNIVERSITY SUBMITTED FOR YEN FUTURES: EXAMINING HEDGING EFFECTIVENESS BIAS AND CROSS-CURRENCY HEDGING RESULTS ROBERT T. DAIGLER FLORIDA INTERNATIONAL UNIVERSITY SUBMITTED FOR THE FIRST ANNUAL PACIFIC-BASIN FINANCE CONFERENCE The

More information

Stock option grants have become an. Final Approval Copy. Valuation of Stock Option Grants Under Multiple Severance Risks GURUPDESH S.

Stock option grants have become an. Final Approval Copy. Valuation of Stock Option Grants Under Multiple Severance Risks GURUPDESH S. Valuaion of Sock Opion Gran Under Muliple Severance Rik GURUPDESH S. PANDHER i an aian profeor in he deparmen of finance a DePaul Univeriy in Chicago, IL. gpandher@depaul.edu GURUPDESH S. PANDHER Execuive

More information

INVESTIGATION OF THE INFLUENCE OF UNEMPLOYMENT ON ECONOMIC INDICATORS

INVESTIGATION OF THE INFLUENCE OF UNEMPLOYMENT ON ECONOMIC INDICATORS INVESTIGATION OF THE INFLUENCE OF UNEMPLOYMENT ON ECONOMIC INDICATORS Ilona Tregub, Olga Filina, Irina Kondakova Financial Universiy under he Governmen of he Russian Federaion 1. Phillips curve In economics,

More information

Trading Strategies for Sliding, Rolling-horizon, and Consol Bonds

Trading Strategies for Sliding, Rolling-horizon, and Consol Bonds Trading Sraegie for Sliding, Rolling-horizon, and Conol Bond MAREK RUTKOWSKI Iniue of Mahemaic, Poliechnika Warzawka, -661 Warzawa, Poland Abrac The ime evoluion of a liding bond i udied in dicree- and

More information

Outline. Role of Aggregate Planning. Role of Aggregate Planning. Logistics and Supply Chain Management. Aggregate Planning

Outline. Role of Aggregate Planning. Role of Aggregate Planning. Logistics and Supply Chain Management. Aggregate Planning Logisics and upply Chain Managemen Aggregae Planning 1 Ouline Role of aggregae planning in a supply chain The aggregae planning problem Aggregae planning sraegies mplemening aggregae planning in pracice

More information

Empirical heuristics for improving Intermittent Demand Forecasting

Empirical heuristics for improving Intermittent Demand Forecasting Empirical heuriic for improving Inermien Demand Forecaing Foio Peropoulo 1,*, Konanino Nikolopoulo 2, Georgio P. Spihouraki 1, Vailio Aimakopoulo 1 1 Forecaing & Sraegy Uni, School of Elecrical and Compuer

More information

DOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR

DOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR Invesmen Managemen and Financial Innovaions, Volume 4, Issue 3, 7 33 DOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR Ahanasios

More information

Part 1: White Noise and Moving Average Models

Part 1: White Noise and Moving Average Models Chaper 3: Forecasing From Time Series Models Par 1: Whie Noise and Moving Average Models Saionariy In his chaper, we sudy models for saionary ime series. A ime series is saionary if is underlying saisical

More information

Two Compartment Body Model and V d Terms by Jeff Stark

Two Compartment Body Model and V d Terms by Jeff Stark Two Comparmen Body Model and V d Terms by Jeff Sark In a one-comparmen model, we make wo imporan assumpions: (1) Linear pharmacokineics - By his, we mean ha eliminaion is firs order and ha pharmacokineic

More information

GLAS Team Member Quarterly Report. June , Golden, Colorado (Colorado School of Mines)

GLAS Team Member Quarterly Report. June , Golden, Colorado (Colorado School of Mines) GLAS Team ember Quarerly Repor An Nguyen, Thomas A Herring assachuses Insiue of Technology Period: 04/01/2004 o 06/30//2004 eeings aended Tom Herring aended he eam meeing near GSFC a he end of June, 2004.

More information

Measuring macroeconomic volatility Applications to export revenue data, 1970-2005

Measuring macroeconomic volatility Applications to export revenue data, 1970-2005 FONDATION POUR LES ETUDES ET RERS LE DEVELOPPEMENT INTERNATIONAL Measuring macroeconomic volailiy Applicaions o expor revenue daa, 1970-005 by Joël Cariolle Policy brief no. 47 March 01 The FERDI is a

More information

If You Are No Longer Able to Work

If You Are No Longer Able to Work If You Are No Longer Able o Work NY STRS A Guide for Making Disabiliy Reiremen Decisions INTRODUCTION If you re forced o sop working because of a serious illness or injury, you and your family will be

More information

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins) Alligaor egg wih calculus We have a large alligaor egg jus ou of he fridge (1 ) which we need o hea o 9. Now here are wo accepable mehods for heaing alligaor eggs, one is o immerse hem in boiling waer

More information

The Chase Problem (Part 2) David C. Arney

The Chase Problem (Part 2) David C. Arney The Chae Problem Par David C. Arne Inroducion In he previou ecion, eniled The Chae Problem Par, we dicued a dicree model for a chaing cenario where one hing chae anoher. Some of he applicaion of hi kind

More information

Modeling Energy American Options in the Non-Markovian Approach

Modeling Energy American Options in the Non-Markovian Approach Modeling Energy American Opion in he Non-Markovian Approach Valery Kholodnyi Vienna Auria 06.05.015 VERBUND AG www.verbund.com Ouline Ouline Inroducion Mehodology he Non-Markovian Approach Modeling Energy

More information

Principal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya.

Principal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya. Principal componens of sock marke dynamics Mehodology and applicaions in brief o be updaed Andrei Bouzaev, bouzaev@ya.ru Why principal componens are needed Objecives undersand he evidence of more han one

More information

The Greek financial crisis: growing imbalances and sovereign spreads. Heather D. Gibson, Stephan G. Hall and George S. Tavlas

The Greek financial crisis: growing imbalances and sovereign spreads. Heather D. Gibson, Stephan G. Hall and George S. Tavlas The Greek financial crisis: growing imbalances and sovereign spreads Heaher D. Gibson, Sephan G. Hall and George S. Tavlas The enry The enry of Greece ino he Eurozone in 2001 produced a dividend in he

More information

HOUSE PRICES AND RENTS: AN EQUILIBRIUM ASSET PRICING APPROACH

HOUSE PRICES AND RENTS: AN EQUILIBRIUM ASSET PRICING APPROACH DOCUMENTO DE TRABAJO HOUSE PRICES AND RENTS: AN EQUILIBRIUM ASSET PRICING APPROACH Documeno de Trabajo n.º 0304 Juan Ayuo and Fernando Reoy BANCO DE ESPAÑA SERVICIO DE ESTUDIOS HOUSE PRICES AND RENTS:

More information

Supplementary Appendix for Depression Babies: Do Macroeconomic Experiences Affect Risk-Taking?

Supplementary Appendix for Depression Babies: Do Macroeconomic Experiences Affect Risk-Taking? Supplemenary Appendix for Depression Babies: Do Macroeconomic Experiences Affec Risk-Taking? Ulrike Malmendier UC Berkeley and NBER Sefan Nagel Sanford Universiy and NBER Sepember 2009 A. Deails on SCF

More information

The Maturity Structure of Volatility and Trading Activity in the KOSPI200 Futures Market

The Maturity Structure of Volatility and Trading Activity in the KOSPI200 Futures Market The Mauriy Srucure of Volailiy and Trading Aciviy in he KOSPI200 Fuures Marke Jong In Yoon Division of Business and Commerce Baekseok Univerisy Republic of Korea Email: jiyoon@bu.ac.kr Received Sepember

More information

Price elasticity of demand for crude oil: estimates for 23 countries

Price elasticity of demand for crude oil: estimates for 23 countries Price elasiciy of demand for crude oil: esimaes for 23 counries John C.B. Cooper Absrac This paper uses a muliple regression model derived from an adapaion of Nerlove s parial adjusmen model o esimae boh

More information

Order Flows, Delta Hedging and Exchange Rate Dynamics

Order Flows, Delta Hedging and Exchange Rate Dynamics rder Flows Dela Hedging and Exchange Rae Dynamics Bronka Rzepkowski # Cenre d Eudes rospecives e d Informaions Inernaionales (CEII) ABSTRACT This paper proposes a microsrucure model of he FX opions and

More information

When Do TIPS Prices Adjust to Inflation Information?

When Do TIPS Prices Adjust to Inflation Information? When Do TIPS Prices Adjus o Inflaion Informaion? Quenin C. Chu a, *, Deborah N. Piman b, Linda Q. Yu c Augus 15, 2009 a Deparmen of Finance, Insurance, and Real Esae. The Fogelman College of Business and

More information

Representing Periodic Functions by Fourier Series. (a n cos nt + b n sin nt) n=1

Representing Periodic Functions by Fourier Series. (a n cos nt + b n sin nt) n=1 Represening Periodic Funcions by Fourier Series 3. Inroducion In his Secion we show how a periodic funcion can be expressed as a series of sines and cosines. We begin by obaining some sandard inegrals

More information

INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES

INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES OPENGAMMA QUANTITATIVE RESEARCH Absrac. Exchange-raded ineres rae fuures and heir opions are described. The fuure opions include hose paying

More information

The Equivalent Loan Principle and the Value of Corporate Promised Cash Flows. David C. Nachman*

The Equivalent Loan Principle and the Value of Corporate Promised Cash Flows. David C. Nachman* he Equivalen Loan Principle and he Value of Corporae Promied Cah Flow by David C. Nachman* Revied February, 2002 *J. Mack Robinon College of Buine, Georgia Sae Univeriy, 35 Broad Sree, Alana, GA 30303-3083.

More information

MACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR

MACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR MACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR The firs experimenal publicaion, which summarised pas and expeced fuure developmen of basic economic indicaors, was published by he Minisry

More information

Term Structure of Prices of Asian Options

Term Structure of Prices of Asian Options Term Srucure of Prices of Asian Opions Jirô Akahori, Tsuomu Mikami, Kenji Yasuomi and Teruo Yokoa Dep. of Mahemaical Sciences, Risumeikan Universiy 1-1-1 Nojihigashi, Kusasu, Shiga 525-8577, Japan E-mail:

More information

The Real Business Cycle paradigm. The RBC model emphasizes supply (technology) disturbances as the main source of

The Real Business Cycle paradigm. The RBC model emphasizes supply (technology) disturbances as the main source of Prof. Harris Dellas Advanced Macroeconomics Winer 2001/01 The Real Business Cycle paradigm The RBC model emphasizes supply (echnology) disurbances as he main source of macroeconomic flucuaions in a world

More information

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees

More information

Lecture III: Finish Discounted Value Formulation

Lecture III: Finish Discounted Value Formulation Lecure III: Finish Discouned Value Formulaion I. Inernal Rae of Reurn A. Formally defined: Inernal Rae of Reurn is ha ineres rae which reduces he ne presen value of an invesmen o zero.. Finding he inernal

More information

On the Connection Between Multiple-Unicast Network Coding and Single-Source Single-Sink Network Error Correction

On the Connection Between Multiple-Unicast Network Coding and Single-Source Single-Sink Network Error Correction On he Connecion Beween Muliple-Unica ework Coding and Single-Source Single-Sink ework Error Correcion Jörg Kliewer JIT Join work wih Wenao Huang and Michael Langberg ework Error Correcion Problem: Adverary

More information

SPECIAL REPORT May 4, Shifting Drivers of Inflation Canada versus the U.S.

SPECIAL REPORT May 4, Shifting Drivers of Inflation Canada versus the U.S. Paul Ferley Assisan Chief Economis 416-974-7231 paul.ferley@rbc.com Nahan Janzen Economis 416-974-0579 nahan.janzen@rbc.com SPECIAL REPORT May 4, 2010 Shifing Drivers of Inflaion Canada versus he U.S.

More information

Variance Swap. by Fabrice Douglas Rouah

Variance Swap. by Fabrice Douglas Rouah Variance wap by Fabrice Douglas Rouah www.frouah.com www.volopa.com In his Noe we presen a deailed derivaion of he fair value of variance ha is used in pricing a variance swap. We describe he approach

More information

The Response of Term Rates to Fed Announcements *

The Response of Term Rates to Fed Announcements * Revied: June The Repone o Term Rae o Fed Announcemen Abrac In February 4, 994 he Federal Reerve began he pracice o announcing change in he argeed level or he ederal und rae immediaely aer uch deciion were

More information

State Machines: Brief Introduction to Sequencers Prof. Andrew J. Mason, Michigan State University

State Machines: Brief Introduction to Sequencers Prof. Andrew J. Mason, Michigan State University Inroducion ae Machines: Brief Inroducion o equencers Prof. Andrew J. Mason, Michigan ae Universiy A sae machine models behavior defined by a finie number of saes (unique configuraions), ransiions beween

More information

An empirical analysis about forecasting Tmall air-conditioning sales using time series model Yan Xia

An empirical analysis about forecasting Tmall air-conditioning sales using time series model Yan Xia An empirical analysis abou forecasing Tmall air-condiioning sales using ime series model Yan Xia Deparmen of Mahemaics, Ocean Universiy of China, China Absrac Time series model is a hospo in he research

More information

Multiple Structural Breaks in the Nominal Interest Rate and Inflation in Canada and the United States

Multiple Structural Breaks in the Nominal Interest Rate and Inflation in Canada and the United States Deparmen of Economics Discussion Paper 00-07 Muliple Srucural Breaks in he Nominal Ineres Rae and Inflaion in Canada and he Unied Saes Frank J. Akins, Universiy of Calgary Preliminary Draf February, 00

More information

Explore the Application of Financial Engineering in the Management of Exchange Rate Risk

Explore the Application of Financial Engineering in the Management of Exchange Rate Risk SHS Web o Conerence 17, 01006 (015) DOI: 10.1051/ hcon/01517 01006 C Owned by he auhor, publihed by EDP Science, 015 Explore he Applicaion o Financial Engineering in he Managemen o Exchange Rae Rik Liu

More information

Option Value and Dynamic Programming Model Estimates of Social Security Disability Insurance Application Timing

Option Value and Dynamic Programming Model Estimates of Social Security Disability Insurance Application Timing DISCUSSION PAPER SERIES IZA DP No. 941 Opion Value and Dynamic Programming Model Eimae of Social Securiy Diabiliy Inurance Applicaion Timing Richard V. Burkhauer J. S. Buler Gulcin Gumu November 2003 Forchunginiu

More information

AP Calculus BC 2010 Scoring Guidelines

AP Calculus BC 2010 Scoring Guidelines AP Calculus BC Scoring Guidelines The College Board The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in, he College Board

More information

Banking, Inside Money and Outside Money

Banking, Inside Money and Outside Money Banking, Inide Mone and Ouide Mone Hongfei Sun Deparmen of Economic Univeri of Torono (Job Marke Paper) Abrac Thi paper preen an inegraed heor of mone and banking. I addre he following queion: when boh

More information