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A closedform solution for options with stochastic volatility with applications to bond and currency options
 Review of Financial Studies
, 1993
"... I use a new technique to derive a closedform solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond option ..."
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Cited by 704 (4 self)
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I use a new technique to derive a closedform solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond options and foreign currency options. Simulations show that correlation between volatility and the spot asset’s price is important for explaining return skewness and strikeprice biases in the BlackScholes (1973) model. The solution technique is based on characteristic functions and can be applied to other problems. Many plaudits have been aptly used to describe Black and Scholes ’ (1973) contribution to option pricing theory. Despite subsequent development of option theory, the original BlackScholes formula for a European call option remains the most successful and widely used application. This formula is particularly useful because it relates the distribution of spot returns I thank Hans Knoch for computational assistance. I am grateful for the suggestions of Hyeng Keun (the referee) and for comments by participants
A ClosedForm GARCH Option Pricing Model
, 1999
"... This paper develops a closedform option pricing formula for a spot asset whose variance follows a GARCH process. The model allows for correlation between returns of the spot asset and variance and also admits multiple lags in the dynamics of the GARCH process. The singlefactor (onelag) version of ..."
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Cited by 33 (2 self)
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This paper develops a closedform option pricing formula for a spot asset whose variance follows a GARCH process. The model allows for correlation between returns of the spot asset and variance and also admits multiple lags in the dynamics of the GARCH process. The singlefactor (onelag) version of this model contains Heston’s (1993) stochastic volatility model as a diffusion limit and therefore unifies the discretetime GARCH and continuoustime stochastic volatility literature of option pricing. The new model provides the first readily computed option formula for a random volatility model in which current volatility is easily estimated from historical asset prices observed at discrete intervals. Empirical analysis on S&P 500 index options shows the singlefactor version of the GARCH model to be a substantial improvement over the BlackScholes (1973) model. The GARCH model continues to substantially outperform the BlackScholes model even when the BlackScholes model is updated every period and uses implied volatilities from option prices, while the parameters of the GARCH model are held constant and volatility is filtered from the history of asset prices. The improvement is due largely to the ability of the GARCH model to describe the correlation of volatility with spot returns. This allows the GARCH model to capture strikeprice biases in the BlackScholes model that give rise to the skew in implied volatilities in the index options market.
The Risk Premium of Volatility Implicit in Currency Options
 Journal of Business and Economic Statistics
, 1998
"... This paper provides an empirical investigation of the risk neutral variance process and the market price of variance risk implied in the foreign currency options market. There are three principal contributions. First, the parameters of Heston's (1993) meanreverting square root stochastic volatili ..."
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Cited by 17 (1 self)
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This paper provides an empirical investigation of the risk neutral variance process and the market price of variance risk implied in the foreign currency options market. There are three principal contributions. First, the parameters of Heston's (1993) meanreverting square root stochastic volatility model are estimated using dollar/mark option prices from 1987 to 1992. Second, it is shown that these implied parameters can be combined with historical moments of the dollar/mark exchange rate to deduce an estimate of the market price of variance risk. These estimates are found to be nonzero, time varying, and of sufficient magnitude to imply that the compensation for variance risk is a significant component of the risk premia in the currency market. Finally, the outofsample test suggests that the historical variance and the Hull and White implied variance contain no additional information than those imbedded in the Heston implied variance. KEY WORDS: Market price of variance ...
The Predictive Power of Implied Stochastic Variance from Currency Options
, 1996
"... This paper investigates the predictive power of implied variances extracted from currency options. Under the assumption that the options market is informationally efficient and that options are priced according to the model of Hull and White (1987), implied variances are estimated from transaction p ..."
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Cited by 6 (2 self)
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This paper investigates the predictive power of implied variances extracted from currency options. Under the assumption that the options market is informationally efficient and that options are priced according to the model of Hull and White (1987), implied variances are estimated from transaction prices of currency options traded on PHLX. If implied variances are efficient, variance forecasts from time series models should have no additional predictive power in predicting subsequently realized market variances. The insample tests suggest that implied variances contain incremental information in the GARCH models for conditional variance. In contrast with recent findings on stock and stock index options, the insample and outofsample tests indicate that the implied variance is a superior, but biased forecast of future variance; and that the variance forecasts from GARCH and MA(60) models do not contain significant incremental information in predicting future variance. Key Words: Impl...
Financial regimeswitching vector autoregression
, 2005
"... A regime switching vector autoregression (RSVAR) is defined as a vector autoregression in which the parameters of the vector autoregression are functions of a set of discrete indices, which consitute the regimes. This process can be applied to interest rate models, default models, and other finan ..."
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A regime switching vector autoregression (RSVAR) is defined as a vector autoregression in which the parameters of the vector autoregression are functions of a set of discrete indices, which consitute the regimes. This process can be applied to interest rate models, default models, and other financial models. This can be done in the "objective" or Pmeasure or the riskneutral or Qmeasure of finance or other measures. One set of applications include calculation of prices, cashflows, capital, reserves, defaults, and other variables. Another set includes transactions using these including purchases and sales, producing and/or sending reports, advisory services, portfolio strategy, etc.