Option pricing under stochastic volatility: the exponential Ornstein-Uhlenbeck model

Details Option pricing under stochastic volatility: the exponential Ornstein-Uhlenbeck model Option pricing under stochastic volatility: the exponential Ornstein-Uhlenbeck model

2008-04-16

arxiv.org/abs/0804.2589v2

J. Stat. Mech. (2008) P06010

Economy

Quantitative Finance

Pricing of Securities

26 pages, 6 colored figures

Scientific paper

10.1088/1742-5468/2008/06/P06010

We study the pricing problem for a European call option when the volatility of the underlying asset is random and follows the exponential Ornstein-Uhlenbeck model. The random diffusion model proposed is a two-dimensional market process that takes a log-Brownian motion to describe price dynamics and an Ornstein-Uhlenbeck subordinated process describing the randomness of the log-volatility. We derive an approximate option price that is valid when (i) the fluctuations of the volatility are larger than its normal level, (ii) the volatility presents a slow driving force toward its normal level and, finally, (iii) the market price of risk is a linear function of the log-volatility. We study the resulting European call price and its implied volatility for a range of parameters consistent with daily Dow Jones Index data.

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