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## Stochastic Risk Premiums, Stochastic Skewness (2008)

Venue: | in Currency Options, and Stochastic Discount Factors in International Economies,” |

Citations: | 35 - 5 self |

### Citations

5046 |
The pricing of options and corporate liabilities
- Black, Scholes
- 1973
(Show Context)
Citation Context ...ncy derivatives and the distributional properties of the exchange rate (Garman and Kohlhagen (1983), Dumas, Jennergren, and Naslund (1995), Bates (1996), and Bakshi and Chen (1997)). On the normative side, exchange rate models can be used to advocate monetary and fiscal policy rules and for prescribing central bank interventions. In this paper, we develop dynamic models of stochastic discount factors in international economies that are consistent with three distinct, yet interrelated, phenomena observed in currency markets. First, the risk-reversal quotes, as measured by the difference in the Black and Scholes (1973) implied volatilities between out-of-money call and put currency options, show substantial time-variation and often switch signs. This options market feature is symptomatic of stochastic skewness in the conditional currency return distribution. Second, the butterfly spread quotes, defined as the average out-of-money call and put implied volatilities minus the at-the-money counterpart, are uniformly positive across different option maturities and different underlying currencies, indicating fat-tailed risk-neutral currency return distributions. Third, extant empirical studies have documented str... |

3849 | A New Approach to Linear Filtering and Prediction Problems - Kalman - 1960 |

1975 | A theory of the term structure of interest rates - Cox, Ingersoll, et al. - 1985 |

1865 | Continuous Martingales and Brownian Motion - Revuz, Yor - 1999 |

1796 |
A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix
- Newey, West
- 1987
(Show Context)
Citation Context ...= BF[10] + SIV + RR[10]/2, and (v) IV p[10] = BF[10] + SIV−RR[10]/2. For the purpose of estimation, the volatility quotes are converted into out-of-the-money option prices. In this calculation, the maturity-matched domestic and foreign interest rates are constructed using LIBOR and swap rates from Bloomberg. Table I reports the mean, the standard deviation, and the t-statistics on the significance of the sample mean for risk-reversal and butterfly spread series, all in percentages of the corresponding atthe-money implied volatility (SIV). The t-statistics adjust serial dependence according to Newey and West (1987), with the number of lags optimally chosen according to Andrews (1991) based on an AR(1) specification. Average butterfly spreads are uniformly positive across all maturities, implying that out-of-themoney option implied volatilities on average are significantly higher than the at-the-money implied volatility. The lowest t-statistic is 10.98. Regardless of the currency pair, the butterfly spread quotes are strongly supportive of excess kurtosis in the risk-neutral return conditional distribution. The sign and magnitudes of risk-reversals are informative about the asymmetry of the conditional r... |

1184 |
Heteroskedasticity and Autocorrelation Consistent Covariance
- Andrews
- 1991
(Show Context)
Citation Context ...purpose of estimation, the volatility quotes are converted into out-of-the-money option prices. In this calculation, the maturity-matched domestic and foreign interest rates are constructed using LIBOR and swap rates from Bloomberg. Table I reports the mean, the standard deviation, and the t-statistics on the significance of the sample mean for risk-reversal and butterfly spread series, all in percentages of the corresponding atthe-money implied volatility (SIV). The t-statistics adjust serial dependence according to Newey and West (1987), with the number of lags optimally chosen according to Andrews (1991) based on an AR(1) specification. Average butterfly spreads are uniformly positive across all maturities, implying that out-of-themoney option implied volatilities on average are significantly higher than the at-the-money implied volatility. The lowest t-statistic is 10.98. Regardless of the currency pair, the butterfly spread quotes are strongly supportive of excess kurtosis in the risk-neutral return conditional distribution. The sign and magnitudes of risk-reversals are informative about the asymmetry of the conditional return distribution. Consider JPYUSD where the sample averages of the r... |

1124 | Asset Pricing - Cochrane - 2001 |

1083 |
Limit Theorems for Stochastic Processes
- Jacod, Shiryaev
- 1987
(Show Context)
Citation Context ...Duffie (1992)). We further assume that M ht itself is a semimartingale. The ratio of M h t at two time horizons will henceforth be referred as the stochastic discount factor, or the pricing kernel. We use Xh to summarize the aggregate uncertainty in economy h and represent the state-price deflator via the following multiplicative decomposition: M ht = exp ( − Z t 0 rhs ds ) E ( − Z t 0 γhs dX h s ) , h = 1,2, . . . ,N, (1) where rht denotes the instantaneous interest rate in economy h, γht denotes the market price of risk in economy h, and E (·) denotes the Doleans-Dade exponential operator (Jacod and Shiryaev (1987)), which can be interpreted as the Radon-Nikodym derivative that takes us from the statistical measure P to the economy-h risk-neutral measure Q h: dQ h dP ∣∣∣∣ t ≡ E ( − Z t 0 γhs dX h s ) . (2) In equation (1), both rt and γt can be stochastic. We can think of Xh as the return shocks to the aggregate wealth in the economy. The shocks Xh can be multi-dimensional, in which case γht dXht denotes an inner product. In representative agent economies, the stochastic discount factor can be interpreted as the ratio of the marginal utilities of consumption over two time horizons. No-arbitrage dictate... |

1000 | Option pricing when underlying stock returns are discontinuous
- Merton
- 1976
(Show Context)
Citation Context ...folio as the benchmark. Investors demand a higher risk premium when their wealth declines relative to the global portfolio. A negative shock to the country-specific risk components and a positive shock to the global risk factor both generate a negative impact on the relative wealth of the economy and is hence associated with a rise in risk premiums. 2 Finally, the estimation identifies a jump component in each economy that arrives an infinite number of times within any finite time intervals. This currency-options based finding contradicts with traditional compound Poisson jump specifications (Merton (1976)), but strengthens the findings from recent empirical works on equity index options (Carr, Geman, Madan, and Yor (2002), Carr and Wu (2003), Huang and Wu (2004), and Wu (2004)). More interestingly, our multi-economy estimation identifies a significant downward jump component but not an upward jump component in the stochastic discount factors, suggesting that although the economy can receive both negative and positive shocks, investors are only concerned with downside jumps as a potential source of risk. Upside jumps are not priced. Traditional literature often studies the behavior of risk prem... |

889 |
Martingale and arbitrage in multiperiod security markets
- Harrison, Kreps
- 1979
(Show Context)
Citation Context ...ructures are needed to internalize the evidence from currency returns and currency options? How do the different types of risks (say, global versus country-specific) vary over time and how are they priced differently? How are the risk premium dynamics related to observed stochastic skewness and kurtosis in the conditional currency return distribution? The thrust of this research is to answer these questions from both theoretical and empirical perspectives. In any economy precluding arbitrage, there always exists a stochastic discount factor that links future payoffs to their intrinsic values (Harrison and Kreps (1979)). In a complete market, this stochastic discount factor is unique, and the ratio of the stochastic discount factors in the two economies determines the exchange rate between them. In the setting of Lucas (1982)), for instance, the equilibrium home-currency price of a foreign currency is the ratio of the foreign-country marginal utility to the home-country counterpart. Therefore, exchange rates offer a direct unfiltered window to the stochastic 1 discount factors and the relative risk-taking behaviors of investors in international economies. In this paper, we propose to identify the dynamics o... |

665 |
Dynamic Asset Pricing Theory
- Duffie
- 1992
(Show Context)
Citation Context ... three currency pairs. Section V discusses the estimation results and Section VI concludes. I. Stochastic Discount Factors in International Economies and Exchange Rate Dynamics We describe a set of N economies by fixing a filtered complete probability space {Ω,F ,P ,(F t)0≤t≤T }, with some fixed horizon T . We assume no arbitrage in each economy. Therefore, for each economy, we can identify at least one strictly positive process, M ht (h = 1, . . . ,N), which we call the state-price deflator, such that the deflated gains process associated with any admissible trading strategy is a martingale (Duffie (1992)). We further assume that M ht itself is a semimartingale. The ratio of M h t at two time horizons will henceforth be referred as the stochastic discount factor, or the pricing kernel. We use Xh to summarize the aggregate uncertainty in economy h and represent the state-price deflator via the following multiplicative decomposition: M ht = exp ( − Z t 0 rhs ds ) E ( − Z t 0 γhs dX h s ) , h = 1,2, . . . ,N, (1) where rht denotes the instantaneous interest rate in economy h, γht denotes the market price of risk in economy h, and E (·) denotes the Doleans-Dade exponential operator (Jacod and Shi... |

547 | Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche mark options
- Bates
- 1996
(Show Context)
Citation Context ...ween exchange rates and fundamentals. See, for example, Dumas (1992), Mark (1995), Evans and Lyons (2002), Engel and West (2004), and Pavlova and Rigobon (2004), for recent contributions. Starting with Lucas (1982), exchange rates constitute crucial building blocks for testable multi-period equilibrium models of the international economy. More generally, the endogenously derived models help us appreciate the links between the price of forward-looking currency derivatives and the distributional properties of the exchange rate (Garman and Kohlhagen (1983), Dumas, Jennergren, and Naslund (1995), Bates (1996), and Bakshi and Chen (1997)). On the normative side, exchange rate models can be used to advocate monetary and fiscal policy rules and for prescribing central bank interventions. In this paper, we develop dynamic models of stochastic discount factors in international economies that are consistent with three distinct, yet interrelated, phenomena observed in currency markets. First, the risk-reversal quotes, as measured by the difference in the Black and Scholes (1973) implied volatilities between out-of-money call and put currency options, show substantial time-variation and often switch signs... |

504 | Yield Spreads and Interest Rate Movements: A Bird’s Eye View." - Campbell, Shiller - 1991 |

484 | A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables - Ang, Piazzesi - 2003 |

443 | Forward and spot exchange rates’,
- Fama
- 1984
(Show Context)
Citation Context ...call and put currency options, show substantial time-variation and often switch signs. This options market feature is symptomatic of stochastic skewness in the conditional currency return distribution. Second, the butterfly spread quotes, defined as the average out-of-money call and put implied volatilities minus the at-the-money counterpart, are uniformly positive across different option maturities and different underlying currencies, indicating fat-tailed risk-neutral currency return distributions. Third, extant empirical studies have documented strongly time-varying currency risk premiums (Fama (1984), Bekaert and Hodrick (1992), Dumas and Solnik (1995), Engel (1996), Bansal (1997), Backus, Foresi, and Telmer (2001), and Brennan and Xia (2005)). What are the sources of stochastic risk premiums in international economies? What minimal theoretical structures are needed to internalize the evidence from currency returns and currency options? How do the different types of risks (say, global versus country-specific) vary over time and how are they priced differently? How are the risk premium dynamics related to observed stochastic skewness and kurtosis in the conditional currency return distribu... |

420 | The determinants of credit spread changes. - Collin-Dufresne, Goldstein, et al. - 2001 |

418 | The jump-risk premia implicit in options: Evidence from an integrated time-series study
- Pan
- 2002
(Show Context)
Citation Context ...ific risk factors. Our framework allows the risk premiums on the two types of risks to follow separate dynamics. Within this general setup, we analyze what minimal structures are necessary to capture the stylized evidence in currency returns and currency options. We then derive tractable forms for option pricing and for the characteristic function of the currency returns. Section III describes the currency and currency options data set for dollar-yen, dollar-pound, and pound-yen exchange rates. Section IV presents a joint estimation 1Prominent examples include Jackwerth and Rubinstein (1996), Pan (2002), Engle and Rosenberg (2002), Bakshi, Kapadia, and Madan (2003), Bakshi and Kapadia (2003), Broadie, Chernov, and Johannes (2004), Eraker (2004), and Bliss and Panigirtzoglou (2004). Recently, Driessen and Maenhout (2004) investigate the nature of jump and volatility risks using equity index options from three countries. 3 approach using the time-series of currency returns and currency option prices on the three currency pairs. Section V discusses the estimation results and Section VI concludes. I. Stochastic Discount Factors in International Economies and Exchange Rate Dynamics We describe a ... |

409 | Option valuation using the Fast Fourier Transform
- Carr, Madan
- 1999
(Show Context)
Citation Context ...ons: φQs = e iu(rh−r f )tEN g ( e−ψ g[u]Πt ) EN h ( e−ψ h[u]Λht ) EN f ( e−ψ f [u]Λ ft ) = eiu(r h−r f )te−bg(t)z0−cg(t)−bh(t)y h 0−ch(t)−b f (t)y f 0−c f (t), (28) where ( z0,yh0,y f 0 ) are the time-0 realized levels of the three risk premium rates (Z,Y h,Y f ) and the coefficients [b(t) ,c(t)] on each risk premium rate take the same functional forms: bc(t) = 2ψc(1−e−ηct) 2ηc−(ηc−κN c) ( 1−e−ηht ) , cc(t) = κθσ2v [ 2ln ( 1− ηc−κN c2ηc ( 1− e−ηct )) +(ηc −κN c)t ] , (29) with ηc = √( κN c )2 +2σ2vψc and for c = g,h, f , respectively. Given the generalized Fourier transform, we can now follow Carr and Madan (1999) and use fast Fourier inversion to obtain option prices. D. Characteristic Function under Measure P For estimation, we also need to derive the log likelihood function for the currency returns. We first derive the characteristic function of the log currency returns under the statistical measure P and then obtain the density of the currency return via fast Fourier inversion. Given the P -dynamics for the currency return in (13), we derive its characteristic function as, φPs ≡ EP ( eius h f t ) , = EP ( e iu ( (rh−r f )t+ ((√ ξh− √ ξ f ) W gΠt + 1 2 Πt(ξ h−ξ f ) ))) ×EP ( e iu (( W h Λht +Jh Λht ... |

400 | The forward discount anomaly and the risk premium: a survey of recent evidence,
- ENGEL
- 1996
(Show Context)
Citation Context ... often switch signs. This options market feature is symptomatic of stochastic skewness in the conditional currency return distribution. Second, the butterfly spread quotes, defined as the average out-of-money call and put implied volatilities minus the at-the-money counterpart, are uniformly positive across different option maturities and different underlying currencies, indicating fat-tailed risk-neutral currency return distributions. Third, extant empirical studies have documented strongly time-varying currency risk premiums (Fama (1984), Bekaert and Hodrick (1992), Dumas and Solnik (1995), Engel (1996), Bansal (1997), Backus, Foresi, and Telmer (2001), and Brennan and Xia (2005)). What are the sources of stochastic risk premiums in international economies? What minimal theoretical structures are needed to internalize the evidence from currency returns and currency options? How do the different types of risks (say, global versus country-specific) vary over time and how are they priced differently? How are the risk premium dynamics related to observed stochastic skewness and kurtosis in the conditional currency return distribution? The thrust of this research is to answer these questions from... |

393 | The fine structure of asset returns: An empirical investigation - Carr, Geman, et al. |

367 |
Interest Rates and Currency Prices in a Two-Country World”,
- Lucas
- 1982
(Show Context)
Citation Context ..., G13, F31, C52. KEY WORDS: Stochastic discount factors; international economy; stochastic risk premium; stochastic skewness; currency options; foreign exchange rate dynamics; time-changed Levy processes; unscented Kalman filter. Theoretical models of foreign exchange dynamics have positive and normative implications. Positively, the models assist us in understanding the possible departures between exchange rates and fundamentals. See, for example, Dumas (1992), Mark (1995), Evans and Lyons (2002), Engel and West (2004), and Pavlova and Rigobon (2004), for recent contributions. Starting with Lucas (1982), exchange rates constitute crucial building blocks for testable multi-period equilibrium models of the international economy. More generally, the endogenously derived models help us appreciate the links between the price of forward-looking currency derivatives and the distributional properties of the exchange rate (Garman and Kohlhagen (1983), Dumas, Jennergren, and Naslund (1995), Bates (1996), and Bakshi and Chen (1997)). On the normative side, exchange rate models can be used to advocate monetary and fiscal policy rules and for prescribing central bank interventions. In this paper, we deve... |

335 | The Information in Long-Maturity Forward Rates. - Fama, Bliss - 1987 |

329 |
Exchange rates and fundamentals: Evidence on long-horizon predictability.
- Mark
- 1995
(Show Context)
Citation Context ...s an infinite number of times within any finite interval, but only downside jumps appear to be priced. JEL CLASSIFICATION CODES: G12, G13, F31, C52. KEY WORDS: Stochastic discount factors; international economy; stochastic risk premium; stochastic skewness; currency options; foreign exchange rate dynamics; time-changed Levy processes; unscented Kalman filter. Theoretical models of foreign exchange dynamics have positive and normative implications. Positively, the models assist us in understanding the possible departures between exchange rates and fundamentals. See, for example, Dumas (1992), Mark (1995), Evans and Lyons (2002), Engel and West (2004), and Pavlova and Rigobon (2004), for recent contributions. Starting with Lucas (1982), exchange rates constitute crucial building blocks for testable multi-period equilibrium models of the international economy. More generally, the endogenously derived models help us appreciate the links between the price of forward-looking currency derivatives and the distributional properties of the exchange rate (Garman and Kohlhagen (1983), Dumas, Jennergren, and Naslund (1995), Bates (1996), and Bakshi and Chen (1997)). On the normative side, exchange rate m... |

309 | Post-'87 Crash Fears in S&P 500 Futures Options - Bates - 1998 |

302 | Order flow and exchange rate dynamics
- Lyons, 2002a
(Show Context)
Citation Context ... number of times within any finite interval, but only downside jumps appear to be priced. JEL CLASSIFICATION CODES: G12, G13, F31, C52. KEY WORDS: Stochastic discount factors; international economy; stochastic risk premium; stochastic skewness; currency options; foreign exchange rate dynamics; time-changed Levy processes; unscented Kalman filter. Theoretical models of foreign exchange dynamics have positive and normative implications. Positively, the models assist us in understanding the possible departures between exchange rates and fundamentals. See, for example, Dumas (1992), Mark (1995), Evans and Lyons (2002), Engel and West (2004), and Pavlova and Rigobon (2004), for recent contributions. Starting with Lucas (1982), exchange rates constitute crucial building blocks for testable multi-period equilibrium models of the international economy. More generally, the endogenously derived models help us appreciate the links between the price of forward-looking currency derivatives and the distributional properties of the exchange rate (Garman and Kohlhagen (1983), Dumas, Jennergren, and Naslund (1995), Bates (1996), and Bakshi and Chen (1997)). On the normative side, exchange rate models can be used to adv... |

281 | Value versus growth: The international evidence - Fama, French - 1998 |

278 | Production-based asset pricing and the link between stock returns and economic fluctuations. - Cochrane - 1991 |

274 | Micro Effects of Macro Announcements: Real-time price discovery in Foreign Exchange - Andersen, Bollerslev, et al. - 2003 |

266 | What moves the stock and bond markets? A variance decomposition for long−term asset returns, - Campbell, Ammer - 1993 |

256 | Exchange Rates and Fundamentals, - Engel, West - 2006 |

240 |
Dynamics Equilibrium and the Real Exchange Rate in a Spatially Separated World
- Dumas
(Show Context)
Citation Context ...nt that arrives an infinite number of times within any finite interval, but only downside jumps appear to be priced. JEL CLASSIFICATION CODES: G12, G13, F31, C52. KEY WORDS: Stochastic discount factors; international economy; stochastic risk premium; stochastic skewness; currency options; foreign exchange rate dynamics; time-changed Levy processes; unscented Kalman filter. Theoretical models of foreign exchange dynamics have positive and normative implications. Positively, the models assist us in understanding the possible departures between exchange rates and fundamentals. See, for example, Dumas (1992), Mark (1995), Evans and Lyons (2002), Engel and West (2004), and Pavlova and Rigobon (2004), for recent contributions. Starting with Lucas (1982), exchange rates constitute crucial building blocks for testable multi-period equilibrium models of the international economy. More generally, the endogenously derived models help us appreciate the links between the price of forward-looking currency derivatives and the distributional properties of the exchange rate (Garman and Kohlhagen (1983), Dumas, Jennergren, and Naslund (1995), Bates (1996), and Bakshi and Chen (1997)). On the normative side, ex... |

235 | Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices.
- Eraker
- 2004
(Show Context)
Citation Context ...e analyze what minimal structures are necessary to capture the stylized evidence in currency returns and currency options. We then derive tractable forms for option pricing and for the characteristic function of the currency returns. Section III describes the currency and currency options data set for dollar-yen, dollar-pound, and pound-yen exchange rates. Section IV presents a joint estimation 1Prominent examples include Jackwerth and Rubinstein (1996), Pan (2002), Engle and Rosenberg (2002), Bakshi, Kapadia, and Madan (2003), Bakshi and Kapadia (2003), Broadie, Chernov, and Johannes (2004), Eraker (2004), and Bliss and Panigirtzoglou (2004). Recently, Driessen and Maenhout (2004) investigate the nature of jump and volatility risks using equity index options from three countries. 3 approach using the time-series of currency returns and currency option prices on the three currency pairs. Section V discusses the estimation results and Section VI concludes. I. Stochastic Discount Factors in International Economies and Exchange Rate Dynamics We describe a set of N economies by fixing a filtered complete probability space {Ω,F ,P ,(F t)0≤t≤T }, with some fixed horizon T . We assume no arbitrage in ... |

228 | Price Formation and Liquidity in the US Treasury Market: The Response to Public Information.” - Fleming, Remolona - 1999 |

189 | Time-Changed Levy Processes and Option Pricing,”
- Carr, Wu
- 2004
(Show Context)
Citation Context ...iterature in using equity index options in a single country to study the stand-alone behavior of the stochastic discount factor in that economy, we exploit the link in (3) and use currency returns and currency options to study the joint dynamics of stochastic discount factors in international economies. II. Model with Stochastic Risk Premium and Stochastic Skewness We propose a class of models for the stochastic discount factors that are flexible enough to generate stochastic risk premiums and stochastic skewness in currency returns. Formally, using the language of time-changed Levy process (Carr and Wu (2004b)), we specify the stochastic discount factor for country h as, M ht = exp ( −rht ) exp ( −W gΠht − 1 2 Πht ) exp ( − ( W hΛht + JhΛht ) − ( 1 2 + kJh [−1] ) Λht ) , (4) which decomposes the stochastic discount factor into three orthogonal components. The first component captures the contribution from interest rates. Since a dominant proportion of exchange rate movements is independent of interest rate movements, we assume deterministic interest rates for simplicity and use rh to denote the continuously compounded spot interest rate of the relevant maturity. 5 The second component incorporate... |

173 | Meteor Showers or Heat Waves? Heteroskedastic Intraday Volatility in the Foreign Exchange Market, - Engle, Ito, et al. - 1990 |

162 |
Characterizing Predictable Components in Excess Returns on Equity and Foreign Exchange Markets,
- Bekaert, Hodrick
- 1992
(Show Context)
Citation Context ...currency options, show substantial time-variation and often switch signs. This options market feature is symptomatic of stochastic skewness in the conditional currency return distribution. Second, the butterfly spread quotes, defined as the average out-of-money call and put implied volatilities minus the at-the-money counterpart, are uniformly positive across different option maturities and different underlying currencies, indicating fat-tailed risk-neutral currency return distributions. Third, extant empirical studies have documented strongly time-varying currency risk premiums (Fama (1984), Bekaert and Hodrick (1992), Dumas and Solnik (1995), Engel (1996), Bansal (1997), Backus, Foresi, and Telmer (2001), and Brennan and Xia (2005)). What are the sources of stochastic risk premiums in international economies? What minimal theoretical structures are needed to internalize the evidence from currency returns and currency options? How do the different types of risks (say, global versus country-specific) vary over time and how are they priced differently? How are the risk premium dynamics related to observed stochastic skewness and kurtosis in the conditional currency return distribution? The thrust of this res... |

159 | The dynamics of stochastic volatility: Evidence from underlying and options markets. - Jones - 2003 |

155 |
The world price of foreign exchange risk
- Dumas, Solnik
- 1995
(Show Context)
Citation Context ...antial time-variation and often switch signs. This options market feature is symptomatic of stochastic skewness in the conditional currency return distribution. Second, the butterfly spread quotes, defined as the average out-of-money call and put implied volatilities minus the at-the-money counterpart, are uniformly positive across different option maturities and different underlying currencies, indicating fat-tailed risk-neutral currency return distributions. Third, extant empirical studies have documented strongly time-varying currency risk premiums (Fama (1984), Bekaert and Hodrick (1992), Dumas and Solnik (1995), Engel (1996), Bansal (1997), Backus, Foresi, and Telmer (2001), and Brennan and Xia (2005)). What are the sources of stochastic risk premiums in international economies? What minimal theoretical structures are needed to internalize the evidence from currency returns and currency options? How do the different types of risks (say, global versus country-specific) vary over time and how are they priced differently? How are the risk premium dynamics related to observed stochastic skewness and kurtosis in the conditional currency return distribution? The thrust of this research is to answer these ... |

146 |
Foreign currency option values
- Garman, Kohlhagen
- 1983
(Show Context)
Citation Context ...y, the models assist us in understanding the possible departures between exchange rates and fundamentals. See, for example, Dumas (1992), Mark (1995), Evans and Lyons (2002), Engel and West (2004), and Pavlova and Rigobon (2004), for recent contributions. Starting with Lucas (1982), exchange rates constitute crucial building blocks for testable multi-period equilibrium models of the international economy. More generally, the endogenously derived models help us appreciate the links between the price of forward-looking currency derivatives and the distributional properties of the exchange rate (Garman and Kohlhagen (1983), Dumas, Jennergren, and Naslund (1995), Bates (1996), and Bakshi and Chen (1997)). On the normative side, exchange rate models can be used to advocate monetary and fiscal policy rules and for prescribing central bank interventions. In this paper, we develop dynamic models of stochastic discount factors in international economies that are consistent with three distinct, yet interrelated, phenomena observed in currency markets. First, the risk-reversal quotes, as measured by the difference in the Black and Scholes (1973) implied volatilities between out-of-money call and put currency options, s... |

143 | Empirical pricing kernels.
- Rosenberg, Engle
- 2002
(Show Context)
Citation Context ...ctors. Our framework allows the risk premiums on the two types of risks to follow separate dynamics. Within this general setup, we analyze what minimal structures are necessary to capture the stylized evidence in currency returns and currency options. We then derive tractable forms for option pricing and for the characteristic function of the currency returns. Section III describes the currency and currency options data set for dollar-yen, dollar-pound, and pound-yen exchange rates. Section IV presents a joint estimation 1Prominent examples include Jackwerth and Rubinstein (1996), Pan (2002), Engle and Rosenberg (2002), Bakshi, Kapadia, and Madan (2003), Bakshi and Kapadia (2003), Broadie, Chernov, and Johannes (2004), Eraker (2004), and Bliss and Panigirtzoglou (2004). Recently, Driessen and Maenhout (2004) investigate the nature of jump and volatility risks using equity index options from three countries. 3 approach using the time-series of currency returns and currency option prices on the three currency pairs. Section V discusses the estimation results and Section VI concludes. I. Stochastic Discount Factors in International Economies and Exchange Rate Dynamics We describe a set of N economies by fixing... |

141 | A Theory of the Nominal Term Structure of Interest Rates - Constantinides - 1992 |

138 | Stock Return Characteristics, Skew Laws, - Bakshi, Kapadia, et al. - 2003 |

137 | Bond Yields and the Federal Reserve”, - Piazzesi - 2005 |

122 | Delta-Hedged Gains and the Negative Market Volatility Risk Premium,”
- Bakshi, Kapadia
- 2003
(Show Context)
Citation Context ...of risks to follow separate dynamics. Within this general setup, we analyze what minimal structures are necessary to capture the stylized evidence in currency returns and currency options. We then derive tractable forms for option pricing and for the characteristic function of the currency returns. Section III describes the currency and currency options data set for dollar-yen, dollar-pound, and pound-yen exchange rates. Section IV presents a joint estimation 1Prominent examples include Jackwerth and Rubinstein (1996), Pan (2002), Engle and Rosenberg (2002), Bakshi, Kapadia, and Madan (2003), Bakshi and Kapadia (2003), Broadie, Chernov, and Johannes (2004), Eraker (2004), and Bliss and Panigirtzoglou (2004). Recently, Driessen and Maenhout (2004) investigate the nature of jump and volatility risks using equity index options from three countries. 3 approach using the time-series of currency returns and currency option prices on the three currency pairs. Section V discusses the estimation results and Section VI concludes. I. Stochastic Discount Factors in International Economies and Exchange Rate Dynamics We describe a set of N economies by fixing a filtered complete probability space {Ω,F ,P ,(F t)0≤t≤T }, ... |

116 | The finite moment log stable process and option pricing.
- Carr, Wu
- 2003
(Show Context)
Citation Context ... shock to the country-specific risk components and a positive shock to the global risk factor both generate a negative impact on the relative wealth of the economy and is hence associated with a rise in risk premiums. 2 Finally, the estimation identifies a jump component in each economy that arrives an infinite number of times within any finite time intervals. This currency-options based finding contradicts with traditional compound Poisson jump specifications (Merton (1976)), but strengthens the findings from recent empirical works on equity index options (Carr, Geman, Madan, and Yor (2002), Carr and Wu (2003), Huang and Wu (2004), and Wu (2004)). More interestingly, our multi-economy estimation identifies a significant downward jump component but not an upward jump component in the stochastic discount factors, suggesting that although the economy can receive both negative and positive shocks, investors are only concerned with downside jumps as a potential source of risk. Upside jumps are not priced. Traditional literature often studies the behavior of risk premiums through various types of expectation hypothesis regressions. Under the null hypothesis of zero or constant risk premium, the slope coe... |

114 | The effects of macroeconomic news on high frequency exchange rate behavior - Almeida, Goodhart, et al. - 1998 |

108 | Economic news and bond prices: Evidence from the US treasury market - Balduzzi, Elton, et al. - 2001 |

107 | Bond Risk Premia." - Cochrane, Piazzesi - 2005 |

104 | Affine Term Structure Models and the Forward Premium Anomaly, - Backus, Foresi, et al. - 2001 |

103 | Option-implied risk aversion estimates.
- Bliss, Panigirtzoglou
- 2004
(Show Context)
Citation Context ...mal structures are necessary to capture the stylized evidence in currency returns and currency options. We then derive tractable forms for option pricing and for the characteristic function of the currency returns. Section III describes the currency and currency options data set for dollar-yen, dollar-pound, and pound-yen exchange rates. Section IV presents a joint estimation 1Prominent examples include Jackwerth and Rubinstein (1996), Pan (2002), Engle and Rosenberg (2002), Bakshi, Kapadia, and Madan (2003), Bakshi and Kapadia (2003), Broadie, Chernov, and Johannes (2004), Eraker (2004), and Bliss and Panigirtzoglou (2004). Recently, Driessen and Maenhout (2004) investigate the nature of jump and volatility risks using equity index options from three countries. 3 approach using the time-series of currency returns and currency option prices on the three currency pairs. Section V discusses the estimation results and Section VI concludes. I. Stochastic Discount Factors in International Economies and Exchange Rate Dynamics We describe a set of N economies by fixing a filtered complete probability space {Ω,F ,P ,(F t)0≤t≤T }, with some fixed horizon T . We assume no arbitrage in each economy. Therefore, for each eco... |

85 | International Risk sharing is Better Than You Think, or Exchange Rates are Too Smooth,” GSB, University of Chicago, working paper (available on John Cochrane’s website). - Brandt, Cochrane, et al. - 2004 |

81 | Exchange rates, equity prices, and capital flows - Hau, Rey - 2005 |

80 | Do bonds span the fixed income markets? Theory and evidence for unspanned stochastic volatility, - Collin-Dufresne, Goldstein - 2002 |

77 | Simulated likelihood estimation of diffusions with an application to exchange rate dynamics in incomplete markets - Brandt, Clara, et al. - 2001 |

77 | Asset Pricing Under the Quadratic Class”, - Leippold, Wu - 2002 |

72 | Realtime price discovery in stock, bond, and foreign exchange markets. - Andersen, Bollerslev, et al. - 2007 |

67 | The potential approach to the term-structure of interest rates and foreign exchange rates,” - Rogers - 1997 |

67 | Specification Analysis of Option Pricing Models Based on Time-Changed Levy Processes,”
- Huang, Wu
- 2004
(Show Context)
Citation Context ...y-specific risk components and a positive shock to the global risk factor both generate a negative impact on the relative wealth of the economy and is hence associated with a rise in risk premiums. 2 Finally, the estimation identifies a jump component in each economy that arrives an infinite number of times within any finite time intervals. This currency-options based finding contradicts with traditional compound Poisson jump specifications (Merton (1976)), but strengthens the findings from recent empirical works on equity index options (Carr, Geman, Madan, and Yor (2002), Carr and Wu (2003), Huang and Wu (2004), and Wu (2004)). More interestingly, our multi-economy estimation identifies a significant downward jump component but not an upward jump component in the stochastic discount factors, suggesting that although the economy can receive both negative and positive shocks, investors are only concerned with downside jumps as a potential source of risk. Upside jumps are not priced. Traditional literature often studies the behavior of risk premiums through various types of expectation hypothesis regressions. Under the null hypothesis of zero or constant risk premium, the slope coefficients of these re... |

64 | Stochastic skew in currency options - Carr, Wu |

55 | An exploration of the forward premium puzzle in currency markets,
- Bansal
- 1997
(Show Context)
Citation Context ...signs. This options market feature is symptomatic of stochastic skewness in the conditional currency return distribution. Second, the butterfly spread quotes, defined as the average out-of-money call and put implied volatilities minus the at-the-money counterpart, are uniformly positive across different option maturities and different underlying currencies, indicating fat-tailed risk-neutral currency return distributions. Third, extant empirical studies have documented strongly time-varying currency risk premiums (Fama (1984), Bekaert and Hodrick (1992), Dumas and Solnik (1995), Engel (1996), Bansal (1997), Backus, Foresi, and Telmer (2001), and Brennan and Xia (2005)). What are the sources of stochastic risk premiums in international economies? What minimal theoretical structures are needed to internalize the evidence from currency returns and currency options? How do the different types of risks (say, global versus country-specific) vary over time and how are they priced differently? How are the risk premium dynamics related to observed stochastic skewness and kurtosis in the conditional currency return distribution? The thrust of this research is to answer these questions from both theoretic... |

55 | Recovering probability distributions from contemporaneous security prices,
- Jackerth, Rubinstein
- 1996
(Show Context)
Citation Context ...obal risk factor and country-specific risk factors. Our framework allows the risk premiums on the two types of risks to follow separate dynamics. Within this general setup, we analyze what minimal structures are necessary to capture the stylized evidence in currency returns and currency options. We then derive tractable forms for option pricing and for the characteristic function of the currency returns. Section III describes the currency and currency options data set for dollar-yen, dollar-pound, and pound-yen exchange rates. Section IV presents a joint estimation 1Prominent examples include Jackwerth and Rubinstein (1996), Pan (2002), Engle and Rosenberg (2002), Bakshi, Kapadia, and Madan (2003), Bakshi and Kapadia (2003), Broadie, Chernov, and Johannes (2004), Eraker (2004), and Bliss and Panigirtzoglou (2004). Recently, Driessen and Maenhout (2004) investigate the nature of jump and volatility risks using equity index options from three countries. 3 approach using the time-series of currency returns and currency option prices on the three currency pairs. Section V discusses the estimation results and Section VI concludes. I. Stochastic Discount Factors in International Economies and Exchange Rate Dynamics We... |

54 | Pricing and Hedging Long-Term Options. - Bakshi, Cao, et al. - 2000 |

44 | Time-varying expected returns in international bond markets. - Ilmanen - 1995 |

43 | Asset prices and exchange rates’,
- Pavlova, Rigobon
- 2003
(Show Context)
Citation Context ...ly downside jumps appear to be priced. JEL CLASSIFICATION CODES: G12, G13, F31, C52. KEY WORDS: Stochastic discount factors; international economy; stochastic risk premium; stochastic skewness; currency options; foreign exchange rate dynamics; time-changed Levy processes; unscented Kalman filter. Theoretical models of foreign exchange dynamics have positive and normative implications. Positively, the models assist us in understanding the possible departures between exchange rates and fundamentals. See, for example, Dumas (1992), Mark (1995), Evans and Lyons (2002), Engel and West (2004), and Pavlova and Rigobon (2004), for recent contributions. Starting with Lucas (1982), exchange rates constitute crucial building blocks for testable multi-period equilibrium models of the international economy. More generally, the endogenously derived models help us appreciate the links between the price of forward-looking currency derivatives and the distributional properties of the exchange rate (Garman and Kohlhagen (1983), Dumas, Jennergren, and Naslund (1995), Bates (1996), and Bakshi and Chen (1997)). On the normative side, exchange rate models can be used to advocate monetary and fiscal policy rules and for prescrib... |

41 |
Equilibrium Valuation of Foreign Exchange Claims”,
- Bakshi, Chen
- 1997
(Show Context)
Citation Context ...s and fundamentals. See, for example, Dumas (1992), Mark (1995), Evans and Lyons (2002), Engel and West (2004), and Pavlova and Rigobon (2004), for recent contributions. Starting with Lucas (1982), exchange rates constitute crucial building blocks for testable multi-period equilibrium models of the international economy. More generally, the endogenously derived models help us appreciate the links between the price of forward-looking currency derivatives and the distributional properties of the exchange rate (Garman and Kohlhagen (1983), Dumas, Jennergren, and Naslund (1995), Bates (1996), and Bakshi and Chen (1997)). On the normative side, exchange rate models can be used to advocate monetary and fiscal policy rules and for prescribing central bank interventions. In this paper, we develop dynamic models of stochastic discount factors in international economies that are consistent with three distinct, yet interrelated, phenomena observed in currency markets. First, the risk-reversal quotes, as measured by the difference in the Black and Scholes (1973) implied volatilities between out-of-money call and put currency options, show substantial time-variation and often switch signs. This options market featur... |

36 | The unscented Kalman filter, - Wan, Merwe - 2001 |

34 | Informed and Strategic Order Flow in the Bond Markets. - Pasquariello, Vega - 2007 |

24 | Are the Fama and French Factors Global or CountrySpecific? Arizona - Griffin - 2001 |

22 | International capital markets and foreign exchange risk, Working paper,
- Brennan, Xia
- 2005
(Show Context)
Citation Context ...tochastic skewness in the conditional currency return distribution. Second, the butterfly spread quotes, defined as the average out-of-money call and put implied volatilities minus the at-the-money counterpart, are uniformly positive across different option maturities and different underlying currencies, indicating fat-tailed risk-neutral currency return distributions. Third, extant empirical studies have documented strongly time-varying currency risk premiums (Fama (1984), Bekaert and Hodrick (1992), Dumas and Solnik (1995), Engel (1996), Bansal (1997), Backus, Foresi, and Telmer (2001), and Brennan and Xia (2005)). What are the sources of stochastic risk premiums in international economies? What minimal theoretical structures are needed to internalize the evidence from currency returns and currency options? How do the different types of risks (say, global versus country-specific) vary over time and how are they priced differently? How are the risk premium dynamics related to observed stochastic skewness and kurtosis in the conditional currency return distribution? The thrust of this research is to answer these questions from both theoretical and empirical perspectives. In any economy precluding arbitr... |

19 | The effect of macroeconomic news on beliefs and preferences: evidence from the options market. - Beber, Brandt - 2006 |

19 | Regime-Switching in Foreign Exchange Rates: Evidence From Currency Option Prices,” - Bollen, Gray, et al. - 2000 |

18 | Currency prices, the nominal exchange rate, and security prices in a two country dynamic monetary equilibrium,
- Basak, Gallmeyer
- 1999
(Show Context)
Citation Context ...s dX h s ) . (2) In equation (1), both rt and γt can be stochastic. We can think of Xh as the return shocks to the aggregate wealth in the economy. The shocks Xh can be multi-dimensional, in which case γht dXht denotes an inner product. In representative agent economies, the stochastic discount factor can be interpreted as the ratio of the marginal utilities of consumption over two time horizons. No-arbitrage dictates that the ratio of the stochastic discount factors between two economies determines the exchange rate dynamics between them (Lucas (1982), Dumas (1992), Bakshi and Chen 4 (1997), Basak and Gallmeyer (1999), and Backus, Foresi, and Telmer (2001)). Let Sh f denote the currency-h price of currency f , with h being the home economy, we have Sh ft Sh f0 = M ft /M f 0 M ht /M h 0 , h, f = 1,2, . . . ,N. (3) Equation (3) defines the formal link between the stochastic discount factors in any two economies and the exchange rate movements between them. This link tells us that the time-series of currency returns and currency option prices contain important information about the dynamics of aggregate uncertainties affecting the two economies and how the underlying risks are priced. In complete markets, the... |

16 | Resolving macroeconomic uncertainty in stock and bond markets. Review of Finance 13 - Beber, Brandt |

16 | Dampened power law: Reconciling the tail behavior of financial security returns.
- Wu
- 2006
(Show Context)
Citation Context ... risk components and a positive shock to the global risk factor both generate a negative impact on the relative wealth of the economy and is hence associated with a rise in risk premiums. 2 Finally, the estimation identifies a jump component in each economy that arrives an infinite number of times within any finite time intervals. This currency-options based finding contradicts with traditional compound Poisson jump specifications (Merton (1976)), but strengthens the findings from recent empirical works on equity index options (Carr, Geman, Madan, and Yor (2002), Carr and Wu (2003), Huang and Wu (2004), and Wu (2004)). More interestingly, our multi-economy estimation identifies a significant downward jump component but not an upward jump component in the stochastic discount factors, suggesting that although the economy can receive both negative and positive shocks, investors are only concerned with downside jumps as a potential source of risk. Upside jumps are not priced. Traditional literature often studies the behavior of risk premiums through various types of expectation hypothesis regressions. Under the null hypothesis of zero or constant risk premium, the slope coefficients of these re... |

13 | Asset Prices and Exchange Rates, Review of Financial Studies, - Pavlova, Rigobon - 2004 |

11 | Crash-o-phobia: A Domestic Fear or a Worldwide Phenonemon - Foresi, S, et al. - 2005 |

10 |
The world price of jump and volatility risk, Working paper,
- Driessen, Maenhout
- 2004
(Show Context)
Citation Context ... stylized evidence in currency returns and currency options. We then derive tractable forms for option pricing and for the characteristic function of the currency returns. Section III describes the currency and currency options data set for dollar-yen, dollar-pound, and pound-yen exchange rates. Section IV presents a joint estimation 1Prominent examples include Jackwerth and Rubinstein (1996), Pan (2002), Engle and Rosenberg (2002), Bakshi, Kapadia, and Madan (2003), Bakshi and Kapadia (2003), Broadie, Chernov, and Johannes (2004), Eraker (2004), and Bliss and Panigirtzoglou (2004). Recently, Driessen and Maenhout (2004) investigate the nature of jump and volatility risks using equity index options from three countries. 3 approach using the time-series of currency returns and currency option prices on the three currency pairs. Section V discusses the estimation results and Section VI concludes. I. Stochastic Discount Factors in International Economies and Exchange Rate Dynamics We describe a set of N economies by fixing a filtered complete probability space {Ω,F ,P ,(F t)0≤t≤T }, with some fixed horizon T . We assume no arbitrage in each economy. Therefore, for each economy, we can identify at least one stric... |

10 | International capital asset pricing: evidence from options - Mo, Wu - 2007 |

8 | Specification and risk premiums: The information in S&P 500 futures options, Working paper, - Broadie, Chernov, et al. - 2004 |

7 | Evidence of risk premiums in foreign currency futures markets - McCurdy, Morgan - 1992 |

5 | Realignment Risk and Currency Option Pricing in Target Zones. - Dumas, Jennergren, et al. - 1995 |

4 | Information content of cross-sectional option prices: A comparison of alternative currency option pricing models on the Japanese yen - Dupoyet |

3 | Jmps and stochastic volatility: exchange rate processes implicit in deutshce mark options - unknown authors - 1996 |

3 |
Stochastic skew in currency options, Working paper, Bloomberg and Baruch College.
- Carr, Wu
- 2004
(Show Context)
Citation Context ...iterature in using equity index options in a single country to study the stand-alone behavior of the stochastic discount factor in that economy, we exploit the link in (3) and use currency returns and currency options to study the joint dynamics of stochastic discount factors in international economies. II. Model with Stochastic Risk Premium and Stochastic Skewness We propose a class of models for the stochastic discount factors that are flexible enough to generate stochastic risk premiums and stochastic skewness in currency returns. Formally, using the language of time-changed Levy process (Carr and Wu (2004b)), we specify the stochastic discount factor for country h as, M ht = exp ( −rht ) exp ( −W gΠht − 1 2 Πht ) exp ( − ( W hΛht + JhΛht ) − ( 1 2 + kJh [−1] ) Λht ) , (4) which decomposes the stochastic discount factor into three orthogonal components. The first component captures the contribution from interest rates. Since a dominant proportion of exchange rate movements is independent of interest rate movements, we assume deterministic interest rates for simplicity and use rh to denote the continuously compounded spot interest rate of the relevant maturity. 5 The second component incorporate... |

1 | A nonlinear factor analysis of S&P 500 index option returns - unknown authors - 2006 |

1 | The dynamics and the term structure of risk premia in foreign exchange markets. Working paper - unknown authors - 1995 |

1 |
Exchange ratex and fundamentals,
- Engel, West
- 2004
(Show Context)
Citation Context ...any finite interval, but only downside jumps appear to be priced. JEL CLASSIFICATION CODES: G12, G13, F31, C52. KEY WORDS: Stochastic discount factors; international economy; stochastic risk premium; stochastic skewness; currency options; foreign exchange rate dynamics; time-changed Levy processes; unscented Kalman filter. Theoretical models of foreign exchange dynamics have positive and normative implications. Positively, the models assist us in understanding the possible departures between exchange rates and fundamentals. See, for example, Dumas (1992), Mark (1995), Evans and Lyons (2002), Engel and West (2004), and Pavlova and Rigobon (2004), for recent contributions. Starting with Lucas (1982), exchange rates constitute crucial building blocks for testable multi-period equilibrium models of the international economy. More generally, the endogenously derived models help us appreciate the links between the price of forward-looking currency derivatives and the distributional properties of the exchange rate (Garman and Kohlhagen (1983), Dumas, Jennergren, and Naslund (1995), Bates (1996), and Bakshi and Chen (1997)). On the normative side, exchange rate models can be used to advocate monetary and fisc... |