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.Comment: 26 pages, 6 colored figure
