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

Josep Perelló, Ronnie Sircar, Jaume Masoliver

Research output: Contribution to journalArticle

23 Scopus citations

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.

Original languageEnglish (US)
Article numberP06010
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2008
Issue number6
DOIs
StatePublished - Jun 1 2008

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Financial instruments and regulation
  • Models of financial markets
  • Risk measure and management
  • Stochastic processes (experiment)

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