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

Josep Perelló (), Ronnie Sircar and Jaume Masoliver

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Abstract: 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.

Date: 2008-04, Revised 2008-05
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Citations: View citations in EconPapers (14)

Published in J. Stat. Mech. (2008) P06010

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:0804.2589

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