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Modern Stochastics: Theory and Applications


Pricing the European call option in the model with stochastic volatility driven by Ornstein–Uhlenbeck process. Exact formulas
Volume 2, Issue 3 (2015): PRESTO-2015, pp. 233–249
Pub. online: 25 September 2015      Type: Research Article      Open accessOpen Access
Received
29 July 2015
Revised
13 September 2015
Accepted
14 September 2015
Published
25 September 2015

Abstract

We consider the Black–Scholes model of financial market modified to capture the stochastic nature of volatility observed at real financial markets. For volatility driven by the Ornstein–Uhlenbeck process, we establish the existence of equivalent martingale measure in the market model. The option is priced with respect to the minimal martingale measure for the case of uncorrelated processes of volatility and asset price, and an analytic expression for the price of European call option is derived. We use the inverse Fourier transform of a characteristic function and the Gaussian property of the Ornstein–Uhlenbeck process.

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Copyright
© 2015 The Author(s). Published by VTeX
Open access article under the CC BY license.

Keywords
Financial markets stochastic volatility Ornstein–Uhlenbeck process option pricing

MSC2010
91B24 91B25 91G20

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