Abstract
We study the pricing problem for a European call option when the volatility of theunderlying asset is random and follows the exponential Ornstein–Uhlenbeck model. Therandom diffusion model proposed is a two-dimensional market process that takes alog-Brownian motion to describe price dynamics and an Ornstein–Uhlenbeck subordinatedprocess describing the randomness of the log-volatility. We derive an approximate optionprice 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) themarket price of risk is a linear function of the log-volatility. We study the resultingEuropean call price and its implied volatility for a range of parameters consistent withdaily Dow Jones index data.
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