Recovering Risk-Neutral Densities from Exchange Rate Options: Evidence in Turkey

Size: px
Start display at page:

Download "Recovering Risk-Neutral Densities from Exchange Rate Options: Evidence in Turkey"

Transcription

1 CENTRAL BANK OF THE REPUBLIC OF TURKEY WORKING PAPER NO: 10/03 Recoveing Risk-Neutal Densities fom Exchange Rate Options: Evidence in Tukey Mach 2010 Halil İbahim AYDIN Ahmet DEĞERLİ Pına ÖZLÜ

2 Cental Bank of the Republic of Tukey 2010 Addess: Cental Bank of the Republic of Tukey Head Office Reseach and Monetay Policy Depatment İstiklal Caddesi No: 10 Ulus Ankaa Tukey Phone: Facsimile: The views expessed in this woking pape ae those of the autho(s) and do not necessaily epesent the official views of the Cental Bank of the Republic of Tukey. The Woking Pape Seies ae extenally efeeed. The efeeeing pocess is managed by the Reseach and Monetay Policy Depatment.

3 Recoveing Risk-Neutal Densities fom Exchange Rate Options: Evidence in Tukey Halil İbahim Aydın γ Ahmet Değeli γ Pına Özlü γ Abstact This pape uses ove-the-counte cuency options data to investigate maket expectations on Tukish Lia-U.S. Dolla exchange ate. We extact option implied density functions to examine the evolution of maket sentiment ove the possible values of futue exhange ates. Uncetainty is well measued by option-implied pobabilities. Estimated densities fo selected days point out an incease in uncetainty in foeign exchange maket duing financial tubulence peiods. We make infeences about the effectiveness of policy measues and see how the maket peception changed thoughout the cisis. We uncove the effectiveness of policy measues by obseving shinking densities and confidence bands. Keywods: Options Risk neutal density Maket expectations. JEL Codes: G13 G19 F31 This pape has benefited fom Refet Gükaynak s comments. We ae gateful to Selim Elekdağ Özgü Özel and Güsu Keleş fo helpful comments on a pevious daft. The views expessed in this pape do not necessaily epesent those of the Cental Bank of the Republic of Tukey. All emaining eos ae ous. γ Reseach and Monetay Policy Depatment Cental Bank of the Republic of Tukey; Head Office Istiklal Caddesi: No.10 Ulus; Ankaa; TURKEY Coesponding autho: Halil İbahim Aydın phone: (312) ; fax: (312)

4 I. Intoduction Options makets ae vey impotant fo academics maket paticipants and policy makes. They povide a ich souce of infomation about investos expectations and maket uncetainty about the futue couse of the financial asset pices. Options contacts give the ight to buy o sell an asset in the futue at a pice (stike) set now. Options have a value since thee is a chance that the options can be execised that is the undelying asset pice will be moe/less than a paticula stike pice. Hence when we look at options with diffeent stike pices the pices at which such contacts tade now give us infomation about the maket s view of the chances that the pice of the undelying asset will be above/below these stike pices. The common way of dealing with the infomation embedded in option pices is to extact implied isk-neutal pobability density function (RND) a commonly used indicato to gauge expectations about futue pice of a financial asset unde isk neutal assumption of the pefeences of the investos. The impact of monetay policy decisions on maket expectations the pobability that inteest ate may pevail inside a specific ange o the iskiness of a cuency position can be evealed though the infomation content of RNDs. Recently an inceasing numbe of studies have investigated the shape of the isk-neutal pobability distibution of futue asset pices using options on inteest ates equity pices and exchange ates in line with the deepening of the deivative makets. Many studies on diffeent assets indicate the usefulness of RNDs. 1 The evidence is in favo of the intepetation that the estimates of RNDs do not help foecast the futue but eveal the maket sentiment that is useful fo the policy stance of the cental banks. Most cental banks tack the changes in maket sentiment via the estimates of RNDs. 2 Estimates of RND ae commonly studied in the context of fundamental economic questions elated to an impotant event o a possible change in egime o announcements of economic news that could affect expectations. Fo example Baha (1997) compaes RNDs aound announcements of inflation epots to test the change in maket sentiment using options on thee-month steling inteest ate. He povides a vey infomative discussion about RNDs in assessing monetay conditions and 1 See Coutant et al. (2001) Jondeau and Rockinge (2000) Melick and Thomas (1997). 2 See Csavas (2008) Bha and Chiaella (2000) Sydal (1999) Nakamua and Shiatsuka (1999). 2

5 cedibility of the monetay policy. He agues that the cental bank cedibility measued as the diffeence between the makets peceived distibution of the futue ate of inflation and taget inflation can be assessed via RNDs. Since thee is no diect instument available to compute RND fo inflation he suggests using the RND of long-tem inteest ates to measue uncetainty ove futue inflation. Campa et al. (1999) compute RNDs on coss ates within the Exchange Rate Mechanism of the Euopean Monetay System to assess the cedibility of commitments to exchange ate taget zones and detemine whethe the bandwidths ae consistent with the maket expectations. The RND could also be utilized in testing the ationality and measuing isk attitude of investos which ae highly impotant fo policy makes. This study aims to extact the isk-neutal densities embedded in ove-thecounte (OTC) exchange ate options in Tukey. To the best of ou knowledge this is the fist attempt to ecove RND fo TL/USD exchange ates. While the numbe of studies on RNDs fo developed economies is lage thee ae only few studies fo emeging makets due to unavailability of the options data. Gowth in the deivative activities in Tukey motivates us to undestand elevant infomation concening maket expectations contained in the pices of options. The liteatue on RND estimation coves a wide ange of techniques including paametic non-paametic and stuctual models. 3 While some methods may not be convenient due to the lack of data fo options the othes may yield distoted density functions inconsistent with empiical statistics o pobability theoy. Fo instance models with volatility smile cuve fitting as in Shimko (1993) may lead to negative pobabilities. To cicumvent these shotcomings we apply Malz (1997) method which ensues positive density. Moeove the Malz method is analytically tactable since it equies only thee obsevations to uncove the undelying density. We investigated the infomation content of RNDs when financial makets wee subject to a geate uncetainty duing the peiod 2006 and We make infeences about the effectiveness of monetay policy measues and see how the maket peception changed thoughout the cisis. Fo both peiods we obseved that the estimated densities signaled moe uncetainty duing the cisis times and the monetay policy measues wee successful in educing the uncetainty. 3 Studies such as Baha (1997) Campa et al. (1998) Jondeau and Rockinge (2000) Bliss and Panigitzoglu (2004) povide infomative discussions about vaious RND methods. 3

6 The plan of the emainde of this pape is as follows. We intoduce ou data in section 2. In section 3 we biefly pesent the method employed. Section 4 descibes the case studies and section 5 concludes. II. Data Deivatives ae fowad maket instuments and thei volume has exceeded the volume of spot maket instuments in the global economy. 4 Thee ae two diffeent types of deivatives makets distinguished by whethe they ae taded in an oganized maket o not. Exchange-taded deivatives ae taded in specialized and oganized makets. The othe type is the OTC maket whee tading takes place diectly between paties without an oganized maket o intemediay. The volume of OTC deivatives maket is geneally highe than that of exchange-taded deivatives maket. In Tukey thee ae both oganized and unoganized deivatives makets. Oganized deivatives maket Tukish Deivatives Exchange (TURKDEX) is located in İzmi. The poducts taded in TURKDEX ae futue contacts on stock index inteest ates cuencies and commodities. Thee ae no options contacts taded in TURKDEX. Howeve thee ae options contacts on exchange ates taded in OTC maket. It is woth mentioning a few wods on options quotations befoe documenting the details of the data and the methodology we adopt. The options ae taded in both exchange taded (oganized) and OTC (unoganized) makets. But quotations in two makets diffe fom each othe. In exchange taded makets the quotations ae given in tems of stike levels and option pices. Wheeas in OTC makets the quotations ae given in tems of deltas 5 and implied volatilities. Using the Black-Scholes fomula it is easy to eveal the stike pice fom delta and option pice fom implied volatility. The OTC quotation facilitates the scaling of the asset pice movements in makets whee financial assets display volatile pice pattens. Fo example foeign exchange ates ae quickly changing in shot peiods of time. It is vey had to detemine constant stike levels fo such assets. A pactical solution adapted in the maket is to quote in tems of deltas instead of stike pices. Ultimately the implied volatility takes the ole of option pice and delta takes the ole of stike pice. 4 See BIS statistics fo global OTC deivatives. 5 Delta is a paamete showing how close the asset pice to the stike pice (i.e. moneyness of the option). 4

7 Thee ae thee option combinations which ae heavily employed in cuency options makets. These ae at-the-money staddle (atm) isk evesal () and stangle (st). 6 While at-the-money staddle options have 50 delta isk evesals and stangles can have diffeent delta levels. Since 25 delta is the most liquid one we choose 25 delta isk evesal and stangle in line with the Malz (1996) appoach we adopt. These option types in cuency options makets enable investos to get infomation about the behavio of moments of expected values of the undelying exchange ate. Fo instance the staddle indicates the expected volatility of the exchange ate. Similaly isk evesal and stangle give infomation about the skewness and kutosis of the distibution of futue exchange ate espectively. The dataset consists of OTC foeign cuency options quoted in tems of implied volatility and delta. We used options on Tukish Lia against US Dolla. Matuity is taken as one month. Risk fee inteest ates used in the option pices ae detemined fom USD and TL LIBOR makets at the coesponding matuities. The dataset coves the daily obsevations between 2006 and We used the settlement pices of options which ae detemined at the close of tading day. 7 It is impotant to take into account the liquidity of USD/TL options maket. Unfotunately the depth and volume of the ove-the-counte maket in Tukey is low. The liquidity in the options makets may be even lowe duing the cisis peiod. Theefoe the RND functions may not tuly eflect all changes in maket sentiment in shot peiods. Thus fo event study puposes it may be bette to look at changes in the RND function at somewhat lowe fequencies. We choose the time intevals at least as one week. The dates efe to the time peiods befoe the financial tubulence duing the tubulence and afte the policy measues taken by Cental Bank of the Republic of Tukey (CBRT). We focus on two case studies to undestand how the maket sentiment changed duing financial tumoil expeienced in the second half of 2000 s May-June 2006 and Septembe-Octobe Fo the fist peiod we gaph RNDs fo the days of May 8 May 15 June 13 and July The second case study deals with the global financial cisis which was intensified by the bankuptcy of Lehman Bothes in Septembe To investigate the effects of the cisis on the financial maket we 6 See Appendix fo details. 7 See Melick and Thomas (1998) Södelind and Svensson (1997). 5

8 examine the days of Septembe 8 Septembe 16 Octobe 22 and Octobe We make infeences about the effectiveness of policy measues and see how the maket peception changed thoughout the cisis. III. Methodology The density extacted fom the taded options is called the isk neutal density (i.e. RND) which povides the set of pobabilities that investos would attach to futue asset pices in a wold in which investos ae isk-neutal. The intuition behind RND is closely linked to Aow-Debeu pices of contingent claims. Since deivatives ae contacts on futue events the pices of deivatives today eflect the possibility of the ealization of those events. The picing of contingent claims in finance liteatue is based on the isk neutal valuation pinciple. The concept of isk neutal valuation dates back to ealy effots of Samuelson (1965) on option picing. Samuelson (1965) deives the andom value of the option at execise. His fomulation included two paametes the expected ate of etun on the stock pice and the discount ate of the options. Retun paamete is the expected etun fom the stock pice if investos hold it until the matuity of the option. Discounting paamete is the oppotunity cost of investing in option. Since the option pice is embedded with uncetainty the discounting paamete should include the isk within options as well as altenative iskless investments. Both paametes of the models depend upon the unique isk chaacteistics of the undelying stock and the option. Howeve in an options contact both the deivative and its undelying asset ae subject to the same souce of pice changes o the same souces of isk. Thus uncetainty suounding the teminal stock pice affects isk attitude of the investos towads both assets. Decisions on holding the stock o the option ae both affected by the same isk. Accodingly option pice does not depend on the isk pefeence of the investos as long as the discounting and etun paametes eflect the same degee of isk avesion. This famewok fist advocated by Cox and Ross (1976) implies the ielevance of isk pefeences of investos to the option pice and captues the essence of isk neutal picing. The mechanics of isk neutal valuation is as follows. One can calculate the option pice by consideing isk neutal investo s behavio. In this setup the expected etun on undelying asset and discounting ate substituted with isk-fee inteest ate. 6

9 A isk neutal investo can hedge the shot/long position (whateve he pefes) by taking the opposite in the othe asset. Shot position in call option fo instance can be hedged by long position in the undelying asset. By this appoach the option pice can be calculated whateve the isk pefeence the investos have; because isk avesion is ielevant to the option pice. It is impotant to note that the state pices of contingent claims in an Aow- Debeu economy depend on the likelihood of the states and on the attitude of the agents towads those states. In ou appoach investos ae assumed to be isk neutal. Thus the effects of isk-avesion ae embedded in isk neutal pobabilities. That is likelihood of financial asset pices embedded in the options pices eflects the investos expectations as well as isk avesions about the unknown futue. This peception seves as the main pilla of the liteatue on RNDs and the basis fo ou analysis. The geneal conclusion of isk neutal valuation is that pice of options can be deduced fom the expectation of option payoff. Mathematically speaking the expectation of asset payoff is an integal with espect to teminal asset pice. Accodingly the pice of a Euopean style call option C (K) at time t with matuity τ and stike pice K can be simplified as an integal unde isk neutal pobability measue τ C( K ) = e ( S K ) p( S ) ds K T T T (1) whee S T denotes the asset pice at matuity. p (S T ) is the pobability associated with pice S T at matuity based on the teminal asset pice. Almost all option picing models in mathematical finance liteatue deal with this integal epesentation. The models ae based on vaious pobability distibution assumptions fo the teminal asset pice. The seminal wok of Black and Scholes (1973) is founded upon the assumption that the distibution of the pice S T is lognomal i.e.; the asset pice at matuity follows a geometic Bownian motion with constant volatility. This assumption yields a closed fom fomula fo the option pice. Howeve empiical facts show that financial asset pices do not admit geometic Bownian motions. Statistical popeties of asset etuns exhibit significant dispesion fom Black-Scholes assumptions. The etuns ae not nomally distibuted; leptokutic kenels have bette 7

10 fit pefomance than nomal densities. Moeove the volatility is not constant fo the options with diffeent stike pices. Volatilities acoss stikes show vaiations pesenting volatility smile pattens. Volatilities fo options with diffeent time-tomatuities ae also diffeent fom each othe leading to a tem stuctue of volatilities. The vaiations of volatilities fo diffeent stike pices and matuities endeed the bith of the concept of implied volatility. Implied volatility is the volatility implied by the maket pice of the option. When plugged into the Black-Scholes fomula implied volatility yields a theoetical option pice that is equal to the maket pice of the option. Implied volatility is used to emedy the shotcomings of constant volatility assumption of Black-Scholes model. It shows the chaacteistic featues of options with diffeent stikes. Fo this eason it is used as the actual pice of option. Maket pactitiones use implied volatility in Black-Scholes model as a tool of quotation. Especially in OTC makets a tade pesents his bid-ask pices fo the options in tems of its volatility. Howeve this does not mean that Black-Scholes model is the pope model fo option picing o ageed upon model of the maket. Rathe it is the model with which the pactitiones use to detemine the option pice fom volatility quotes. Due to the limitations of Black-Scholes model the liteatue on options picing focused on flexible distibutions fo financial asset etuns. A numbe of diffeent stochastic pocesses ae examined fo the etuns of the undelying asset. Results indicate that a numbe of stochastic pocesses can be matched fo asset etuns but the estimation of model paametes gets complicated as the numbe of paametes inceases. Thus assigning a stochastic pocess fo the undelying asset is the geneal methodology of option picing but its use in RND estimation is limited. Due to the lage numbe of paametes involved in estimation we opt to use a non-paametic method fo RND estimation. Most of the RND estimation techniques ae based on the wok of Beeden and Litzenbege (1978) who showed that RND could be deived fom the second deivative of call pices with espect to stike pices. 2 C = e 2 K τ p( K) One can infe the RND by numeical diffeentiation of call options with espect to stikes when thee ae sufficient obsevations. Howeve such diect estimation of (2) 8

11 RND is not geneally possible due to the lack of available option pices. Also these kinds of models lead to unstable density estimates 8. Thus diect numeical evaluation is egaded as an inaccuate way of density extaction and eseach focus shifted to indiect methods. A numbe of indiect density estimation methods ae poposed to cicumvent the shotcomings of diect density estimations. One of these attempts is documented in Malz (1997). The pocedue is a non-paametic estimation of RND. It is based on the idea of fitting a cuve fo volatility smile on implied volatility and delta space. Malz suggests estimating RND of exchange ates by using the infomation embedded in staddle stangle and isk evesal options. Since volatilities fo diffeent stike levels vay the model needs to build volatility as a function of stike pice (delta). To this aim Malz (1997) poposes a second ode Taylo appoximation to delta-implied volatility cuve aound the point δ 0 =0.5 as follows ˆ t ( δ ) atm + b ( δ δ ) + b st ( δ δ ) 2 0 = 0 t 1 t 0 2 t b (3) 0 whee atm t t and st t ae volatilities of at-the-money isk evesal and stangle (o buttefly) options. The intuition behind this appoach is such that the atm and st show the level skew and cuvatue of volatility smiles espectively. This infomation is captued by Taylo appoximation. Plugging implied volatilities of options with deltas and 0.75 one can deduce the paametes as b 0 =1 b 1 =-2 and b 2 =16. The cuve fitting step needs caution since both sides of the equation includes implied volatility. Right hand side is the implied volatility and left hand side includes the tem delta which is itself a function of volatility. This equies us to find a unique solution fo implied volatility using numeical pocedues. Once the implied volatility function is estimated option pices ae found by plugging implied volatility into Black-Scholes fomula. Then indiect estimation of the isk neutal density is caied out via Beeden and Litzenbege (1978) fomula given in equation 2. 8 See Jondeau Poon and Rockinge (2007). 9

12 IV. Empiical Evidence One of the impotant goals of the CBRT is to ensue financial stability in domestic makets. Afte the adopt of fee-float exchange ate egime the intevention of the Bank to FX maket diminished consideably. The beginning of fee float peiod coincided with the independence of CBRT and an ageement with IMF to intevene only in limited amounts in the foeign exchange maket. The Bank was committed to intevene to smooth out exteme movements in exchange ates. Nevetheless in cetain peiods when financial makets wee hit by extenal shocks the Bank actively intevened to stabilize the makets. Tukish economy expeienced two financial lage maket tubulences duing the second half of 2000 s one in May-June 2006 and the othe in Septembe-Octobe The Bank took seveal pecautionay measues to stabilize the financial maket volatility. Duing the May-June 2006 peiod the fist measue taken was to suspend the daily foeign exchange puchase auctions that the Bank had been caying out stating fom May Aftewads the Monetay Policy Committee (MPC) held an inteim meeting on June 7 when policy ates wee hiked by 175 basis points. Though the fluctuations in financial makets eased to some extent the volatility intensified in the last week of June putting pessue on exchange ates and medium and long-tem inteest ates. The MPC held anothe inteim meeting on June 25 and not only inceased policy ates by a futhe 225 basis points but also took a numbe of measues egading TL and foeign exchange liquidity duing the meeting. To incease the flexibility of monetay policy and gadually educe the excess liquidity the Bank also initiated Tukish Lia Deposit Buying Auctions with standad matuities of one and two weeks as of June 26. In the meeting held in July 2006 the MPC aised inteest ates by a futhe 25 basis points in ode to alleviate the seconday effects of the exchange ate inceases and impove inflation expectations. Consequently the ovenight boowing ate was inceased by 425 basis points in total fom June 7 to July 20. The policy measues taken by the Bank povided stability in the financial makets in a shot peiod of time. Poblems in global cedit makets in autumn 2008 have aised concens on the global financial system and advesely affected the global liquidity flows. Cental banks acted pomptly and took actions in a coodinated manne. The cisis had its 10

13 advese effects on Tukish foeign exchange makets in Octobe. The tubulence intensifies on Octobe 22. In line with the effots in the global economy the Bank attempted to maintain healthy functioning of the domestic maket though pe-cautionay measues. Ongoing foeign exchange buying auctions wee suspended and selling auctions wee intoduced to inject foeign exchange liquidity into the maket. The Foeign Exchange Deposit Maket within the Bank was e-opened. This decision led to foeign exchange deposit tansactions among banks in tems of both US dolla and Euo and pevented the decline in the flow of foeign exchange liquidity. The matuity of the FX deposit boowed has been extended and the lending ate was educed. Simila to the tumoil in 2006 the policy measues taken by the Bank wee successful in achieving stability in the maket by the end of Octobe It is woth noting the diffeences between the implied volatility and RND gaphs befoe we depict the figues. While the figues of implied volatility povides infomation about the futue dispesion of the asset pice fom one obseved option pice the implied isk-neutal density on the othe hand povides infomation about the entie distibution of the ultimate asset pice fom seveal option pices. Also the RND could yield infomation about the highe moments of the teminal asset pice as long as these moments ae consistent acoss diffeent estimation models. Much of the infomation contained in RND functions can be captued though a ange of summay statistics shown in Table 1. The mean is the aveage value of all possible futue outcomes. The standad deviation is a measue of dispesion of the implied RND and commonly used to measue maket uncetainty. Skewness chaacteizes the distibution of pobability eithe side of the mean and povides a measue of asymmety fo the distibution. Fo example a positively skewed distibution is one fo which thee is less pobability attached to outcomes highe than the mean than to outcomes below the mean. Kutosis is a measue of how peaked a distibution is o the likelihood of exteme outcomes. The geate this likelihood the fatte the tails of the distibution. 11

14 Table 1: Desciptive Statistics of Risk Neutal Densities May-June Month Mean Vaiance Skewness Kutosis Standad Lowe Uppe Deviation Bound* Bound* 8-May May Jun Jul Septembe-Octobe Month Mean Vaiance Skewness Kutosis Standad Lowe Uppe Deviation Bound* Bound* 8-Sep Sep Oct Oct * Lowe and uppe bounds efe to 5 and 95 pecent confidence levels. Figues 1 and 2 pesent the implied volatilities acoss execise pices duing the two tumoil peiods in Tukey. The implied volatility cuve pesents the volatility pices of the options fo diffeent execise pices. The value in the y-axis is egaded as the pice of the option in tems of volatility. The x-axis denotes the execise pices. Accodingly the pice of the option is at the lowest level when the option is at-themoney (i.e. execise pice is close to spot pice). As the execise pice goes up o down the volatility pice of the option inceases. Howeve the incease in option volatility may be highe fo high stikes than low stikes and vice vesa. This effect is known as the volatility skew o smik. This patten appeaed in stock options maket afte the 1987 cash. Volatility skew may be seen in cuency options as well. This means that the maket feas the depeciation of the local cuency and willing to pay moe fo the possible depeciation than appeciation o vice vesa. The volatility skew is moe appaent when the maket volatility gets highe and highe. Befoe May 2006 tubulence the implied volatility diffeence between in-the money and out-of-the money options was low on May wheeas it widens duing the tubulence on June depicted in Figue 1. Simila patten can be obseved duing the Septembe-Octobe 2008 tubulence shown in Figue 2. The figues on RND indicate the pobabilities attached to diffeent pice levels of the undelying asset. The x-axis denotes the futue values of spot TL/USD exchange ates. The peceived isk neutal occuence pobabilities of these exchange 12

15 ate levels ae pesented in the y-axis. A numbe of illustations of RND functions ae given in Figues 3-4 and changes in thei shapes befoe and afte the financial tumoil ae pesented in 2006 and Changes in the width of the confidence inteval infom us about changes in maket uncetainty about futue asset pice levels. Figue 1. Implied Volatility Cuve fo May-June May Jun May Jul-06 Implied volatility Exchange Rates Figue 2. Implied Volatility Cuve fo Septembe-Octobe Sep Oct Sep Oct Implied Volatility Exchange Rates Figue 3 compaes the one month implied RND fo TL/USD option on dates befoe and afte the financial tumoil in We see that as the tumoil intensifies by June 13 the confidence intevals get wide suggesting the feas of lage movements of exchange ates. The ight tail of RND function gets fatte indicating the ising uncetainty in the maket sentiment o the peceived incease in the pobability of a lage depeciation. The RND gaph on July shows that the width of the confidence inteval become naowe afte the Bank intevened in the maket. The 13

16 good news is that the decease of uncetainty about expected futue exchange ate level can be visualized fom RND figues and confidence bands. Figue 3. Implied RND fo the one-month TL/USD foeign exchange ate in May-June May Jun May Jul-06 Pobability Exchange Rates A simila analysis on changes in implied RND function following the global cisis in Septembe 2008 is given in Figue 4. We gaph the RND functions befoe and afte the bankuptcy of Lehman Bothes on Septembe When we compae the RND functions befoe and afte the bankuptcy of Lehman Bothes we see that the confidence intevals widens as the cisis intensifies and then diminished afte the policy measues taken by the end of Octobe. Case studies on RND functions show that policy measues including the foeign exchange intevention deceases pospective uncetainty in the foeign exchange makets. Figue 4. Implied RND fo the one-month TL/USD foeign exchange ate in Septembe-Octobe Sep Oct Sep Oct Pobability Exchange Rates It is impotant not to ead too much infomation fom gaphs of isk-neutal distibutions (BIS 1999). The RNDs do not povide the actual pobabilities of futue 14

17 asset pices. Rathe they give the values that option maket paticipants attach to hedges of diffeent possible outcomes. Thus the liteatue is much moe inteested in the intuitive notion captued by the change in the shape of RND. Also isk neutality of the RND stands fo the assumption that individuals in the maket ae isk-neutal. Moeove OTC makets compise of institutional investos who tend to be less isk avese. 9 The time seies epesentations of TL/USD and RND implied standad deviation povided in Figues 5 and 6 convey how the maket uncetainty about the expected outcome changed ove time and illustate the ise in uncetainty in foeign exchange maket duing financial tubulence peiods. Figue 5: Nominal Exchange Rate (TL/USD) TL/USD Figue 6: RND Implied Standad Deviation RND Implied Standad Deviation V. Conclusion Gükaynak and Wolfes (2005) show that isk neutality assumption can not be ejected in a maket fo institutional investos. 15

18 V. Conclusion Option implied isk neutal densities povide infomation about maket expectations. In this pape we estimate the isk-neutal pobability density (RND) functions fo TL/USD cuency options. We apply the method poposed by Malz (1996) due to its analytical tactability and simplicity. We investigated the infomation content of RNDs when financial makets wee subject to a geate uncetainty duing the peiod 2006 and We make infeences about the effectiveness of monetay policy measues and see how the maket peception changed thoughout the cisis. Fo both peiods we obseved the widening of the confidence intevals as the financial tubulence hit the maket implying feas of lage movements in exchange ates. We uncove the effectiveness of policy measues by obseving shinking densities and confidence bands. The oveall esult is such that the Bank was successful in stabilizing the makets duing ecent financial tubulences and the infomation content of RNDs facilitates to undestand how maket paticipants view the futue and pices of isk associated with futue outcome. 16

19 REFERENCES Baha B Implied Risk-Neutal Pobability Density Functions fom Option Pices: Theoy and Application. Bank of England Woking Pape No Bank fo Intenational Settlements Estimating and Intepeting Pobability Density Functions. BIS Pape No. 6. Bha R. Chiaella C Expectations of Monetay Policy in Austalia Implied by the Pobability Distibution of Inteest Rate Deivatives. Euopean Jounal of Finance Vol. 6(2) Black F. Scholes M The Picing of Options and Copoate Liabilities. Jounal of Political Economy Vol.81 (3) Bliss R. Panigitzoglu N Option-implied Risk Avesion Estimates. Jounal of Finance Vol.59 (1) Beeden D. Litzenbege R Pices of State-Contingent Claims Implicit in Option Pices. Jounal of Business Vol.51 (4) Campa J. Chang K. Refalo J An Options-Based Analysis of Emeging Maket Exchange Rate Expectations: Bazil s Real Plan NBER Woking Pape No Campa J. Chang K. Reide R Implied Exchange Rate Distibutions: Evidence fom OTC Option Makets. Jounal of Intenational Money and Finance Vol: 17(1) Coutant S. E. Jondeau E. Rockinge M Reading PIBOR Futues Option Smiles: The 1997 Fench Snap Election. Jounal of Banking and Finance Vol. 25(11) Cox C. Ross A The Valuation of Options fo Altenative Stochastic Pocesses. Jounal of Financial Economics Vol.3 (1) Csávás C Density Foecast Evaluation and the Effect of Risk-neutal Cental Moments on the Cuency Risk Pemium: Tests Based on Eu/Huf Option- Implied Densities Cental Bank of Hungay Woking Pape No.3. Gükaynak R. Wolfes J Macoeconomic Deivatives: An Initial Analysis of Maket-Based Maco Foecasts Uncetainty and Risk. NBER Intenational Semina on Macoeconomics 2005 (2) Jondeau E. Poon S. Rockinge M Financial Modeling Unde Non-Gaussian Distibutions. Spinge-Velag New Yok. 17

20 Jondeau E. Rockinge M Reading the Smile: The Message Conveyed by Methods Which Infe Risk Neutal Densities. Jounal of Intenational Money and Finance Vol. 19 (6) Malz A Using Option Pices to Estimate Realignment Pobabilities in the Euopean Monetay System: The Case of Steling-Mak. Jounal of Intenational Money and Finance Vol.15 (5) Malz A Estimating the Pobability Distibution of the Futue Exchange Rate fom Option Pices. Jounal of Deivatives Vol. 5 (2) Melick W. Thomas C Recoveing an Asset s Implied PDF fom Option Pices: An Application to Cude Oil Duing the Gulf Cisis. Jounal of Financial and Quantitative Analysis Vol. 32 (1) Melick W. Thomas C Confidence Intevals and Constant Matuity Seies fo Pobability Measues Extacted fom Option Pices. Confeence Pape Bank of Canada. Nakamua H. Shiatsuka S Extacting Maket Expectations fom Option Pices: Case Studies in Japanese Option Makets. Monetay and Economic Studies Institute fo Monetay and Economic Studies Bank of Japan Woking Pape Vol. 17(1) Samuelson P Rational Theoy of Waant Picing Industial Management Review Vol Shimko D Bounds of Pobability. Risk Vol Södelind P. Svensson L New Techniques to Extact Maket Expectations fom Financial Instuments. Jounal of Monetay Economics Vol. 40(2) Sydal S A Study of Implied Risk-Neutal Density Functions in the Nowegian Option Maket. Noges Bank Woking Pape No

INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS

INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS Vesion:.0 Date: June 0 Disclaime This document is solely intended as infomation fo cleaing membes and othes who ae inteested in

More information

Chapter 3 Savings, Present Value and Ricardian Equivalence

Chapter 3 Savings, Present Value and Ricardian Equivalence Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,

More information

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts

More information

An Introduction to Omega

An Introduction to Omega An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei isk-ewad chaacteistics? The Finance Development Cente 2002 1 Fom

More information

Ilona V. Tregub, ScD., Professor

Ilona V. Tregub, ScD., Professor Investment Potfolio Fomation fo the Pension Fund of Russia Ilona V. egub, ScD., Pofesso Mathematical Modeling of Economic Pocesses Depatment he Financial Univesity unde the Govenment of the Russian Fedeation

More information

How Much Should a Firm Borrow. Effect of tax shields. Capital Structure Theory. Capital Structure & Corporate Taxes

How Much Should a Firm Borrow. Effect of tax shields. Capital Structure Theory. Capital Structure & Corporate Taxes How Much Should a Fim Boow Chapte 19 Capital Stuctue & Copoate Taxes Financial Risk - Risk to shaeholdes esulting fom the use of debt. Financial Leveage - Incease in the vaiability of shaeholde etuns that

More information

9:6.4 Sample Questions/Requests for Managing Underwriter Candidates

9:6.4 Sample Questions/Requests for Managing Underwriter Candidates 9:6.4 INITIAL PUBLIC OFFERINGS 9:6.4 Sample Questions/Requests fo Managing Undewite Candidates Recent IPO Expeience Please povide a list of all completed o withdawn IPOs in which you fim has paticipated

More information

Valuation of Floating Rate Bonds 1

Valuation of Floating Rate Bonds 1 Valuation of Floating Rate onds 1 Joge uz Lopez us 316: Deivative Secuities his note explains how to value plain vanilla floating ate bonds. he pupose of this note is to link the concepts that you leaned

More information

The transport performance evaluation system building of logistics enterprises

The transport performance evaluation system building of logistics enterprises Jounal of Industial Engineeing and Management JIEM, 213 6(4): 194-114 Online ISSN: 213-953 Pint ISSN: 213-8423 http://dx.doi.og/1.3926/jiem.784 The tanspot pefomance evaluation system building of logistics

More information

YIELD TO MATURITY ACCRUED INTEREST QUOTED PRICE INVOICE PRICE

YIELD TO MATURITY ACCRUED INTEREST QUOTED PRICE INVOICE PRICE YIELD TO MATURITY ACCRUED INTEREST QUOTED PRICE INVOICE PRICE Septembe 1999 Quoted Rate Teasuy Bills [Called Banke's Discount Rate] d = [ P 1 - P 1 P 0 ] * 360 [ N ] d = Bankes discount yield P 1 = face

More information

Exam #1 Review Answers

Exam #1 Review Answers xam #1 Review Answes 1. Given the following pobability distibution, calculate the expected etun, vaiance and standad deviation fo Secuity J. State Pob (R) 1 0.2 10% 2 0.6 15 3 0.2 20 xpected etun = 0.2*10%

More information

Software Engineering and Development

Software Engineering and Development I T H E A 67 Softwae Engineeing and Development SOFTWARE DEVELOPMENT PROCESS DYNAMICS MODELING AS STATE MACHINE Leonid Lyubchyk, Vasyl Soloshchuk Abstact: Softwae development pocess modeling is gaining

More information

Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing

Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow

More information

est using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.

est using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years. 9.2 Inteest Objectives 1. Undestand the simple inteest fomula. 2. Use the compound inteest fomula to find futue value. 3. Solve the compound inteest fomula fo diffeent unknowns, such as the pesent value,

More information

Trading Volume and Serial Correlation in Stock Returns in Pakistan. Abstract

Trading Volume and Serial Correlation in Stock Returns in Pakistan. Abstract Tading Volume and Seial Coelation in Stock Retuns in Pakistan Khalid Mustafa Assistant Pofesso Depatment of Economics, Univesity of Kaachi e-mail: khalidku@yahoo.com and Mohammed Nishat Pofesso and Chaiman,

More information

Financial Planning and Risk-return profiles

Financial Planning and Risk-return profiles Financial Planning and Risk-etun pofiles Stefan Gaf, Alexande Kling und Jochen Russ Pepint Seies: 2010-16 Fakultät fü Mathematik und Witschaftswissenschaften UNIERSITÄT ULM Financial Planning and Risk-etun

More information

Controlling the Money Supply: Bond Purchases in the Open Market

Controlling the Money Supply: Bond Purchases in the Open Market Money Supply By the Bank of Canada and Inteest Rate Detemination Open Opeations and Monetay Tansmission Mechanism The Cental Bank conducts monetay policy Bank of Canada is Canada's cental bank supevises

More information

The Predictive Power of Dividend Yields for Stock Returns: Risk Pricing or Mispricing?

The Predictive Power of Dividend Yields for Stock Returns: Risk Pricing or Mispricing? The Pedictive Powe of Dividend Yields fo Stock Retuns: Risk Picing o Mispicing? Glenn Boyle Depatment of Economics and Finance Univesity of Cantebuy Yanhui Li Depatment of Economics and Finance Univesity

More information

A framework for the selection of enterprise resource planning (ERP) system based on fuzzy decision making methods

A framework for the selection of enterprise resource planning (ERP) system based on fuzzy decision making methods A famewok fo the selection of entepise esouce planning (ERP) system based on fuzzy decision making methods Omid Golshan Tafti M.s student in Industial Management, Univesity of Yazd Omidgolshan87@yahoo.com

More information

Channel selection in e-commerce age: A strategic analysis of co-op advertising models

Channel selection in e-commerce age: A strategic analysis of co-op advertising models Jounal of Industial Engineeing and Management JIEM, 013 6(1):89-103 Online ISSN: 013-0953 Pint ISSN: 013-843 http://dx.doi.og/10.396/jiem.664 Channel selection in e-commece age: A stategic analysis of

More information

ON THE (Q, R) POLICY IN PRODUCTION-INVENTORY SYSTEMS

ON THE (Q, R) POLICY IN PRODUCTION-INVENTORY SYSTEMS ON THE R POLICY IN PRODUCTION-INVENTORY SYSTEMS Saifallah Benjaafa and Joon-Seok Kim Depatment of Mechanical Engineeing Univesity of Minnesota Minneapolis MN 55455 Abstact We conside a poduction-inventoy

More information

The impact of migration on the provision. of UK public services (SRG.10.039.4) Final Report. December 2011

The impact of migration on the provision. of UK public services (SRG.10.039.4) Final Report. December 2011 The impact of migation on the povision of UK public sevices (SRG.10.039.4) Final Repot Decembe 2011 The obustness The obustness of the analysis of the is analysis the esponsibility is the esponsibility

More information

Chapter 11: Aggregate Demand II, Applying the IS-LM Model Th LM t

Chapter 11: Aggregate Demand II, Applying the IS-LM Model Th LM t Equilibium in the - model The cuve epesents equilibium in the goods maket. Chapte :, Applying the - Model Th t C ( T) I( ) G The cuve epesents money maket equilibium. M L(, ) The intesection detemines

More information

Japan s trading losses reach JPY20 trillion

Japan s trading losses reach JPY20 trillion IEEJ: Mach 2014. All Rights Reseved. Japan s tading losses each JPY20 tillion Enegy accounts fo moe than half of the tading losses YANAGISAWA Akia Senio Economist Enegy Demand, Supply and Foecast Goup

More information

HEALTHCARE INTEGRATION BASED ON CLOUD COMPUTING

HEALTHCARE INTEGRATION BASED ON CLOUD COMPUTING U.P.B. Sci. Bull., Seies C, Vol. 77, Iss. 2, 2015 ISSN 2286-3540 HEALTHCARE INTEGRATION BASED ON CLOUD COMPUTING Roxana MARCU 1, Dan POPESCU 2, Iulian DANILĂ 3 A high numbe of infomation systems ae available

More information

Promised Lead-Time Contracts Under Asymmetric Information

Promised Lead-Time Contracts Under Asymmetric Information OPERATIONS RESEARCH Vol. 56, No. 4, July August 28, pp. 898 915 issn 3-364X eissn 1526-5463 8 564 898 infoms doi 1.1287/ope.18.514 28 INFORMS Pomised Lead-Time Contacts Unde Asymmetic Infomation Holly

More information

Loyalty Rewards and Gift Card Programs: Basic Actuarial Estimation Techniques

Loyalty Rewards and Gift Card Programs: Basic Actuarial Estimation Techniques Loyalty Rewads and Gift Cad Pogams: Basic Actuaial Estimation Techniques Tim A. Gault, ACAS, MAAA, Len Llaguno, FCAS, MAAA and Matin Ménad, FCAS, MAAA Abstact In this pape we establish an actuaial famewok

More information

Definitions and terminology

Definitions and terminology I love the Case & Fai textbook but it is out of date with how monetay policy woks today. Please use this handout to supplement the chapte on monetay policy. The textbook assumes that the Fedeal Reseve

More information

Define What Type of Trader Are you?

Define What Type of Trader Are you? Define What Type of Tade Ae you? Boke Nightmae srs Tend Ride By Vladimi Ribakov Ceato of Pips Caie 20 of June 2010 1 Disclaime and Risk Wanings Tading any financial maket involves isk. The content of this

More information

Questions for Review. By buying bonds This period you save s, next period you get s(1+r)

Questions for Review. By buying bonds This period you save s, next period you get s(1+r) MACROECONOMICS 2006 Week 5 Semina Questions Questions fo Review 1. How do consumes save in the two-peiod model? By buying bonds This peiod you save s, next peiod you get s() 2. What is the slope of a consume

More information

Optimal Capital Structure with Endogenous Bankruptcy:

Optimal Capital Structure with Endogenous Bankruptcy: Univesity of Pisa Ph.D. Pogam in Mathematics fo Economic Decisions Leonado Fibonacci School cotutelle with Institut de Mathématique de Toulouse Ph.D. Dissetation Optimal Capital Stuctue with Endogenous

More information

A Capacitated Commodity Trading Model with Market Power

A Capacitated Commodity Trading Model with Market Power A Capacitated Commodity Tading Model with Maket Powe Victo Matínez-de-Albéniz Josep Maia Vendell Simón IESE Business School, Univesity of Navaa, Av. Peason 1, 08034 Bacelona, Spain VAlbeniz@iese.edu JMVendell@iese.edu

More information

CONCEPT OF TIME AND VALUE OFMONEY. Simple and Compound interest

CONCEPT OF TIME AND VALUE OFMONEY. Simple and Compound interest CONCEPT OF TIME AND VALUE OFMONEY Simple and Compound inteest What is the futue value of shs 10,000 invested today to ean an inteest of 12% pe annum inteest payable fo 10 yeas and is compounded; a. Annually

More information

Ignorance is not bliss when it comes to knowing credit score

Ignorance is not bliss when it comes to knowing credit score NET GAIN Scoing points fo you financial futue AS SEEN IN USA TODAY SEPTEMBER 28, 2004 Ignoance is not bliss when it comes to knowing cedit scoe By Sanda Block USA TODAY Fom Alabama comes eassuing news

More information

Comparing Availability of Various Rack Power Redundancy Configurations

Comparing Availability of Various Rack Power Redundancy Configurations Compaing Availability of Vaious Rack Powe Redundancy Configuations By Victo Avela White Pape #48 Executive Summay Tansfe switches and dual-path powe distibution to IT equipment ae used to enhance the availability

More information

Things to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request.

Things to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request. Retiement Benefit 1 Things to Remembe Complete all of the sections on the Retiement Benefit fom that apply to you equest. If this is an initial equest, and not a change in a cuent distibution, emembe to

More information

Tjalling C. Koopmans Research Institute

Tjalling C. Koopmans Research Institute Tjalling C. Koopmans Reseach Institute Tjalling C. Koopmans Reseach Institute Utecht School of Economics Utecht Univesity Kiekenpitplein 1-3584 EC Utecht The Nethelands telephone +31 30 53 9800 fax +31

More information

Firstmark Credit Union Commercial Loan Department

Firstmark Credit Union Commercial Loan Department Fistmak Cedit Union Commecial Loan Depatment Thank you fo consideing Fistmak Cedit Union as a tusted souce to meet the needs of you business. Fistmak Cedit Union offes a wide aay of business loans and

More information

Strategic Asset Allocation and the Role of Alternative Investments

Strategic Asset Allocation and the Role of Alternative Investments Stategic Asset Allocation and the Role of Altenative Investments DOUGLAS CUMMING *, LARS HELGE HAß, DENIS SCHWEIZER Abstact We intoduce a famewok fo stategic asset allocation with altenative investments.

More information

The Supply of Loanable Funds: A Comment on the Misconception and Its Implications

The Supply of Loanable Funds: A Comment on the Misconception and Its Implications JOURNL OF ECONOMICS ND FINNCE EDUCTION Volume 7 Numbe 2 Winte 2008 39 The Supply of Loanable Funds: Comment on the Misconception and Its Implications. Wahhab Khandke and mena Khandke* STRCT Recently Fields-Hat

More information

Supply chain information sharing in a macro prediction market

Supply chain information sharing in a macro prediction market Decision Suppot Systems 42 (2006) 944 958 www.elsevie.com/locate/dss Supply chain infomation shaing in a maco pediction maket Zhiling Guo a,, Fang Fang b, Andew B. Whinston c a Depatment of Infomation

More information

AMB111F Financial Maths Notes

AMB111F Financial Maths Notes AMB111F Financial Maths Notes Compound Inteest and Depeciation Compound Inteest: Inteest computed on the cuent amount that inceases at egula intevals. Simple inteest: Inteest computed on the oiginal fixed

More information

Fixed Income Attribution: Introduction

Fixed Income Attribution: Introduction 18th & 19th Febuay 2015, Cental London Fixed Income Attibution: A compehensive undestanding of Fixed Income Attibution and the challenging data issues aound this topic Delegates attending this two-day

More information

YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH

YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH nd INTERNATIONAL TEXTILE, CLOTHING & ESIGN CONFERENCE Magic Wold of Textiles Octobe 03 d to 06 th 004, UBROVNIK, CROATIA YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH Jana VOBOROVA; Ashish GARG; Bohuslav

More information

An Analysis of Manufacturer Benefits under Vendor Managed Systems

An Analysis of Manufacturer Benefits under Vendor Managed Systems An Analysis of Manufactue Benefits unde Vendo Managed Systems Seçil Savaşaneil Depatment of Industial Engineeing, Middle East Technical Univesity, 06531, Ankaa, TURKEY secil@ie.metu.edu.t Nesim Ekip 1

More information

Referral service and customer incentive in online retail supply Chain

Referral service and customer incentive in online retail supply Chain Refeal sevice and custome incentive in online etail supply Chain Y. G. Chen 1, W. Y. Zhang, S. Q. Yang 3, Z. J. Wang 4 and S. F. Chen 5 1,,3,4 School of Infomation Zhejiang Univesity of Finance and Economics

More information

Experimentation under Uninsurable Idiosyncratic Risk: An Application to Entrepreneurial Survival

Experimentation under Uninsurable Idiosyncratic Risk: An Application to Entrepreneurial Survival Expeimentation unde Uninsuable Idiosyncatic Risk: An Application to Entepeneuial Suvival Jianjun Miao and Neng Wang May 28, 2007 Abstact We popose an analytically tactable continuous-time model of expeimentation

More information

Life Insurance Purchasing to Reach a Bequest. Erhan Bayraktar Department of Mathematics, University of Michigan Ann Arbor, Michigan, USA, 48109

Life Insurance Purchasing to Reach a Bequest. Erhan Bayraktar Department of Mathematics, University of Michigan Ann Arbor, Michigan, USA, 48109 Life Insuance Puchasing to Reach a Bequest Ehan Bayakta Depatment of Mathematics, Univesity of Michigan Ann Abo, Michigan, USA, 48109 S. David Pomislow Depatment of Mathematics, Yok Univesity Toonto, Ontaio,

More information

Liquidity and Insurance for the Unemployed

Liquidity and Insurance for the Unemployed Liquidity and Insuance fo the Unemployed Robet Shime Univesity of Chicago and NBER shime@uchicago.edu Iván Wening MIT, NBER and UTDT iwening@mit.edu Fist Daft: July 15, 2003 This Vesion: Septembe 22, 2005

More information

Comparing Availability of Various Rack Power Redundancy Configurations

Comparing Availability of Various Rack Power Redundancy Configurations Compaing Availability of Vaious Rack Powe Redundancy Configuations White Pape 48 Revision by Victo Avela > Executive summay Tansfe switches and dual-path powe distibution to IT equipment ae used to enhance

More information

Financing Terms in the EOQ Model

Financing Terms in the EOQ Model Financing Tems in the EOQ Model Habone W. Stuat, J. Columbia Business School New Yok, NY 1007 hws7@columbia.edu August 6, 004 1 Intoduction This note discusses two tems that ae often omitted fom the standad

More information

arxiv:1110.2612v1 [q-fin.st] 12 Oct 2011

arxiv:1110.2612v1 [q-fin.st] 12 Oct 2011 Maket inefficiency identified by both single and multiple cuency tends T.Toká 1, and D. Hováth 1, 1 Sos Reseach a.s., Stojáenská 3, 040 01 Košice, Slovak Republic Abstact axiv:1110.2612v1 [q-fin.st] 12

More information

Effect of Contention Window on the Performance of IEEE 802.11 WLANs

Effect of Contention Window on the Performance of IEEE 802.11 WLANs Effect of Contention Window on the Pefomance of IEEE 82.11 WLANs Yunli Chen and Dhama P. Agawal Cente fo Distibuted and Mobile Computing, Depatment of ECECS Univesity of Cincinnati, OH 45221-3 {ychen,

More information

Mean-Reverting-Ebit-Based Stock Option Evaluation: Theory and Practice

Mean-Reverting-Ebit-Based Stock Option Evaluation: Theory and Practice Jounal of Applied Finance & aning, vol. 3, no. 5, 03, 35-36 ISSN: 79-6580 pint vesion, 79-6599 online Scienpess Ltd, 03 Mean-Reveting-bit-ased Stoc Option valuation: Theoy and Pactice Hassan l Ibami Abstact

More information

Semipartial (Part) and Partial Correlation

Semipartial (Part) and Partial Correlation Semipatial (Pat) and Patial Coelation his discussion boows heavily fom Applied Multiple egession/coelation Analysis fo the Behavioal Sciences, by Jacob and Paticia Cohen (975 edition; thee is also an updated

More information

Chris J. Skinner The probability of identification: applying ideas from forensic statistics to disclosure risk assessment

Chris J. Skinner The probability of identification: applying ideas from forensic statistics to disclosure risk assessment Chis J. Skinne The pobability of identification: applying ideas fom foensic statistics to disclosue isk assessment Aticle (Accepted vesion) (Refeeed) Oiginal citation: Skinne, Chis J. (2007) The pobability

More information

How do investments in heat pumps affect household energy consumption?

How do investments in heat pumps affect household energy consumption? Discussion Papes Statistics Noway Reseach depatment No. 737 Apil 203 Bente Halvosen and Bodil Meethe Lasen How do investments in heat pumps affect household enegy consumption? Discussion Papes No. 737,

More information

Electricity transmission network optimization model of supply and demand the case in Taiwan electricity transmission system

Electricity transmission network optimization model of supply and demand the case in Taiwan electricity transmission system Electicity tansmission netwok optimization model of supply and demand the case in Taiwan electicity tansmission system Miao-Sheng Chen a Chien-Liang Wang b,c, Sheng-Chuan Wang d,e a Taichung Banch Gaduate

More information

Concept and Experiences on using a Wiki-based System for Software-related Seminar Papers

Concept and Experiences on using a Wiki-based System for Software-related Seminar Papers Concept and Expeiences on using a Wiki-based System fo Softwae-elated Semina Papes Dominik Fanke and Stefan Kowalewski RWTH Aachen Univesity, 52074 Aachen, Gemany, {fanke, kowalewski}@embedded.wth-aachen.de,

More information

Liquidity and Insurance for the Unemployed*

Liquidity and Insurance for the Unemployed* Fedeal Reseve Bank of Minneapolis Reseach Depatment Staff Repot 366 Decembe 2005 Liquidity and Insuance fo the Unemployed* Robet Shime Univesity of Chicago and National Bueau of Economic Reseach Iván Wening

More information

Agenda. Exchange Rates, Business Cycles, and Macroeconomic Policy in the Open Economy, Part 2. The supply of and demand for the dollar

Agenda. Exchange Rates, Business Cycles, and Macroeconomic Policy in the Open Economy, Part 2. The supply of and demand for the dollar Agenda Exchange Rates, Business Cycles, and Macoeconomic Policy in the Open Economy, Pat 2 How Exchange Rates ae Detemined (again) The IS-LM Model fo an Open Economy Macoeconomic Policy in an Open Economy

More information

Contingent capital with repeated interconversion between debt and equity

Contingent capital with repeated interconversion between debt and equity Contingent capital with epeated inteconvesion between debt and equity Zhaojun Yang 1, Zhiming Zhao School of Finance and Statistics, Hunan Univesity, Changsha 410079, China Abstact We develop a new type

More information

THE CARLO ALBERTO NOTEBOOKS

THE CARLO ALBERTO NOTEBOOKS THE CARLO ALBERTO NOTEBOOKS Mean-vaiance inefficiency of CRRA and CARA utility functions fo potfolio selection in defined contibution pension schemes Woking Pape No. 108 Mach 2009 Revised, Septembe 2009)

More information

Basic Financial Mathematics

Basic Financial Mathematics Financial Engineeing and Computations Basic Financial Mathematics Dai, Tian-Shy Outline Time Value of Money Annuities Amotization Yields Bonds Time Value of Money PV + n = FV (1 + FV: futue value = PV

More information

Open Economies. Chapter 32. A Macroeconomic Theory of the Open Economy. Basic Assumptions of a Macroeconomic Model of an Open Economy

Open Economies. Chapter 32. A Macroeconomic Theory of the Open Economy. Basic Assumptions of a Macroeconomic Model of an Open Economy Chapte 32. A Macoeconomic Theoy of the Open Economy Open Economies An open economy is one that inteacts feely with othe economies aound the wold. slide 0 slide 1 Key Macoeconomic Vaiables in an Open Economy

More information

Converting knowledge Into Practice

Converting knowledge Into Practice Conveting knowledge Into Pactice Boke Nightmae srs Tend Ride By Vladimi Ribakov Ceato of Pips Caie 20 of June 2010 2 0 1 0 C o p y i g h t s V l a d i m i R i b a k o v 1 Disclaime and Risk Wanings Tading

More information

Patent renewals and R&D incentives

Patent renewals and R&D incentives RAND Jounal of Economics Vol. 30, No., Summe 999 pp. 97 3 Patent enewals and R&D incentives Fancesca Conelli* and Mak Schankeman** In a model with moal hazad and asymmetic infomation, we show that it can

More information

Dual channel closed-loop supply chain coordination with a reward-driven remanufacturing policy

Dual channel closed-loop supply chain coordination with a reward-driven remanufacturing policy Intenational Jounal of Poduction Reseach ISSN: -753 Pint 1366-588X Online Jounal homepage: http://www.tandfonline.com/loi/tps Dual channel closed-loop supply chain coodination with a ewad-diven emanufactuing

More information

Continuous Compounding and Annualization

Continuous Compounding and Annualization Continuous Compounding and Annualization Philip A. Viton Januay 11, 2006 Contents 1 Intoduction 1 2 Continuous Compounding 2 3 Pesent Value with Continuous Compounding 4 4 Annualization 5 5 A Special Poblem

More information

Database Management Systems

Database Management Systems Contents Database Management Systems (COP 5725) D. Makus Schneide Depatment of Compute & Infomation Science & Engineeing (CISE) Database Systems Reseach & Development Cente Couse Syllabus 1 Sping 2012

More information

DNB WORKING PAPER. DNB Working Paper. A macroprudential approach to address liquidity risk with the Loan-to-deposit ratio. No. 372 / February 2013

DNB WORKING PAPER. DNB Working Paper. A macroprudential approach to address liquidity risk with the Loan-to-deposit ratio. No. 372 / February 2013 DNB Woking Pape No. 372 / Febuay 2013 Jan Willem van den End DNB WORKING PAPER A macopudential appoach to addess liquidity isk with the Loan-to-deposit atio A macopudential appoach to addess liquidity

More information

UNIT CIRCLE TRIGONOMETRY

UNIT CIRCLE TRIGONOMETRY UNIT CIRCLE TRIGONOMETRY The Unit Cicle is the cicle centeed at the oigin with adius unit (hence, the unit cicle. The equation of this cicle is + =. A diagam of the unit cicle is shown below: + = - - -

More information

Saving and Investing for Early Retirement: A Theoretical Analysis

Saving and Investing for Early Retirement: A Theoretical Analysis Saving and Investing fo Ealy Retiement: A Theoetical Analysis Emmanuel Fahi MIT Stavos Panageas Whaton Fist Vesion: Mach, 23 This Vesion: Januay, 25 E. Fahi: MIT Depatment of Economics, 5 Memoial Dive,

More information

AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM

AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM Main Golub Faculty of Electical Engineeing and Computing, Univesity of Zageb Depatment of Electonics, Micoelectonics,

More information

Spirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project

Spirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project Spiotechnics! Septembe 7, 2011 Amanda Zeingue, Michael Spannuth and Amanda Zeingue Dieential Geomety Poject 1 The Beginning The geneal consensus of ou goup began with one thought: Spiogaphs ae awesome.

More information

NBER WORKING PAPER SERIES FISCAL ZONING AND SALES TAXES: DO HIGHER SALES TAXES LEAD TO MORE RETAILING AND LESS MANUFACTURING?

NBER WORKING PAPER SERIES FISCAL ZONING AND SALES TAXES: DO HIGHER SALES TAXES LEAD TO MORE RETAILING AND LESS MANUFACTURING? NBER WORKING PAPER SERIES FISCAL ZONING AND SALES TAXES: DO HIGHER SALES TAXES LEAD TO MORE RETAILING AND LESS MANUFACTURING? Daia Bunes David Neumak Michelle J. White Woking Pape 16932 http://www.nbe.og/papes/w16932

More information

883 Brochure A5 GENE ss vernis.indd 1-2

883 Brochure A5 GENE ss vernis.indd 1-2 ess x a eu / u e a. p o.eu c e / :/ http EURAXESS Reseaches in Motion is the gateway to attactive eseach caees in Euope and to a pool of wold-class eseach talent. By suppoting the mobility of eseaches,

More information

Financial Derivatives for Computer Network Capacity Markets with Quality-of-Service Guarantees

Financial Derivatives for Computer Network Capacity Markets with Quality-of-Service Guarantees Financial Deivatives fo Compute Netwok Capacity Makets with Quality-of-Sevice Guaantees Pette Pettesson pp@kth.se Febuay 2003 SICS Technical Repot T2003:03 Keywods Netwoking and Intenet Achitectue. Abstact

More information

Data Center Demand Response: Avoiding the Coincident Peak via Workload Shifting and Local Generation

Data Center Demand Response: Avoiding the Coincident Peak via Workload Shifting and Local Generation (213) 1 28 Data Cente Demand Response: Avoiding the Coincident Peak via Wokload Shifting and Local Geneation Zhenhua Liu 1, Adam Wieman 1, Yuan Chen 2, Benjamin Razon 1, Niangjun Chen 1 1 Califonia Institute

More information

GESTÃO FINANCEIRA II PROBLEM SET 1 - SOLUTIONS

GESTÃO FINANCEIRA II PROBLEM SET 1 - SOLUTIONS GESTÃO FINANCEIRA II PROBLEM SET 1 - SOLUTIONS (FROM BERK AND DEMARZO S CORPORATE FINANCE ) LICENCIATURA UNDERGRADUATE COURSE 1 ST SEMESTER 2010-2011 Chapte 1 The Copoation 1-13. What is the diffeence

More information

College Enrollment, Dropouts and Option Value of Education

College Enrollment, Dropouts and Option Value of Education College Enollment, Dopouts and Option Value of Education Ozdagli, Ali Tachte, Nicholas y Febuay 5, 2008 Abstact Psychic costs ae the most impotant component of the papes that ae tying to match empiical

More information

Intertemporal Macroeconomics

Intertemporal Macroeconomics Intetempoal Macoeconomics Genot Doppelhofe* May 2009 Fothcoming in J. McCombie and N. Allington (eds.), Cambidge Essays in Applied Economics, Cambidge UP This chapte eviews models of intetempoal choice

More information

Do Bonds Span the Fixed Income Markets? Theory and Evidence for Unspanned Stochastic Volatility

Do Bonds Span the Fixed Income Markets? Theory and Evidence for Unspanned Stochastic Volatility Do Bonds Span the Fied Income Makets? Theoy and Evidence fo Unspanned Stochastic olatility PIERRE COLLIN-DUFRESNE and ROBERT S. GOLDSTEIN July, 00 ABSTRACT Most tem stuctue models assume bond makets ae

More information

30 H. N. CHIU 1. INTRODUCTION. Recherche opérationnelle/operations Research

30 H. N. CHIU 1. INTRODUCTION. Recherche opérationnelle/operations Research RAIRO Rech. Opé. (vol. 33, n 1, 1999, pp. 29-45) A GOOD APPROXIMATION OF THE INVENTORY LEVEL IN A(Q ) PERISHABLE INVENTORY SYSTEM (*) by Huan Neng CHIU ( 1 ) Communicated by Shunji OSAKI Abstact. This

More information

Review Graph based Online Store Review Spammer Detection

Review Graph based Online Store Review Spammer Detection Review Gaph based Online Stoe Review Spamme Detection Guan Wang, Sihong Xie, Bing Liu, Philip S. Yu Univesity of Illinois at Chicago Chicago, USA gwang26@uic.edu sxie6@uic.edu liub@uic.edu psyu@uic.edu

More information

SUGGESTED SOLUTIONS. 21404 Strategic Financial Management. CA Professional (Strategic Level II) Examination June 2014

SUGGESTED SOLUTIONS. 21404 Strategic Financial Management. CA Professional (Strategic Level II) Examination June 2014 SUGGESTED SOLUTIONS 21404 Stategic Financial Management CA Pofessional (Stategic Level II) Examination June 2014 THE INSTITUTE OF CHARTERED ACCOUNTANTS OF SRI LANKA All Rights Reseved Answe No. 01 (a)

More information

Money Market Funds Intermediation and Bank Instability

Money Market Funds Intermediation and Bank Instability Fedeal Reseve Bank of New Yok Staff Repots Money Maket Funds Intemediation and Bank Instability Maco Cipiani Antoine Matin Buno M. Paigi Staff Repot No. 599 Febuay 013 Revised May 013 This pape pesents

More information

Efficient Redundancy Techniques for Latency Reduction in Cloud Systems

Efficient Redundancy Techniques for Latency Reduction in Cloud Systems Efficient Redundancy Techniques fo Latency Reduction in Cloud Systems 1 Gaui Joshi, Emina Soljanin, and Gegoy Wonell Abstact In cloud computing systems, assigning a task to multiple seves and waiting fo

More information

An application of stochastic programming in solving capacity allocation and migration planning problem under uncertainty

An application of stochastic programming in solving capacity allocation and migration planning problem under uncertainty An application of stochastic pogamming in solving capacity allocation and migation planning poblem unde uncetainty Yin-Yann Chen * and Hsiao-Yao Fan Depatment of Industial Management, National Fomosa Univesity,

More information

An Efficient Group Key Agreement Protocol for Ad hoc Networks

An Efficient Group Key Agreement Protocol for Ad hoc Networks An Efficient Goup Key Ageement Potocol fo Ad hoc Netwoks Daniel Augot, Raghav haska, Valéie Issany and Daniele Sacchetti INRIA Rocquencout 78153 Le Chesnay Fance {Daniel.Augot, Raghav.haska, Valéie.Issany,

More information

An Epidemic Model of Mobile Phone Virus

An Epidemic Model of Mobile Phone Virus An Epidemic Model of Mobile Phone Vius Hui Zheng, Dong Li, Zhuo Gao 3 Netwok Reseach Cente, Tsinghua Univesity, P. R. China zh@tsinghua.edu.cn School of Compute Science and Technology, Huazhong Univesity

More information

Risk Sensitive Portfolio Management With Cox-Ingersoll-Ross Interest Rates: the HJB Equation

Risk Sensitive Portfolio Management With Cox-Ingersoll-Ross Interest Rates: the HJB Equation Risk Sensitive Potfolio Management With Cox-Ingesoll-Ross Inteest Rates: the HJB Equation Tomasz R. Bielecki Depatment of Mathematics, The Notheasten Illinois Univesity 55 Noth St. Louis Avenue, Chicago,

More information

Internet auctions are characterized by the separation of

Internet auctions are characterized by the separation of Shibo Li, Kannan Sinivasan, & Baohong Sun Intenet Auction Featues as Quality Signals Intenet auction companies have developed innovative tools that enable selles to eveal moe infomation about thei cedibility

More information

Performance Analysis of an Inverse Notch Filter and Its Application to F 0 Estimation

Performance Analysis of an Inverse Notch Filter and Its Application to F 0 Estimation Cicuits and Systems, 013, 4, 117-1 http://dx.doi.og/10.436/cs.013.41017 Published Online Januay 013 (http://www.scip.og/jounal/cs) Pefomance Analysis of an Invese Notch Filte and Its Application to F 0

More information

CHAPTER 10 Aggregate Demand I

CHAPTER 10 Aggregate Demand I CHAPTR 10 Aggegate Demand I Questions fo Review 1. The Keynesian coss tells us that fiscal policy has a multiplied effect on income. The eason is that accoding to the consumption function, highe income

More information

FI3300 Corporate Finance

FI3300 Corporate Finance Leaning Objectives FI00 Copoate Finance Sping Semeste 2010 D. Isabel Tkatch Assistant Pofesso of Finance Calculate the PV and FV in multi-peiod multi-cf time-value-of-money poblems: Geneal case Pepetuity

More information

The Personal-Tax Advantages of Equity

The Personal-Tax Advantages of Equity The Pesonal-Tax Advantages of Equity Richad C. Geen and Buton Hollifield Gaduate School of Industial Administation Canegie Mellon Univesity Decembe 23, 999 Discussions with Piee Collin Dufesne, Bob Dammon,

More information

Office of Family Assistance. Evaluation Resource Guide for Responsible Fatherhood Programs

Office of Family Assistance. Evaluation Resource Guide for Responsible Fatherhood Programs Office of Family Assistance Evaluation Resouce Guide fo Responsible Fathehood Pogams Contents Intoduction........................................................ 4 Backgound..........................................................

More information

Evaluating the impact of Blade Server and Virtualization Software Technologies on the RIT Datacenter

Evaluating the impact of Blade Server and Virtualization Software Technologies on the RIT Datacenter Evaluating the impact of and Vitualization Softwae Technologies on the RIT Datacente Chistophe M Butle Vitual Infastuctue Administato Rocheste Institute of Technology s Datacente Contact: chis.butle@it.edu

More information

A Note on Risky Bond Valuation

A Note on Risky Bond Valuation A Note on Risky Bond Valuation C. H. Hui Banking Poliy Depatment Hong Kong Monetay Authoity 0th Floo,, Gaden Road, Hong Kong Email: Cho-Hoi_Hui@hkma.gov.hk C. F. Lo Physis Depatment The Chinese Univesity

More information