Option Pricing Under Stochastic Volatility: The Exponential Ornstein-Uhlenbeck Model

Journal of Statistical Mechanics, 2008

27 Pages Posted: 22 Jul 2008

See all articles by Josep Perelló

Josep Perelló

University of Barcelona - Department of Physics

Ronnie Sircar

Princeton University - Department of Operations Research and Financial Engineering

Jaume Masoliver

University of Barcelona - Department of Physics

Date Written: July, 18 2008

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.

Suggested Citation

Perello, Josep and Sircar, Ronnie and Masoliver, Jaume, Option Pricing Under Stochastic Volatility: The Exponential Ornstein-Uhlenbeck Model (July, 18 2008). Journal of Statistical Mechanics, 2008, Available at SSRN: https://ssrn.com/abstract=1162711

Josep Perello (Contact Author)

University of Barcelona - Department of Physics ( email )

Diagonal, 647
Barcelona, E-08028
Spain
+34 9 34021150 (Phone)
+34 34021149 (Fax)

Ronnie Sircar

Princeton University - Department of Operations Research and Financial Engineering ( email )

Princeton, NJ 08544
United States

Jaume Masoliver

University of Barcelona - Department of Physics ( email )

Barcelona, E-08028
Spain
00 34 3 402 11 59 (Phone)
00 34 3 402 11 49 (Fax)

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