Empirical Performance of Alternative Option Pricing Models

Singular risk-neutral valuation equations

“…Bates [8] introduced jumps of the asset price into the Heston model with the goal of explaining the volatility smile. The model was tested on real data in Bakshi et al [4], but did not perform well enough, and the authors called for a model with jumps in the volatility as well. An affine model with jumps in the volatility was proposed by Duffie et al [13].…”

American option pricing under stochastic volatility: an empirical evaluation

“…In a comprehensive study based on S&P 500 data, (Bakshi et al 1997) compare a number of popular alternative models and conclude that overall, stochastic volatility models appear to provide the main source of option pricing improvement when considering various combinations of stochastic volatility with stochastic interest rates and stochastic jumps.…”

“…For example, Bakshi et al (1997) use cross-sectional information contained in option prices with different maturities and strike prices resulting in implied volatilities in order to infer estimates for the structural parameters of the stochastic volatility model. On the other hand, it appears that these implied structural parameters deviate substantially from their time-series counterparts (e.g., (Bakshi et al 1997) use implied volatilities to estimate the correlation coefficient of the asset return innovation with that of its stochastic volatility as 0.76 whereas their estimate based on the underlying asset time-series is 0.23.)…”

“…For example, Bakshi et al (1997) use cross-sectional information contained in option prices with different maturities and strike prices resulting in implied volatilities in order to infer estimates for the structural parameters of the stochastic volatility model. On the other hand, it appears that these implied structural parameters deviate substantially from their time-series counterparts (e.g., (Bakshi et al 1997) use implied volatilities to estimate the correlation coefficient of the asset return innovation with that of its stochastic volatility as 0.76 whereas their estimate based on the underlying asset time-series is 0.23.) As an alternative, (Zhang and Shu 2003) proposed to use a two-step procedure to estimate first, via the indirect inference method of Gourieroux et al (1993), structural parameters for the underlying asset, followed by a second set of additional parameters needed for option pricing via a market price calibration based on least-squares.…”

Volatility estimation from observed option prices

“…Empirical work suggests that a more realistic model would include both stochastic volatility and a jump component. For example, Bates (1996) and Bakshi et al (1997) have analysed such models and their results indicate that models with both stochastic volatility and jump diffusion provide a better fit to the empirical observations than data based on deterministic volatility. Andersen and Andersen (1999) note that models with both stochastic volatility and jump diffusion are not easy to work with in practical applications.…”