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An Adaptive Method for Valuing an Option on Assets with Uncertainty in Volatility

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  • Sergei Fedotov
  • Stephanos Panayides

Abstract

We present an adaptive approach for valuing the European call option on assets with stochastic volatility. The essential feature of the method is a reduction of uncertainty in latent volatility due to a Bayesian learning procedure. Starting from a discrete-time stochastic volatility model, we derive a recurrence equation for the variance of the innovation term in latent volatility equation. This equation describes a reduction of uncertainty in volatility which is crucial for option pricing. To implement the idea of adaptive control, we use the risk-minimization procedure involving random volatility with uncertainty. By using stochastic dynamic programming and a Bayesian approach, we derive a recurrence equation for the risk inherent in writing the option. This equation allows us to find the fair price of the European call option. We illustrate numerically that the adaptive procedure leads to a decrease in option price.

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  • Sergei Fedotov & Stephanos Panayides, 2004. "An Adaptive Method for Valuing an Option on Assets with Uncertainty in Volatility," Papers cond-mat/0410294, arXiv.org, revised Jan 2006.
    • Handle: RePEc:arx:papers:cond-mat/0410294
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    References listed on IDEAS

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    1. Sergei Fedotov & Abby Tan, 2005. "Long Memory Stochastic Volatility In Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(03), pages 381-392.
    2. Sergei Fedotov & Sergei Mikhailov, 2001. "Option Pricing For Incomplete Markets Via Stochastic Optimization: Transaction Costs, Adaptive Control And Forecast," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 179-195.
    3. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
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