Valuation Methods of a Life Insurance Company
|
|
- Bruce Parks
- 8 years ago
- Views:
Transcription
1 Valuao Mehods of a Lfe Isurace Comay
2 ISORY PRODUC ASSESSMEN : PROFI ESING E PROFI ESING IN 3 SEPS Equalece Prcle radoal Marg Prof esg COMMON CRIERIA O EVALUAE E PROFIABILIY Ne Prese Value Ieral Rae of Reur Relao bewee IRR ad COMPANY ASSESSMEN : MEODS EMBEDDED VALUE Numercal eamle Embedded Value adaages Embedded Value dsadaages APPRAISAL VALUE VALUE ADDED Numercal eamle Value Added comoes OAL RAE OF REURN Numercal eamle CRIICAL APPROAC E PROBLEM REE KINDS OF VALUAION Value of a comay Icrease he alue of a comay Profably of a comay FINAL REMARKS ABOU CRIICAL APPROAC SENSIIVIY ANALYSIS APPROAC SENSIIVIY ESIMAION INERDEPENDENCE BEWEEN PARAMEERS APPLICAION Edowme wh aual remums Edowme wh sgle remum erm surace wh aual remums emorary mmedae lfe auy SIMULANEOUS SENSIIVIY CONCLUSION ON E SENSIIVIY ANALYSIS CONCLUSION ANNEXE BASIC ACUARIAL FORMULAE NUMERICAL APPLICAION NUMERICAL EXAMPLE NUMERICAL APPLICAION BONUS FORMULA REFERENCES
3 sory radoally lfe assurace comaes hae reored facal resuls o shareholders o he bass of he sauory requremes of he surace comaes' legslao. So he mos commo measure of a lfe surace comay's facal year was he sauory eargs from oerao. hs has bee a coee measure sce also rereses he amou of moey whch ca be ad o olcyholder or ad he form of ddeds. he major dsadaage o relyg uo sauory eargs as a measure of how well a comay s dog s ha sauory accoug eds o be desged o roec agas solecy ad herefore by s ery aure suffers from oer coserasm. Sauory eargs do o measure how well a comay s dog o a gog cocer bass. For eamle caal esed acqurg busess acquso eeses ad aluao sra s mmedaely wre off. Successful acquso of rofable ew busess resuls a mmedae loss followed by a subseque ehaced seres of rofs. Alhough suable for solecy esg he sauory aroach by chargg he caal cos of ew busess o reeue ad gorg he fuure surlus sream arbuable o ew busess fals o dslay ay accoug erod a meagful accou of he radg acy of ha erod. For mos roducs a slowdow sales wll resul a mmedae crease sauory eargs ad geerally mos would o regard a slowdow sales as beg a sg of a healhy comay! So s clear ha sauory eargs are he wrog mehod o measure he healh of he comay. Largely as a resul of he adequaces of sauory accoug US surers were requred by he Secures Echage Commsso he early 970 s o beg o reor eargs o shareholders o a Geerally Acceed Accoug Prcles GAAP bass. he major adaage o GAAP accoug s ha does aem o roduce eargs ha reflec how well or how badly he surace comay had erformed a form whch s useful o maageme. Wh GAAP geerally a crease sales wll o deress GAAP eargs o he same degree as would sauory eargs. Uforuaely because 00% of acquso coss are o deferred creased sales wll sll deress GAAP eargs o some ee. Addoally margs for coserasm are ormally roduced o he assumos ad GAAP mgh suffer from he loc- rcle. Oce assumos are se for a arcular geerao or brach of busess he assumos cao be chaged uless fuure losses are lely. Aoher major dsadaage o GAAP s ha GAAP eargs may ary sgfcaly bewee wo decal comaes deedg o he objeceess of maageme esablshg assumos. herefore oerall GAAP s o a good rogoscaor for how well a comay s dog. Durg he erods of flucuao eres raes whch occurred he US durg he md-970 s ad early 980 s some US comaes bega o loo a cash flows as a measure of how well her comaes were dog. he real adaage o usg cash flows as a measureme ool s ha s he oly bass ha loos a real moey. Bu s really oly a mmedae solecy es. Cash flow s o a measure of how well a comay s dog. 3
4 I he 80 s here were ew roducs for eamle u led roducs he crease comeo mergers ad resrucurg decrease rof margs due o creased comeo ec. he resul has bee a greaer eed o be able o maage ad corol surace oeraos he face of creasg flucuaos ad uceray. I s eresg o oe ha solecy ad rofably cao be showed by he same mehod. Solecy s a cosra whch deermes he secury margs ad mehods o use. Profably res o show how well a comay s dog elmag he cos effec of he frs year ad ag he fuure rofs o accou. I shor we ca say ha four os hae corbued o he adoo of aluao mehods ard comeo bewee surers Iesors' ressure o hae comrehese resuls Producs' eoluo owards greaer flebly Deregulao facal corol of solecy ad o more arff aroal such as sadard moraly ables 2 Produc assessme : Prof esg We ow ha he acquso of rofable ew busess resuls a mmedae loss due o he acquso eeses ad he frs ayme o echcal resere. Aferwards we hoe ha a seres of rofs wll follow. he Prof esg aes fuure rofs o accou ad he decreases he effec of he esme of he frs year. o calculae or o esmae hese fuure rofs we use eeced alues. I fac hese fuure rofs come from he rof ad loss accou. ere s a eamle of a surace accou. We hae o he lef he charges ad o he rgh he come. Prof ad loss accou Deah clams ad Release of reseres Amous ad o maury Premums receed Surreder alues ad Ieres ad gas receed Eeses curred ad commssos ad Bous ad Icrease reseres aes Prof durg he year ycally we hae he followg cure for he Prof esg whch rereses he eeced rofs of he rof ad loss accou each year. 4
5 Prof esg I s ery commo o hae a loss followed by a seres of rofs. Bu where does come from? Is he Prof esg relaed wh he acuaral rules? Yes s ad we wll see hs he e chaer. 2. he Prof esg 3 ses We wll see he relaosh bewee he Equalece Prcle ad he Prof esg 3 ses. Sarg from he Equalece Prcle we oba he radoal Marg ad he afer some modfcaos we oba he Prof esg. 2.. Equalece Prcle Equalece Prcle has he followg defo: Acuaral Prese Value APV of Premums equals o APV of Beefs lus APV of Charges. Usg a radoal edowme for a male aged of durao years we hae he followg alcao P'' ä A α γ ä Where ä he e sgle remum for a -year emorary lfe auy-due whch rodes for aual aymes of u as log as he beefcary les. A he e sgle remum for a edowme whch rodes for a ayme of a he ed of he year of deah f occurs wh he frs years oherwse a he ed of he h year. 5
6 6 α acquso eeses γ admsrao eeses he we hae our eamle ha he oal remum equals o he edowme beef lus he acquso eeses oly he frs year lus he oal admsrao eeses. We suose ha he colleco eeses are egraed he admsrao eeses radoal Marg Usg he bes esmae sead of rude assumos we ca rewre he formula as follows we symbolse he bes esmae bass wh he sar. 0 0 '' B u L ä A M ä P γ α Where Bous Lase beef robably o lase Marg radoal B L u M he wo las eressos are he surreder beef ad he bous. hs s radoally how he rof s calculaed. he Prof s o recogsed yearly bu a he begg of he corac for he whole durao Prof esg Iserg reseres rewrg he formula wh sums o he me ad regroug we oba 0 '' 0 α γ G I V V B u L q P Where eres eared Reseres Prof I V G I he sum we ca see he rof from he accoug G. he surace rofs are dscoued wh he facor.
7 he eleme braces a he ed of he sum s he dfferece bewee he resere a he ed of he year ad he oher a he begg of he year. I fac each erm of he sum s a le of he Prof ad Loss accou. So he Prof esg uses he radoal elemes of he acuaral scece. Of course ay ew eleme ca be sered le for eamle a resurace remum. We ca see ha he Prof esg ca be used as rofably ool or as a rcg ool. 2.2 Commo crera o ealuae he rofably 2.2. Ne Prese Value he Ne Prese Value wh Rs Dscou Rae s defed as follows: 0 G NPV If he Ne Prese Value s ose he roduc s rofable. Profably occurs whe he roduc geeraes a leas o he frs year sra. Rs Dscou Rae he Rs Dscou Rae s defed as he rae of reur led o busess rs of he surace comay. I realy hs rae s ery subjece. I deeds o he maageme he shareholders ad he esors Ieral Rae of Reur he Ieral Rae of Reur s defed as he rae whch ges a Ne Prese Value of zero. 0 G IRR 0 If he Ieral Rae of Reur s hgher ha he Rs Dscou Rae he he roduc s rofable Relao bewee IRR ad 7
8 NPV IRR NPV 0 IRR 3 Comay assessme : Mehods We wll sudy fe mehods whch ealuae a surace comay. I hs chaer all he umercal eamles are based o he daa ge he aee "Numercal alcao ". 3. Embedded Value Embedded Value rereses a he aluao dae a esmae of he asse alue ad he soc of he surace comay. More recsely he Embedded Value of a lfe offce a a arcular aluao dae s ae o be he sum of he shareholders e asses ad he alue of he busess force a he aluao dae. he alue of -force busess a he aluao dae s he rese alue of fuure rofs eeced o emerge from olces already wre. Where Embedded Value Shareholders Ne Asses he Soc: he alue of he busess -force a he aluao dae Ne Asses share caal solecy caal rof hdde reseres surlus Le us see ow hs formula more deal. If we deoe aluao year EV EV a he ed of he year NA Ne Asses a he ed of he year S Soc ealuaes a me year of rof 8
9 for > sauory rof eeced for he year ealuaed for he whole force busess a he me for sauory rof realsed for he year z- dscou facor wh he Rs Dscou Rae We hae he followg formula for Embedded Value EV NA z z z soc We ow ha z rereses he fuure rof eeced o be geeraed resec of resely force busess ad o be rasferable afer allowg for all relea aes o he rof ad loss accou. I he sum we use o ae oly he fuure rofs o accou. Bu we ca wre more elcly. s ew busess year aluao year sauory rof year for s < sauory rof eeced for he year for he busess wre he year s ealuaed G s for s < e sauory rof realsed he year for he buses wre he year s forr s sauory rof realsed he year for he ew busess Summg he G s o he whole years s we oba he sauory rof of he rof ad loss accou: G s s for If we roduce a a rae ha s ad whe he sauory rofs are ose ad a rae f > 0 0 oherwse We ge he followg formula for Embedded Value 9
10 [ ] EV > where s called dsrbuable rof of he year. hs s he sauory rof afer aes. 3.. Numercal eamle Le us ae he followg eamle order o llusrae he Embedded Value. Edowme surace C 00'000 α 4% o Caal β.5% o Premum γ 0.3% o Caal SM978/83 4% P 3970 α 3.8% β % 6% 8% Ieres o e asses.5% γ 0.2% ae rae 0% he eres o e asses s he afer a esme reur eared by he asses ha suor shareholders e asses. I s o uusual for hs rae of reur o be subsaally below he reur eared o asses suorg surace lables because of asses allocao echques used by comaes. I s commo o assg o-eresbearg asses or lower-yeldg asses o suor shareholders e asses ad o allow he hgher-yeldg asses o bac olcyholder lables. Before showg he chars we hae o oce ha we wll rese a rojeco of he aluao mehods. I realy hese mehods are calculaed each year wh he daa of ha year ad used o comare wh fgures of reous years. I our eamle we are eresed he deelome of he resuls hrough me ad he we suose ha we do o chage he assumos ha he assumos mach wh he realy ad ha here s o ew busess. Wh hese assumos he real rof equals he eeced rof. Soc rofle 0
11 % We oce ha he rofle s decreasg. hs s because he aual rofs are early cosa ad he each year he soc has oe rof less because here s o ew busess. Embedded Value rofle % Each year he Embedded Value creases because of he eres eared o e asses ad he aual rof.
12 3..2 Embedded Value adaages Embedded Value aes he fuure rofs of he Prof esg o accou ad he he alue s o oly flueced by he loss of he frs year. Embedded Value allows comarg facal resuls of dffere ds of aces. Vsual rereseao whch seems o be easy o udersad Embedded Value dsadaages Whou ublshg he assumos he resul of he mehod has o real sese. Rs Dscou Rae s o a geeral coce ad furhermore Embedded Value s esecally sese o Rs Dscou Rae. I radoal boo eeg we eer use hs rae. hs rae s oly used Prof esg ad Embedded Value. Embedded Value s sesy o Embedded Value 8% Embedded Value 0% Year 0 Embedded Value wh of 8% equals Embedded Value wh of 0% equals Arasal Value Arasal Value s he eeso of he Embedded Value o he mare alue. So o oba hs alue we hae o cosder he goodwll. Bu he goodwll s a subjece alue whch rereses he alue of he cles he fuure ew busess ec. So hs alue s ery dffcul o ealuae. Arasal Value Embedded Value Goodwll 3.3 Value Added Value Added s a dyamc alue. I s he crease he Embedded Value bewee wo me erods. VA EV EV 2
13 We saw ha he Embedded Value s he alue of he comay he Arasal Value s he mare alue of he comay ad ow we see he Value Added whch s a dyamc measure cosdered o show how well he comay s dog durg a secfed erod. We wll use ow oly Embedded Value because Arasal Value s more comlcaed o alue because of he goodwll. Bu of course hs mehod ad he followg ca also be calculaed wh Arasal Value. o llusrae he Value Added we ca ae he followg eamle. Suose ha a comay has 00 of equy ad es eeryhg ew busess we could hae for eamle: Begg of year Ed of year Ne asses 00 0 Busess force 0 5 Value Added Prof ad loss accou could hae show a loss of 00. hrough hs eamle we oce ha he Value Added seems o be more able o show he rofably ha he sauory rofs Numercal eamle Value Added rofle 60 8% Frs year he Value Added s esecally hgh because he comay sells a rofable roduc a hs me. Aferwards here s o ew busess ad he Value Added decreases. Comarso bewee Value Added ad sauory eargs: 3
14 % Sauory eargs Value Added hs grah s ery eresg because we ca see he dfferece bewee Value Added ad sauory eargs. I hs eamle he wo mehods behae comleely dfferely. he sauory eargs show frs a loss followed by a seres of gas ad he Value Added shows frs a ga followed by a seres of smaller gas. he Value Added seems much more able o show rofably ha he sauory eargs Value Added comoes Sarg wh he defo of he Value Added we wll sl he formula fe comoes VA we oe eres o e asses Rs Dscou Rae a rae dded rae D VA EV EV S S ad we rewre he soc a me - o aoher way order o reare he calculao VA D S S S S we use he formula of he soc ad we oba 4
15 5 > > D S VA ad regroug D S VA We use he formula of sauory rof ad we solae he aes s s D s G s G S VA s D s G s G G S VA we arrage he elemes [ ] s D s G s G G G S VA ad we ge fally hs formula [ ] s D s G s G G G S VA where he fe comoes of he Value Added ca be see
16 VA eres o e asses G 4243 sauory rof of year for he ew busess of year S 4243 corbuo from force busess [ G ] soc of ew busess of year D G s G s caal adjusemes 4 s essseme corbuo from ew busess chage of assumos ademergece of acualeerece ae relef We hae foud fe comoes of he Value Added whch are he followg: Ieres o e asses Corbuo from force busess Corbuo from ew busess Caal adjusmes Chage of assumos ad emergece of acual eerece 3.4 oal Rae of Reur oal Rae of Reur eresses he crease of Embedded Value as a erceage. RR VA D C EV where D shareholders ddeds a he ed of me C shareholders corbuos a he ed of me I s ecessary o do correcos for ddeds ad shareholder corbuo because he Embedded Value s chaged by hese alues. Whe dded s ad he e asses decrease ad he Embedded Value oo. he shareholder s ew s ha he recees dded ad he Value Added. he we hae o ae accou of he dded he oal Rae of Reur. Whe shareholders mae corbuos he Embedded Value creases bu he shareholder s ew s ha he recees he Value Added less wha he corbues. 6
17 3.4. Numercal eamle oal Rae of Reur rofle 8% 6% 8% 4% 2% 0% 8% 6% 4% 2% 0% hs rofle seems o be easy o udersad ad allow fg a smle objece. For eamle oe could say e year we hae o reach a oal Rae of Reur equal o he. 4 Crcal Aroach Ul ow we hae see he aluao mehods. Eeryhg seems o be smle ad we are able o show he rofably of a comay. Bu some asecs of hese mehods could be crcsed. I hs chaer all he umercal eamles are based o he daa ge he aee "Numercal alcao 2". 4. he roblem he resuls of he aluao mehods deed o he model ad he arameers le he reur o esme he bes esmae moraly ec. hese mehods use always he mea of fuure rss. So he adaage s o oba a uque alue bu he dsadaage s o hde he flucuaos. I realy he flucuaos are due o he model he radomess ad he uceray. o choose a model wh a ew o coceualsg real heomea s a smle aroach whch cao reflec eacly he realy. he radomess s he uforeseeably of ees whch follow a robably fuco. Ee whe we erfecly ow he robably law he effece realsao of he ees cao be deermed. I our model arcular he radomess corresods 7
18 o he flucuaos of he reur o esme ad he flucuaos of he real umber of deahs. he esmaos we calculae oday are oly mea alue of fuure realsao. he uceray comes from he merfec owledge of he arameers ad her ossble eoluo hrough he me. For eamle we do o ow eacly he real amou of eeses ad hs amou ca follow a fuure ueeced eoluo. Besdes hese flucuaos roblems here s a erreao roblem. he Value Added ad he oal Rae of Reur are ofe cosdered as rofably ools ee hough hese mehods ca ge a false sgal o he rofably of he comay. o dscuss hs erreao roblem we ae he followg umercal eamle Edowme surace Caal 00'000 α 5% o Caal γ 0.4% o Caal β cluded γ SM988/93 4% P 332 α 5800 Muao eeses 333 8% Ieres o e asses.5% γ 80 6% ae rae 0% We wll use wo secal cases as follows: A rofable case: Prooro of rof reaed 3% A o rofable case: Prooro of rof reaed 5% he rooro of rof reaed s he erceage of rof ha he surace comay was o ee. hs meas he ar whch s o dsrbued o he sured. Le us see ow he chars hese wo cases. 8
19 Value Added Profable case No-rofable case he frs year loos sesble here s o erreao roblem. he surace comay sells a rofable corac whch creases he alue of he comay he frs case. I he secod case he corac s o-rofable ad he alue of he comay decreases. Secod year ad laer. For he frs case we do o oce ay roblem. he Value Added decreases because he comay does o sell ay oher corac. I he secod case he comay does o sell ay oher corac ad he Value Added s ose alhough had sold reously a o-rofable corac. he se esecally bewee he frs ad he secod year s o easy o udersad for he urose of rofably. 9% 8% 7% 6% 5% 4% 3% 2% % 0% -% -2% -3% -4% -5% -6% Profable case oal Rae of Reur 9% 8% 7% 6% 5% 4% 3% 2% % 0% -% -2% -3% -4% -5% -6% No-rofable case We hae eacly he same erreao roblem wh he oal Rae of Reur. I order o udersad wha haes le us aalyse he fgures of he Value Added. 9
20 Profable case Ieres o e asses Corbuo from force busess Corbuo from ew busess Caal adjusme dded Value Added No-rofable case Ieres o e asses Corbuo from force busess Corbuo from ew busess Caal adjusme dded Value Added For he frs year here s o erreao roblem. he dfferece comes from he ew busess ose for he rofable case ad egae for he o-rofable case. For he secod year we hae a erreao roblem. Le us aalyse each comoe of he Value Added: -Ieres o e asses s he same because bous begs oly he hrd year our eamle. -Corbuo from ew busess s he same because we do o sell ay ew coracs. -Caal adjusme s he same because we do o ge ay bous before he hrd year. -he dfferece comes from he corbuo from force busess. Wha s surrsg s ha he o-rofable case hs corbuo s ose ad hs s le a reur effecely he calculao. ha s why he Value Added s ose he orofable case. Fally he roblem of erreao s due o he corbuo from force busess ad more esecally o he Rs Dscou Rae. Le us see ow he fluece of Rs Dscou Rae o Value Added Profable case wh 8% Profable case wh 9% he Rs Dscou Rae s a requreme of reur he frs year bu aferwards hs rae becomes a reur o he soc. Afer he frs year he Value Added calculaed wh a of 9% s hgher ha wh a of 8%. hs s really he source of he erreao roblem. 20
21 4.2 hree ds of aluao We hae o adm ha he Value Added ad he oal Rae of Reur are o able o show drecly he rofably of he comay. Bu he erreao roblem dsaears f we use he aluao mehods he correc coe. Value of a surace comay Icrease of he alue of a comay Profably of a comay 4.2. Value of a comay Of course he alue of a comay s drecly ge by Embedded Value or Arasal Value Icrease he alue of a comay For measurg he crease he alue of a comay we hae o aalyse he Value Added ad s comoes eres o e asses corbuo from force busess corbuo from ew busess caal adjusmes chage of assumos ad emergece of acual eerece ad he oal Rae of Reur. We ca aalyse each o o see f s ose or egae. Ad he we ow whch comoe crease decrease or sagae he alue of he comay. he Value Added ges he real crease. he oal Rae of Reur ges he relae crease ad he comoes of he Value Added allow searao of he comoso of he crease. I our reous eamle dese he fac ha he coracs sold do o mee he crera of Ieral Rae of Reur he reur s ose bu smaller ha he. ha s why he comay creases s alue wh hs roduc Profably of a comay he roblem of erreao comes also because we do o hae a clear defo of rofably. We wll use he followg defo of rofably. I our coe he rofably s he measure of he acy of a comay coeco wh he ew busess ealuaed hrough he fuure rofs eeced o emerge from he ew busess durg a secfed erod of me. Whe we are eresed he rofably of a surace comay seems o be logcal o be esecally eresed he ew busess creaed durg he secfed erod of me. I our coe we ca aalyse he Ieral Rae of Reur of he ew busess ad s NPV. We ca he hae he followg coclusos: 2
22 IRR NPV of ew busess Cocluso > >0 Am of reur reached 0<IRR< <0 Am o reached bu ose reur <0 <0 Loss New busess has also a fluece o he admsrae eeses o he ddeds ec bu we cocerae o he aes. 4.3 Fal remars abou crcal aroach We hae see ha he Value Added ad he oal Rae of Reur cao be drecly cosdered as ools for measurg he rofably. We hae see ha he aluao mehods mus be used he rgh coe. We hae o use he comoes of he Value Added. hs s why we hae defed wha we call alue crease of he alue ad rofably of a surace comay or a rof cere. I our coe we ge a defo of rofably. We hae o foud ay ew mehod we jus ela ha he aluao mehods do o always drecly ge he rgh aswer ad ha we hae o use he rgh coe. 5 Sesy Aalyss As we hae already see he resuls of he aluao mehods deed o he model ad he arameers le he reur o esme he bes esmae moraly ec. hese mehods use always he mea of fuure rss. So he adaage s o oba a uque alue bu he dsadaage s o hde he flucuaos. I realy he flucuaos are due o he model he radomess ad he uceray. he uceray comes from he merfec owledge of he arameers ad her ossble eoluo hrough he me. For eamle we do o ow eacly he real amou of eeses ad hs amou ca follow a ueeced fuure eoluo. 5. Aroach he sesy aalyss s used o aalyse he fluece of he uceray he arameers' alues. For hs urose we creae some scearos wh omsc ad essmsc alues of arameers. We suose ha cera rages of arameer alue are ossble ad we es he reacos of he resul of he mehod wh hose modfcaos of arameer alue. wo ways are ossble he successe sesy aalyss ad he smulaeous sesy aalyss. 22
23 I he successe sesy aalyss he alue of a uque arameer s chaged. he alue of he oher arameers does o chage. he am of hs aalyss s o erac he more flue arameers o he resul of he aluao mehod. I he smulaeous sesy aalyss he alue of he whole arameers s chaged. he am of hs aalyss s o aalyse he wors ad he bes ossble suao ag resecely he essmsc alue of seeral arameers ad ag he omsc alue of seeral arameers. Bu we hae o oce ha some erdeedeces are ossble bewee he arameers. So we hae o model whe s ossble ad relea. I s rue ha he leel of arao of he arameers alue wll fluece he arao he resul of he aluao mehod. Bu o hae a homogeeous comarso we ca ae a cosa erceage of arao for each arameer alue. Of course hs erceage s eerheless arbrary. 5.2 Sesy esmao We wll use curre ecoomc oo: he elascy heorec elascy E R R R Emrcal aromao ˆ E R R R hs s he elascy of he resul R of he aluao mehod eeg wh he arameer. Aferwards we wll oly use he emrcal aromao of he elascy bu o smlfy he erm we wll oly sea abou elascy ad o more abou emrcal aromao of he elascy. We say ha he arameer s elasc f he resul of hs formula s hgher ha ad resecely elasc f he resul of hs formula s lower ha. hs elascy formula s used he successe sesy aalyss bu s ossble o show ha we ca geeralse hs formula for successe sesy aalyss. 5.3 Ierdeedece bewee arameers I our model we hae ae he followg erdeedeces bewee arameers. - We suose ha he eeses deed o he flao ad are erdeede. - he eres rae deeds o flao. - he Rs Dscou Rae ad he eres o e asses deed o he eres rae. - he bous deeds o he bes esmae bass. he followg able shows he arameers whch are chaged he scearos. 23
24 Parameer Symbol Ierdeedace formula Rs Dscou Rae λ Ieres o e asses Prooro of rof reaed Acquso eeses a me Admsrao eeses a me Muao eeses a me Surreder alue a he ed of year ρ R R J CP CP a&& c FA δ MFA CA FA I FG FG δ MFG I FM S ae rae Dded rae D Bes esmae moraly Aual flao rae I Surreder rae u q FM δ MFM I 5.4 Alcao A sesy aalyss s aled o he Prof esg Embedded Value ad s crease wh four ds of roducs a edowme wh aual remums a edowme wh oe sgle remum a erm surace wh aual remums ad a emorary mmedae lfe auy. I hs chaer all he umercal eamles are based o he daa ge he aee "Numercal alcao 3". A successe ad a smulaeous sesy aalyss are doe wh araos of arameer alue of ± 0% Edowme wh aual remums 400 Prof esg for all scearos Frsly we cao see ay sgfca arao hs char. hs s he radoal rofle of a edowme wh aual remums. he oly scearo whch s clearly 24
25 dffere from he ohers s he eese scearo. he ohers seem o be close o he referece scearo. Bu f we aalyse he NPV we hae aoher suao. NPV NPV Elascy IRR IRR Elascy Referece scearo 462.2% Omsc eeses % Pessmsc eeses % Omsc Rs Dscou Rae % 0.00 Pessmsc Rs Dscou Rae % 0.00 Omsc rooro of rof reaed % 0.48 Pessmsc rooro of rof reaed % 0.5 Omsc moraly rae % Pessmsc moraly rae % Omsc aes % Pessmsc aes % Omsc flao % 0.37 Pessmsc flao % 0.35 Omsc surreder alue % Pessms surreder aluec % Omsc surreder rae % Pessmsc surreder rae % hs elascy of eeses meas ha for eamle a arao of 0% he eeses causes a arao of -60.6% he NPV! I hs able he eeses are clearly he arameer o whch he NPV s mos sese he case of a edowme wh aual remums. As he acquso eeses are mora he frs year ad because oly a ar of s zllmersed he dfferece s arcularly relea for he frs year. Aferwards he dfferece s smaller bu s becomes greaer hrough me. A he ed of he corac he dfferece s aga hgher because flao creases he eeses ad a he same me he aual remums remas always he same. he Rs Dscou Rae he rooro of rof reaed ad he moraly are also cosdered elasc arameers. 25
26 5.4.2 Edowme wh sgle remum 700 Prof esg for all scéaros he rofle of hs sgle remum edowme roduc s uusual. We do o hae ay al esme ad we hae some losses a he ed of he corac. As before we cao see ay hgh dfferece hs char. he oly scearo ha s clearly dffere from he ohers s he eese scearo. he ohers seem o be closed o he referece scearo. NPV NPV Elascy Referece scearo 2452 Omsc eeses Pessmsc eeses Omsc rooro of rof reaed Pessmsc rooro of rof reaed Omsc flao Pessmsc flao Omsc surreder alue Pessms surreder aluec Omsc Rs Dscou Rae Pessmsc Rs Dscou Rae Omsc aes Pessmsc aes Omsc moraly rae Pessmsc moraly rae Omsc surreder rae Pessmsc surreder rae
27 I hs case we see ha o arameer ca be cosdered elasc. hs s because he NPV s ery hgh he referece scearo. Furhermore he rofle of he sauory eargs are for eamle o sese o he because we hae a hgh ga a he begg ad less hgh amous aferwards erm surace wh aual remums 000 Prof esg for all scéaros I hs case we hae aga a radoal rofle of sauory eargs. he eese scearo s aga he mos flueal. NPV NPV Elascy IRR IRR Elascy Referece scearo 49 2.% Omsc eeses % Pessmsc eeses % Omsc Rs Dscou Rae % 0.00 Pessmsc Rs Dscou Rae % 0.00 Omsc rooro of rof reaed % 0.5 Pessmsc rooro of rof reaed % 0.54 Omsc moraly rae % Pessmsc moraly rae % Omsc flao % Pessmsc flao % Omsc aes % Pessmsc aes % Omsc surreder rae % Pessmsc surreder rae % Omsc surreder alue % Pessms surreder aluec %
28 We hae eacly he same elasc arameers ha he edowme roduc wh aual remums emorary mmedae lfe auy Prof esg for all scéaros he rofle of sauory eargs s oce aga dffere. A hgh ga he frs year follows by a seres of losses ad he a seres of gas. hs s rcally due o he bous whch decreases. he eese scearo s always he remarable oe. NPV NPV Elascy Referece scearo 643 Omsc rooro of rof reaed Pessmsc rooro of rof reaed Omsc Rs Dscou Rae Pessmsc Rs Dscou Rae Omsc flao Pessmsc flao Omsc eeses Pessmsc eeses Omsc aes Pessmsc aes Omsc moraly rae Pessmsc moraly rae
Critical Approach of the Valuation Methods of a Life Insurance Company under the Traditional European Statutory View
Crcal Aroach of he Valuao Mehods of a Lfe Isurace Comay uder he radoal Euroea Sauory Vew Dr. Paul-Aoe Darbellay ParerRe Belleresrasse 36 C-8034 Zürch Swzerlad Phoe: 4 385 34 63 Fa: 4 385 37 04 E-mal: aulaoe.darbellay@arerre.com
More informationREVISTA INVESTIGACION OPERACIONAL Vol. 25, No. 1, 2004. k n ),
REVISTA INVESTIGACION OPERACIONAL Vol 25, No, 24 RECURRENCE AND DIRECT FORMULAS FOR TE AL & LA NUMBERS Eduardo Pza Volo Cero de Ivesgacó e Maemáca Pura y Aplcada (CIMPA), Uversdad de Cosa Rca ABSTRACT
More informationChapter 4 Multiple-Degree-of-Freedom (MDOF) Systems. Packing of an instrument
Chaper 4 Mulple-Degree-of-Freedom (MDOF Sysems Eamples: Pacg of a srume Number of degrees of freedom Number of masses he sysem X Number of possble ypes of moo of each mass Mehods: Newo s Law ad Lagrage
More informationClaims Reserving When There Are Negative Values in the Runoff Triangle
Clams Reservg Whe There Are Negave Values he Ruo Tragle Erque de Alba ITAM Meco ad Uversy o Waerloo Caada 7 h. Acuaral Research Coerece The Uversy o Waerloo Augus 7-0 00 . INTRODUCTION The may uceraes
More informationPORTFOLIO CHOICE WITH HEAVY TAILED DISTRIBUTIONS 1. Svetlozar Rachev 2 Isabella Huber 3 Sergio Ortobelli 4
PORTFOLIO CHOIC WITH HAVY TAILD DISTRIBUTIONS Sveloar Rachev Isabella Huber 3 Sergo Orobell 4 We are graeful o Boryaa Racheva-Joova Soya Soyaov ad Almra Bglova for he comuaoal aalyss ad helful commes.
More informationStandardized Formula Sheet: Formulas Standard Normal Distribution Table Summary of Financial Ratios
Sadardzed Formula See: Formulas Sadard ormal Dsrbuo Table Summary o Facal Raos Formulas. Prese Value o a Sgle Cas Flow CF PV (. Fuure Value o a Sgle Cas Flow FV CF( 3. Prese Value o a Ordary Auy ( PV PT[
More informationProfessional Liability Insurance Contracts: Claims Made Versus Occurrence Policies
ARICLES ACADÉMIQUES ACADEMIC ARICLES Assuraces e geso des rsques, vol. 79(3-4), ocobre 2011- javer 2012, 251-277 Isurace ad Rsk Maageme, vol. 79(3-4), Ocober 2011- Jauary 2012, 251-277 Professoal Lably
More informationCHAPTER 22 ASSET BASED FINANCING: LEASE, HIRE PURCHASE AND PROJECT FINANCING
CHAPTER 22 ASSET BASED FINANCING: LEASE, HIRE PURCHASE AND PROJECT FINANCING Q.1 Defie a lease. How does i differ from a hire purchase ad isalme sale? Wha are he cash flow cosequeces of a lease? Illusrae.
More informationVladimir PAPI], Jovan POPOVI] 1. INTRODUCTION
Yugoslav Joural of Operaos Research 200 umber 77-9 VEHICLE FLEET MAAGEMET: A BAYESIA APPROACH Vladmr PAPI] Jova POPOVI] Faculy of Traspor ad Traffc Egeerg Uversy of Belgrade Belgrade Yugoslava Absrac:
More informationEXAMPLE 1... 1 EXAMPLE 2... 14 EXAMPLE 3... 18 EXAMPLE 4 UNIVERSAL TRADITIONAL APPROACH... 24 EXAMPLE 5 FLEXIBLE PRODUCT... 26
EXAMLE... A. Edowme... B. ure edowme d Term surce... 4 C. Reseres... 8. Bruo premum d reseres... EXAMLE 2... 4 A. Whoe fe... 4 B. Reseres of Whoe fe... 6 C. Bruo Whoe fe... 7 EXAMLE 3... 8 A.ure edowme...
More informationAmerican Journal of Business Education September 2009 Volume 2, Number 6
Amerca Joural of Bue Educao Sepember 9 Volume, umber 6 Tme Value Of Moe Ad I Applcao I Corporae Face: A Techcal oe O L Relaohp Bewee Formula Je-Ho Che, Alba Sae Uver, USA ABSTRACT Tme Value of Moe (TVM
More information7.2 Analysis of Three Dimensional Stress and Strain
eco 7. 7. Aalyss of Three Dmesoal ress ad ra The cocep of raco ad sress was roduced ad dscussed Par I.-.5. For he mos par he dscusso was cofed o wo-dmesoal saes of sress. Here he fully hree dmesoal sress
More informationGARCH Modelling. Theoretical Survey, Model Implementation and
Maser Thess GARCH Modellg Theorecal Survey, Model Imlemeao ad Robusess Aalyss Lars Karlsso Absrac I hs hess we survey GARCH modellg wh secal focus o he fg of GARCH models o facal reur seres The robusess
More informationLecture 13 Time Series: Stationarity, AR(p) & MA(q)
RS C - ecure 3 ecure 3 Tme Seres: Saoar AR & MAq Tme Seres: Iroduco I he earl 97 s was dscovered ha smle me seres models erformed beer ha he comlcaed mulvarae he oular 96s macro models FRB-MIT-Pe. See
More informationWhy we use compounding and discounting approaches
Comoudig, Discouig, ad ubiased Growh Raes Near Deb s school i Souher Colorado. A examle of slow growh. Coyrigh 000-04, Gary R. Evas. May be used for o-rofi isrucioal uroses oly wihou ermissio of he auhor.
More informationMETHODOLOGY ELECTRICITY, GAS AND WATER DISTRIBUTION INDEX (IDEGA, by its Spanish acronym) (Preliminary version)
MEHODOLOGY ELEY, GAS AND WAE DSBUON NDEX (DEGA, by s Sash acroym) (Prelmary verso) EHNAL SUBDEOAE OPEAONS SUBDEOAE Saago, December 26h, 2007 HDA/GGM/GMA/VM ABLE OF ONENS Pages. roduco 3 2. oceual frameork
More informationEQUITY VALUATION USING DCF: A THEORETICAL ANALYSIS OF THE LONG TERM HYPOTHESES
Ivesme Maaeme ad Facal Iovaos Volume 4 Issue 007 9 EQUIY VALUAION USING DCF: A HEOREICAL ANALYSIS OF HE LONG ERM HYPOHESES Luco Cassa * Adrea Pla ** Slvo Vsmara *** Absrac hs paper maches he sesvy aalyss
More informationExam FM/2 Interest Theory Formulas
Exm FM/ Iere Theory Formul by (/roprcy Th collboro of formul for he ere heory eco of he SO Exm FM / S Exm. Th uy hee free o-copyrghe ocume for ue g Exm FM/. The uhor of h uy hee ug ome oo h uque o h o
More informationA new proposal for computing portfolio valueat-risk for semi-nonparametric distributions
A ew proposal for compug porfolo valuea-rsk for sem-oparamerc dsrbuos Tro-Mauel Ñíguez ad Javer Peroe Absrac Ths paper proposes a sem-oparamerc (SNP) mehodology for compug porfolo value-a-rsk (VaR) ha
More informationUNDERWRITING AND EXTRA RISKS IN LIFE INSURANCE Katarína Sakálová
The process of uderwriig UNDERWRITING AND EXTRA RISKS IN LIFE INSURANCE Kaaría Sakálová Uderwriig is he process by which a life isurace compay decides which people o accep for isurace ad o wha erms Life
More informationThe Unintended Consequences of Tort Reform: Rent Seeking in New York State s Structured Settlements Statutes
The Ueded Cosequeces of Tor Reform: Re Seeg ew Yor Sae s Srucured Selemes Saues Publshed Joural of Foresc Ecoomcs, Volume 3 o, Wer 2 By Lawrece M. Spzma* Professor of Ecoomcs Mahar Hall Sae Uversy of ew
More informations :risk parameter for company size
UNDESTANDING ONLINE TADES: TADING AND EFOMANCE IN COMMON STOCK INVESTMENT Y. C. George L, Y. C. Elea Kag 2 ad Chug-L Chu 3 Deparme of Accoug ad Iformao Techology, Naoal Chug Cheg Uversy, Tawa,.O.C acycl@ccu.edu.w;
More informationPROFIT 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 informationWHAT ARE OPTION CONTRACTS?
WHAT ARE OTION CONTRACTS? By rof. Ashok anekar An oion conrac is a derivaive which gives he righ o he holder of he conrac o do 'Somehing' bu wihou he obligaion o do ha 'Somehing'. The 'Somehing' can be
More informationBullwhip Effect Measure When Supply Chain Demand is Forecasting
J. Basic. Appl. Sci. Res., (4)47-43, 01 01, TexRoad Publicaio ISSN 090-4304 Joural of Basic ad Applied Scieific Research www.exroad.com Bullwhip Effec Measure Whe Supply Chai emad is Forecasig Ayub Rahimzadeh
More informationMorningstar 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 informationIndividual Health Insurance April 30, 2008 Pages 167-170
Individual Healh Insurance April 30, 2008 Pages 167-170 We have received feedback ha his secion of he e is confusing because some of he defined noaion is inconsisen wih comparable life insurance reserve
More informationBusiness School Discipline of Finance. Discussion Paper 2014-005. Modelling the crash risk of the Australian Dollar carry trade
Dscusso Paper: 2014-005 Busess School Dscple of Face Dscusso Paper 2014-005 Modellg he crash rsk of he Ausrala Dollar carry rade Suk-Joog Km Uversy of Sydey Busess School Modellg he crash rsk of he Ausrala
More informationAnomaly Detection of Network Traffic Based on Prediction and Self-Adaptive Threshold
Ieraoal Joural of Fuure Geerao Coucao ad eworkg Vol. 8, o. 6 (15), pp. 5-14 hp://d.do.org/1.1457/fgc.15.8.6. Aoaly Deeco of ework raffc Based o Predco ad Self-Adapve hreshold Haya Wag Depare of Iforao
More informationANOVA Notes Page 1. Analysis of Variance for a One-Way Classification of Data
ANOVA Notes Page Aalss of Varace for a Oe-Wa Classfcato of Data Cosder a sgle factor or treatmet doe at levels (e, there are,, 3, dfferet varatos o the prescrbed treatmet) Wth a gve treatmet level there
More informationPrice Volatility, Trading Activity and Market Depth: Evidence from Taiwan and Singapore Taiwan Stock Index Futures Markets
We-Hsu Kuo Asa e Pacfc al./asa Maageme Pacfc Maageme evew (005) evew 0(), (005) 3-3 0(), 3-3 Prce Volaly, Tradg Acvy ad Marke Deph: Evdece from Tawa ad Sgapore Tawa Sock Idex Fuures Markes We-Hsu Kuo a,*,
More informationMobile Data Mining for Intelligent Healthcare Support
Proceedgs of he 42d Hawa Ieraoal Coferece o ysem ceces - 2009 Moble Daa Mg for Iellge Healhcare uppor Par Delr Haghgh, Arkady Zaslavsky, hoal Krshaswamy, Mohamed Medha Gaber Ceer for Dsrbued ysems ad ofware
More informationCALCULATION OF OMX TALLINN
CALCULATION OF OMX TALLINN CALCULATION OF OMX TALLINN 1. OMX Tallinn index...3 2. Terms in use...3 3. Comuaion rules of OMX Tallinn...3 3.1. Oening, real-ime and closing value of he Index...3 3.2. Index
More informationProving the Computer Science Theory P = NP? With the General Term of the Riemann Zeta Function
Research Joural of Mahemacs ad Sascs 3(2): 72-76, 20 ISSN: 2040-7505 Maxwell Scefc Orgazao, 20 Receved: Jauary 08, 20 Acceped: February 03, 20 Publshed: May 25, 20 Provg he ompuer Scece Theory P NP? Wh
More informationDuration 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 informationThe Time Value of Money
The Tme Value of Moey 1 Iversemet Optos Year: 1624 Property Traded: Mahatta Islad Prce : $24.00, FV of $24 @ 6%: FV = $24 (1+0.06) 388 = $158.08 bllo Opto 1 0 1 2 3 4 5 t ($519.37) 0 0 0 0 $1,000 Opto
More informationInternal model in life insurance : application of least squares monte carlo in risk assessment
Ieral model lfe surace : applcao of leas squares moe carlo rs assessme - Oberla euam Teugua (HSB) - Jae Re (Uversé yo, HSB) - rédérc Plache (Uversé yo, aboraore SA) 04. aboraore SA 50 Aveue Toy Garer -
More informationCHAPTER 2. Time Value of Money 6-1
CHAPTER 2 Tme Value of Moey 6- Tme Value of Moey (TVM) Tme Les Future value & Preset value Rates of retur Autes & Perpetutes Ueve cash Flow Streams Amortzato 6-2 Tme les 0 2 3 % CF 0 CF CF 2 CF 3 Show
More informationNatural Gas Storage Valuation. A Thesis Presented to The Academic Faculty. Yun Li
Naural Gas Sorage Valuao A Thess Preseed o The Academc Faculy by Yu L I Paral Fulfllme Of he Requremes for he Degree Maser of Scece he School of Idusral ad Sysem Egeerg Georga Isue of Techology December
More informationMobile Data Mining for Intelligent Healthcare Support
Moble Daa Mg for Iellge Healhcare uppor Absrac The growh umbers ad capacy of moble devces such as moble phoes coupled wh wdespread avalably of expesve rage of bosesors preses a uprecedeed opporuy for moble
More informationNumerical Solution of the Incompressible Navier-Stokes Equations
Nmercl Solo of he comressble Ner-Sokes qos The comressble Ner-Sokes eqos descrbe wde rge of roblems fld mechcs. The re comosed of eqo mss cosero d wo momem cosero eqos oe for ech Cres eloc comoe. The deede
More informationHarmony search algorithms for inventory management problems
Afrca Joural of Busess Maageme Vol.6 (36), pp. 9864-9873, 2 Sepember, 202 Avalable ole a hp://www.academcourals.org/ajbm DOI: 0.5897/AJBM2.54 ISSN 993-8233 202 Academc Jourals Revew Harmoy search algorhms
More informationChapter 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 informationTraditional Smoothing Techniques
Tradoal Smoohg Techques Smple Movg Average: or Ceered Movg Average, assume s odd: 2 ( 2 ( Weghed Movg Average: W W (or, of course, you could se up he W so ha hey smply add o oe. Noe Lear Movg Averages
More informationThe Term Structure of Interest Rates
The Term Srucure of Ieres Raes Wha is i? The relaioship amog ieres raes over differe imehorizos, as viewed from oday, = 0. A cocep closely relaed o his: The Yield Curve Plos he effecive aual yield agais
More informationEquities: Positions and Portfolio Returns
Foundaions of Finance: Equiies: osiions and orfolio Reurns rof. Alex Shapiro Lecure oes 4b Equiies: osiions and orfolio Reurns I. Readings and Suggesed racice roblems II. Sock Transacions Involving Credi
More informationFORECASTING MODEL FOR AUTOMOBILE SALES IN THAILAND
FORECASTING MODEL FOR AUTOMOBILE SALES IN THAILAND by Wachareepor Chaimogkol Naioal Isiue of Developme Admiisraio, Bagkok, Thailad Email: wachare@as.ida.ac.h ad Chuaip Tasahi Kig Mogku's Isiue of Techology
More informationValue of information sharing in marine mutual insurance
Value of formao sharg mare muual surace Kev L, Joh Lu, Ja Ya 3 ad Je M Deparme of Logscs & Marme Sudes, The Hog Kog Polechc Uvers, Hog Kog. Emal address:.x.l@polu.edu.h. Deparme of Logscs & Marme Sudes,
More informationAPPLICATIONS OF GEOMETRIC
APPLICATIONS OF GEOMETRIC SEQUENCES AND SERIES TO FINANCIAL MATHS The mos powerful force i he world is compoud ieres (Alber Eisei) Page of 52 Fiacial Mahs Coes Loas ad ivesmes - erms ad examples... 3 Derivaio
More informationChapter 6: Business Valuation (Income Approach)
Chaper 6: Business Valuaion (Income Approach) Cash flow deerminaion is one of he mos criical elemens o a business valuaion. Everyhing may be secondary. If cash flow is high, hen he value is high; if he
More informationThe Design of a Forecasting Support Models on Demand of Durian for Domestic Markets and Export Markets by Time Series and ANNs.
The 2 d RMUTP Ieraoal Coferece 2010 Page 108 The Desg of a Forecasg Suppor Models o Demad of Dura for Domesc Markes ad Expor Markes by Tme Seres ad ANNs. Udomsr Nohacho, 1* kegpol Ahakor, 2 Kazuyosh Ish,
More informationEvaluation and Modeling of the Digestion and Absorption of Novel Manufacturing Technology in Food Enterprises
Advace Joural of Food Scece ad Techology 9(6): 482-486, 205 ISSN: 2042-4868; e-issn: 2042-4876 Mawell Scefc Orgazao, 205 Submed: Aprl 9, 205 Acceped: Aprl 28, 205 Publshed: Augus 25, 205 Evaluao ad Modelg
More informationNo Regret Learning in Oligopolies: Cournot vs Bertrand
No Regre Learg Olgopoles: Couro vs Berrad Ur Nadav Georgos Plouras Absrac Couro ad Berrad olgopoles cosue he wo mos prevale models of frm compeo. The aalyss of Nash equlbra each model reveals a uque predco
More informationPerformance Comparisons of Load Balancing Algorithms for I/O- Intensive Workloads on Clusters
Joural of ewor ad Compuer Applcaos, vol. 3, o., pp. 32-46, Jauary 2008. Performace Comparsos of oad Balacg Algorhms for I/O- Iesve Worloads o Clusers Xao Q Deparme of Compuer Scece ad Sofware Egeerg Aubur
More informationDeterminants of Foreign Direct Investment in Malaysia: What Matters Most?
Deermas of Foreg Drec Ivesme Maaysa: Wha Maers Mos? Nursuha Shahrud, Zarah Yusof ad NuruHuda Mohd. Saar Ths paper exames he deermas of foreg drec vesme Maaysa from 970-008. The causay ad dyamc reaoshp
More informationChapter 1.6 Financial Management
Chaper 1.6 Financial Managemen Par I: Objecive ype quesions and answers 1. Simple pay back period is equal o: a) Raio of Firs cos/ne yearly savings b) Raio of Annual gross cash flow/capial cos n c) = (1
More information1. The Time Value of Money
Corporate Face [00-0345]. The Tme Value of Moey. Compoudg ad Dscoutg Captalzato (compoudg, fdg future values) s a process of movg a value forward tme. It yelds the future value gve the relevat compoudg
More informationReturn Calculation of U.S. Treasury Constant Maturity Indices
Reurn Calculaion of US Treasur Consan Mauri Indices Morningsar Mehodolog Paper Sepeber 30 008 008 Morningsar Inc All righs reserved The inforaion in his docuen is he proper of Morningsar Inc Reproducion
More informationTrust Evaluation and Dynamic Routing Decision Based on Fuzzy Theory for MANETs
JOURNAL OF SOFTWARE, VOL. 4, NO. 10, ECEBER 2009 1091 Trus Evaluao ad yamc Roug ecso Based o Fuzzy Theory for ANETs Hogu a, Zhpg Ja ad Zhwe Q School of Compuer Scece ad Techology, Shadog Uversy, Ja, Cha.P.R.
More informationMarkit iboxx USD Liquid Leveraged Loan Index
Mark Boxx USD Lqud Leveraged Loa Idex Sepember 20 Mark Boxx USD Leveraged Loa Idex Idex Gude Coe Overvew... 4 Seleco Crera... 5 Idex Icepo/Rebalacg... 5 Elgbly Crera... 5 Loa Type... 5 Mmum facly ze...
More informationA Re-examination of the Joint Mortality Functions
Norh merican cuarial Journal Volume 6, Number 1, p.166-170 (2002) Re-eaminaion of he Join Morali Funcions bsrac. Heekung Youn, rkad Shemakin, Edwin Herman Universi of S. Thomas, Sain Paul, MN, US Morali
More informationSpline. Computer Graphics. B-splines. B-Splines (for basis splines) Generating a curve. Basis Functions. Lecture 14 Curves and Surfaces II
Lecure 4 Curves and Surfaces II Splne A long flexble srps of meal used by drafspersons o lay ou he surfaces of arplanes, cars and shps Ducks weghs aached o he splnes were used o pull he splne n dfferen
More informationPROBABILITY AND STATISTICS FOR ENGINEERS
VŠB Techcal Uvery of Orava Faculy of Elecrcal Egeerg ad Comuer Scece Dearme of Aled Mahemac PROBABILITY AND STATISTICS FOR ENGINEERS Radm Brš Orava PROBABILITY AND STATISTICS FOR ENGINEERS LESSON INSTRUCTIONS
More informationHIGH FREQUENCY MARKET MAKING
HIGH FREQUENCY MARKET MAKING RENÉ CARMONA AND KEVIN WEBSTER Absrac. Sce hey were auhorzed by he U.S. Secury ad Exchage Commsso 1998, elecroc exchages have boomed, ad by 21 hgh frequecy radg accoued for
More informationCONVERGENCE AND SPATIAL PATTERNS IN LABOR PRODUCTIVITY: NONPARAMETRIC ESTIMATIONS FOR TURKEY 1
CONVERGENCE AND SPAIAL PAERNS IN LABOR PRODUCIVIY: NONPARAMERIC ESIMAIONS FOR URKEY ugrul emel, Ays asel & Peer J. Alberse Workg Paper 993 Forhcomg he Joural of Regoal Aalyss ad Polcy, 999. We would lke
More informationClassic Problems at a Glance using the TVM Solver
C H A P T E R 2 Classc Problems at a Glace usg the TVM Solver The table below llustrates the most commo types of classc face problems. The formulas are gve for each calculato. A bref troducto to usg the
More informationFinancial Time Series Forecasting with Grouped Predictors using Hierarchical Clustering and Support Vector Regression
Ieraoal Joural of Grd Dsrbuo Compug, pp.53-64 hp://dx.do.org/10.1457/jgdc.014.7.5.05 Facal Tme Seres Forecasg wh Grouped Predcors usg Herarchcal Cluserg ad Suppor Vecor Regresso ZheGao a,b,* ad JajuYag
More information- Models: - Classical: : Mastermodel (clay( Curves. - Example: - Independent variable t
Compue Gaphcs Geomec Moelg Iouco - Geomec Moelg (GM) sce e of 96 - Compue asssace fo - Desg: CAD - Maufacug: : CAM - Moels: - Classcal: : Masemoel (cla( cla, poopes,, Mock-up) - GM: mahemacal escpo fo
More informationAnalysis of Coalition Formation and Cooperation Strategies in Mobile Ad hoc Networks
Aalss of oalo Formao ad ooperao Sraeges Moble Ad hoc ewors Pero Mchard ad Ref Molva Isu Eurecom 9 Roue des rêes 06904 Sopha-Apols, Frace Absrac. Ths paper focuses o he formal assessme of he properes of
More informationManaging Learning and Turnover in Employee Staffing*
Maagig Learig ad Turover i Employee Saffig* Yog-Pi Zhou Uiversiy of Washigo Busiess School Coauhor: Noah Gas, Wharo School, UPe * Suppored by Wharo Fiacial Isiuios Ceer ad he Sloa Foudaio Call Ceer Operaios
More informationThe Advertising Market in a Product Oligopoly
The Adversg Mare a Produc Olgooly Ahoy Dues chool o Ecoocs ad Maagee Uversy o Aarhus Århus Dear Ocober 003 Absrac A odel s develoed whch roducers a dereaed roduc are coee rces ad orave adversg. The odel
More informationFINANCIAL MATHEMATICS 12 MARCH 2014
FINNCIL MTHEMTICS 12 MRCH 2014 I ths lesso we: Lesso Descrpto Make use of logarthms to calculate the value of, the tme perod, the equato P1 or P1. Solve problems volvg preset value ad future value autes.
More informationObject Tracking Based on Online Classification Boosted by Discriminative Features
Ieraoal Joural of Eergy, Iformao ad Commucaos, pp.9-20 hp://dx.do.org/10.14257/jec.2013.4.6.02 Objec Trackg Based o Ole Classfcao Boosed by Dscrmave Feaures Yehog Che 1 ad Pl Seog Park 2 1 Qlu Uversy of
More informationDBIQ Regulated Utilities Index
db Ide Develome March 2013 DBIQ Ide Guide DBIQ Regulaed Uiliies Ide Summary The DBIQ Regulaed Uiliies Ide ( Uiliies Ide is a rules-based ide aimig o rack he reurs ou of he regulaed uiliies secor i develoed
More informationMarkit Excess Return Credit Indices Guide for price based indices
Marki Excess Reurn Credi Indices Guide for price based indices Sepember 2011 Marki Excess Reurn Credi Indices Guide for price based indices Conens Inroducion...3 Index Calculaion Mehodology...4 Semi-annual
More informationApproximate hedging for non linear transaction costs on the volume of traded assets
Noame mauscrp No. wll be sered by he edor Approxmae hedgg for o lear rasaco coss o he volume of raded asses Romuald Ele, Emmauel Lépee Absrac Ths paper s dedcaed o he replcao of a covex coge clam hs a
More information10.5 Future Value and Present Value of a General Annuity Due
Chapter 10 Autes 371 5. Thomas leases a car worth $4,000 at.99% compouded mothly. He agrees to make 36 lease paymets of $330 each at the begg of every moth. What s the buyout prce (resdual value of the
More informationECONOMIC CHOICE OF OPTIMUM FEEDER CABLE CONSIDERING RISK ANALYSIS. University of Brasilia (UnB) and The Brazilian Regulatory Agency (ANEEL), Brazil
ECONOMIC CHOICE OF OPTIMUM FEEDER CABE CONSIDERING RISK ANAYSIS I Camargo, F Fgueredo, M De Olvera Uversty of Brasla (UB) ad The Brazla Regulatory Agecy (ANEE), Brazl The choce of the approprate cable
More informationChapter 3. AMORTIZATION OF LOAN. SINKING FUNDS R =
Chapter 3. AMORTIZATION OF LOAN. SINKING FUNDS Objectves of the Topc: Beg able to formalse ad solve practcal ad mathematcal problems, whch the subjects of loa amortsato ad maagemet of cumulatve fuds are
More information2.5 Life tables, force of mortality and standard life insurance products
Soluions 5 BS4a Acuarial Science Oford MT 212 33 2.5 Life ables, force of moraliy and sandard life insurance producs 1. (i) n m q represens he probabiliy of deah of a life currenly aged beween ages + n
More informationINTEREST 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 informationT = 1/freq, T = 2/freq, T = i/freq, T = n (number of cash flows = freq n) are :
Bullets bods Let s descrbe frst a fxed rate bod wthout amortzg a more geeral way : Let s ote : C the aual fxed rate t s a percetage N the otoal freq ( 2 4 ) the umber of coupo per year R the redempto of
More informationThe Increasing Participation of China in the World Soybean Market and Its Impact on Price Linkages in Futures Markets
The Icreasg arcpao of Cha he Word Soybea Marke ad Is Ipac o rce Lkages Fuures Markes by Mara Ace Móz Chrsofoe Rodofo Margao da Sva ad Fabo Maos Suggesed cao fora: Chrsofoe M. A. R. Sva ad F. Maos. 202.
More informationACCOUNTING TURNOVER RATIOS AND CASH CONVERSION CYCLE
Problems ad Persecives of Maageme, 24 Absrac ACCOUNTING TURNOVER RATIOS AND CASH CONVERSION CYCLE Pedro Orí-Ágel, Diego Prior Fiacial saemes, ad esecially accouig raios, are usually used o evaluae acual
More informationCommercial Pension Insurance Program Design and Estimated of Tax Incentives---- Based on Analysis of Enterprise Annuity Tax Incentives
Iteratoal Joural of Busess ad Socal Scece Vol 5, No ; October 204 Commercal Peso Isurace Program Desg ad Estmated of Tax Icetves---- Based o Aalyss of Eterprse Auty Tax Icetves Huag Xue, Lu Yatg School
More informationNikkei Stock Average Volatility Index Real-time Version Index Guidebook
Nikkei Sock Average Volailiy Index Real-ime Version Index Guidebook Nikkei Inc. Wih he modificaion of he mehodology of he Nikkei Sock Average Volailiy Index as Nikkei Inc. (Nikkei) sars calculaing and
More informationThe Analysis of Development of Insurance Contract Premiums of General Liability Insurance in the Business Insurance Risk
The Aalyss of Developmet of Isurace Cotract Premums of Geeral Lablty Isurace the Busess Isurace Rsk the Frame of the Czech Isurace Market 1998 011 Scetfc Coferece Jue, 10. - 14. 013 Pavla Kubová Departmet
More informationLecture 40 Induction. Review Inductors Self-induction RL circuits Energy stored in a Magnetic Field
ecure 4 nducon evew nducors Self-nducon crcus nergy sored n a Magnec Feld 1 evew nducon end nergy Transfers mf Bv Mechancal energy ransform n elecrc and hen n hermal energy P Fv B v evew eformulaon of
More informationPresent Value Methodology
Presen Value Mehodology Econ 422 Invesmen, Capial & Finance Universiy of Washingon Eric Zivo Las updaed: April 11, 2010 Presen Value Concep Wealh in Fisher Model: W = Y 0 + Y 1 /(1+r) The consumer/producer
More informationQuantifying Environmental Green Index For Fleet Management Model
Proceedgs of he Easer Asa Socey for Trasporao Sudes, Vol.9, 20 Quafyg Evromeal ree Idex For Flee Maageme Model Lay Eg TEOH a, Hoo Lg KHOO b a Deparme of Mahemacal ad Acuaral Sceces, Faculy of Egeerg ad
More informationSolving Fuzzy Linear Programming Problems with Piecewise Linear Membership Function
Avalable a hp://pvamu.edu/aam Appl. Appl. Mah. ISSN: 9-966 Vol., Issue December ), pp. Prevously, Vol., Issue, pp. 6 6) Applcaos ad Appled Mahemacs: A Ieraoal Joural AAM) Solvg Fuzzy Lear Programmg Problems
More informationRevision: June 12, 2010 215 E Main Suite D Pullman, WA 99163 (509) 334 6306 Voice and Fax
.3: Inucors Reson: June, 5 E Man Sue D Pullman, WA 9963 59 334 636 Voce an Fax Oerew We connue our suy of energy sorage elemens wh a scusson of nucors. Inucors, lke ressors an capacors, are passe wo-ermnal
More informationChapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m
Chaper 2 Problems 2.1 During a hard sneeze, your eyes migh shu for 0.5s. If you are driving a car a 90km/h during such a sneeze, how far does he car move during ha ime s = 90km 1000m h 1km 1h 3600s = 25m
More informationMORE ON TVM, "SIX FUNCTIONS OF A DOLLAR", FINANCIAL MECHANICS. Copyright 2004, S. Malpezzi
MORE ON VM, "SIX FUNCIONS OF A DOLLAR", FINANCIAL MECHANICS Copyrgh 2004, S. Malpezz I wan everyone o be very clear on boh he "rees" (our basc fnancal funcons) and he "fores" (he dea of he cash flow model).
More informationTime value of money Interest formulas Project evaluations Inflation and CPI Financial risk and financing
2YHUYLHZ )LQDQLDO$QDO\VLV 3ULHU Hioshi Sakamoo Humphey Isiue of ublic Affais Uivesiy of Miesoa Time value of moey Iees fomulas ojec evaluaios Iflaio ad CI iacial isk ad fiacig A5721 Moey - 1 A5721 Moey
More informationMDM 4U PRACTICE EXAMINATION
MDM 4U RCTICE EXMINTION Ths s a ractce eam. It does ot cover all the materal ths course ad should ot be the oly revew that you do rearato for your fal eam. Your eam may cota questos that do ot aear o ths
More informationcooking 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 informationAcceleration Lab Teacher s Guide
Acceleraion Lab Teacher s Guide Objecives:. Use graphs of disance vs. ime and velociy vs. ime o find acceleraion of a oy car.. Observe he relaionship beween he angle of an inclined plane and he acceleraion
More informationIDENTIFICATION OF THE DYNAMICS OF THE GOOGLE S RANKING ALGORITHM. A. Khaki Sedigh, Mehdi Roudaki
IDENIFICAION OF HE DYNAMICS OF HE GOOGLE S RANKING ALGORIHM A. Khak Sedgh, Mehd Roudak Cotrol Dvso, Departmet of Electrcal Egeerg, K.N.oos Uversty of echology P. O. Box: 16315-1355, ehra, Ira sedgh@eetd.ktu.ac.r,
More informationBanks Are Where The Liquidity Is
Prelmary Bas Are Where The Lquy Is Olver Har Harvar Uversy & NBER a Lug Zgales* Uversy of Chcago, NBER & CEPR February 04 Absrac Wha s so secal abou bas ha her emse ofe rggers goverme erveo? I hs aer we
More information