Skew Brownian Motion and Pricing European Options

T. R. A. Corns and S. E. Satchell

The European Journal of Finance, 2007, vol. 13, issue 6, 523-544

Abstract: The volatility smile and systematic mispricing of the Black-Scholes option pricing model are the typical motivation for examining stochastic processes other than geometric Brownian motion to describe the underlying stock price. In this paper a new stochastic process is presented, which is a special case of the skew-Brownian motion of Ito and McKean. The process in question is the sum of a standard Brownian motion and an independent reflecting Brownian motion that is similar in construction to the stochastic representation of a skew-normal random variable. This stochastic process is taken in its exponential form to price European options. The derived option price nests the Black-Scholes equation as a special case and is flexible enough to accommodate stochastic volatility as well as stochastic skewness.

Keywords: Options; skew Brownian motion; skew-normal; skew-symmetric; hedging; non-Gaussian (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (20)

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DOI: 10.1080/13518470701201488

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