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Stochastic Volatility Option Pricing


  • Ball, Clifford A.
  • Roma, Antonio


This paper examines alternative methods for pricing options when the underlying security volatility is stochastic. We show that when there is no correlation between innovations in security price and volatility, the characteristic function of the average variance of the price process plays a pivotal role. It may be used to simplify Fourier option pricing techniques and to implement simple power series methods. We compare these methods for the alternative mean-reverting stochastic volatility models introduced by Stein and Stein (1991) and Heston (1993). We also examine the biases in the Black-Scholes model that are eliminated by allowing for stochastic volatility, and we correct some errors in the Stein and Stein (1991) analysis of this issue.

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  • Ball, Clifford A. & Roma, Antonio, 1994. "Stochastic Volatility Option Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(04), pages 589-607, December.
  • Handle: RePEc:cup:jfinqa:v:29:y:1994:i:04:p:589-607_00

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    References listed on IDEAS

    1. Marcet, Albert & Sargent, Thomas J, 1989. "Convergence of Least-Squares Learning in Environments with Hidden State Variables and Private Information," Journal of Political Economy, University of Chicago Press, vol. 97(6), pages 1306-1322, December.
    2. Holden, Craig W & Subrahmanyam, Avanidhar, 1992. " Long-Lived Private Information and Imperfect Competition," Journal of Finance, American Finance Association, vol. 47(1), pages 247-270, March.
    3. Foster, F Douglas & Viswanathan, S, 1993. "The Effect of Public Information and Competition on Trading Volume and Price Volatility," Review of Financial Studies, Society for Financial Studies, vol. 6(1), pages 23-56.
    4. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    5. Back, Kerry, 1992. "Insider Trading in Continuous Time," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 387-409.
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