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85
Bayesian Analysis of Stochastic Volatility Models
, 1994
"... this article is to develop new methods for inference and prediction in a simple class of stochastic volatility models in which logarithm of conditional volatility follows an autoregressive (AR) times series model. Unlike the autoregressive conditional heteroscedasticity (ARCH) and gener alized ARCH ..."
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Cited by 371 (21 self)
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this article is to develop new methods for inference and prediction in a simple class of stochastic volatility models in which logarithm of conditional volatility follows an autoregressive (AR) times series model. Unlike the autoregressive conditional heteroscedasticity (ARCH) and gener alized ARCH (GARCH) models [see Bollerslev, Chou, and Kroner (1992) for a survey of ARCH modeling], both the mean and logvolatility equations have separate error terms. The ease of evaluating the ARCH likelihood function and the ability of the ARCH specification to accommodate the timevarying volatility found in many economic time series has fostered an explosion in the use of ARCH models. On the other hand, the likelihood function for stochastic volatility models is difficult to evaluate, and hence these models have had limited empirical application
The Variance Gamma Process and Option Pricing.
 European Finance Review
, 1998
"... : A three parameter stochastic process, termed the variance gamma process, that generalizes Brownian motion is developed as a model for the dynamics of log stock prices. The process is obtained by evaluating Brownian motion with drift at a random time given by a gamma process. The two additional par ..."
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Cited by 197 (26 self)
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: A three parameter stochastic process, termed the variance gamma process, that generalizes Brownian motion is developed as a model for the dynamics of log stock prices. The process is obtained by evaluating Brownian motion with drift at a random time given by a gamma process. The two additional parameters are the drift of the Brownian motion and the volatility of the time change. These additional parameters provide control over the skewness and kurtosis of the return distribution. Closed forms are obtained for the return density and the prices of European options. The statistical and risk neutral densities are estimated for data on the S&P500 Index and the prices of options on this Index. It is observed that the statistical density is symmetric with some kurtosis, while the risk neutral density is negatively skewed with a larger kurtosis. The additional parameters also correct for pricing biases of the Black Scholes model that is a parametric special case of the option pricing model d...
Do stock prices and volatility jump? Reconciling evidence from spot and option prices
, 2001
"... This paper studies the empirical performance of jumpdiffusion models that allow for stochastic volatility and correlated jumps affecting both prices and volatility. The results show that the models in question provide reasonable fit to both option prices and returns data in the insample estimation ..."
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Cited by 97 (2 self)
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This paper studies the empirical performance of jumpdiffusion models that allow for stochastic volatility and correlated jumps affecting both prices and volatility. The results show that the models in question provide reasonable fit to both option prices and returns data in the insample estimation period. This contrasts previous findings where stochastic volatility paths are found to be too smooth relative to the option implied dynamics. While the models perform well during the high volatility estimation period, they tend to overprice long dated contracts outofsample. This evidence points towards a too simplistic specification of the mean dynamics of volatility.
Numerical Valuation of High Dimensional Multivariate American Securities
, 1994
"... We consider the problem of pricing an American contingent claim whose payoff depends on several sources of uncertainty. Using classical assumptions from the Arbitrage Pricing Theory, the theoretical price can be computed as the maximum over all possible early exercise strategies of the discounted ..."
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Cited by 95 (0 self)
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We consider the problem of pricing an American contingent claim whose payoff depends on several sources of uncertainty. Using classical assumptions from the Arbitrage Pricing Theory, the theoretical price can be computed as the maximum over all possible early exercise strategies of the discounted expected cash flows under the modified riskneutral information process. Several efficient numerical techniques exist for pricing American securities depending on one or few (up to 3) risk sources. They are either latticebased techniques or finite difference approximations of the BlackScholes diffusion equation. However, these methods cannot be used for highdimensional problems, since their memory requirement is exponential in the
Of Smiles and Smirks: A TermStructure Perspective
 JOURNAL OF FINANCIAL AND QUANTITATIVE ANALYSIS
, 1998
"... An extensive empirical literature in finance has documented not only the presence of anamolies in the BlackScholes model, but also the "termstructures" of these anamolies (for instance, the behavior of the volatility smile or of unconditional returns at different maturities). Theoretical efforts i ..."
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Cited by 79 (3 self)
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An extensive empirical literature in finance has documented not only the presence of anamolies in the BlackScholes model, but also the "termstructures" of these anamolies (for instance, the behavior of the volatility smile or of unconditional returns at different maturities). Theoretical efforts in the literature at addressing these anamolies have largely focussed on two extensions of the BlackScholes model: introducing jumps into the return process, and allowing volatility to be stochastic. This paper employs commonlyused versions of these two classes of models to examine the extent to which the models are theoretically capable of resolving the observed anamolies. We find that each model exhibits some "termstructure" patterns that are fundamentally inconsistent with those observed in the data. As a consequence, neither class of models constitutes an adequate explanation of the empirical evidence, although stochastic volatility models fare better than jumps in this regard.
A Study towards a Unified Approach to the Joint Estimation of Objective and Risk Neutral Measures for the Purpose of Options Valuation
, 1999
"... The purpose of this paper is to bridge two strands of the literature, one pertaining to the objectiveorphysical measure used to model the underlying asset and the other pertaining to the riskneutral measure used to price derivatives. We propose a generic procedure using simultaneously the fundame ..."
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Cited by 74 (4 self)
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The purpose of this paper is to bridge two strands of the literature, one pertaining to the objectiveorphysical measure used to model the underlying asset and the other pertaining to the riskneutral measure used to price derivatives. We propose a generic procedure using simultaneously the fundamental price S t and a set of option contracts ### I it # i=1;m # where m # 1 and # I it is the BlackScholes implied volatility.We use Heston's #1993# model as an example and appraise univariate and multivariate estimation of the model in terms of pricing and hedging performance. Our results, based on the S&P 500 index contract, show that the univariate approach only involving options by and large dominates. Abyproduct of this #nding is that we uncover a remarkably simple volatility extraction #lter based on a polynomial lag structure of implied volatilities. The bivariate approachinvolving both the fundamental and an option appears useful when the information from the cash market ...
On the relationship between the conditional mean and volatility of stock returns: A latent VAR approach
, 2002
"... ..."
Maximum likelihood estimation for stochastic volatility models
 JOURNAL OF FINANCIAL ECONOMICS
, 2007
"... We develop and implement a method for maximum likelihood estimation in closedform of stochastic volatility models. Using Monte Carlo simulations, we compare a full likelihood procedure, where an option price is inverted into the unobservable volatility state, to an approximate likelihood procedure ..."
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Cited by 48 (3 self)
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We develop and implement a method for maximum likelihood estimation in closedform of stochastic volatility models. Using Monte Carlo simulations, we compare a full likelihood procedure, where an option price is inverted into the unobservable volatility state, to an approximate likelihood procedure where the volatility state is replaced by proxies based on the implied volatility of a shortdated atthemoney option. The approximation results in a small loss of accuracy relative to the standard errors due to sampling noise. We apply this method to market prices of index options for several stochastic volatility models, and compare the characteristics of the estimated models. The evidence for a general CEV model, which nests both the affine Heston model and a GARCH model, suggests that the elasticity of variance of volatility lies between that assumed by the two nested models.