Pricing the European call option in the model with stochastic volatility driven by Ornstein–Uhlenbeck process. Exact formulas

Kuchuk-Iatsenko, Sergii; Mishura, Yuliya

doi:10.15559/15-VMSTA36CNF

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

Sergii Kuchuk-Iatsenko Yuliya Mishura

https://doi.org/10.15559/15-VMSTA36CNF

Pub. online: 25 September 2015 Type: Research Article

Open 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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Keywords

Financial markets stochastic volatility Ornstein–Uhlenbeck process option pricing

MSC2010

91B24 91B25 91G20

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