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Partial derivative approach for option pricing in a simple stochastic volatility model

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  • M. Montero

Abstract

We study a market model in which the volatility of the stock may jump at a random time from a fixed value to another fixed value. This model has already been introduced in the literature. We present a new approach to the problem, based on partial differential equations, which gives a different perspective to the issue. Within our framework we can easily consider several forms for the market price of volatility risk, and interpret their financial meaning. We thus recover solutions previously mentioned in the literature as well as obtaining new ones. Copyright Springer-Verlag Berlin/Heidelberg 2004

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  • M. Montero, 2004. "Partial derivative approach for option pricing in a simple stochastic volatility model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 42(1), pages 141-153, November.
    • Handle: RePEc:spr:eurphb:v:42:y:2004:i:1:p:141-153
    DOI: 10.1140/epjb/e2004-00366-7
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    References listed on IDEAS

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    1. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    2. Stefano Herzel, 1998. "A Simple Model for Option Pricing with Jumping Stochastic Volatility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(04), pages 487-505.
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