The Impact of Return Nonnormality on Exchange Options

24 Pages Posted: 28 Mar 2007

Multiple version iconThere are 2 versions of this paper

Date Written: March 2007


The Margrabe formula is used extensively by theorists and practitioners not only on exchange options, but also on executive compensation schemes, real options, weather and commodity derivatives, etc. However, the crucial assumption of bivariate normal distribution is not fully satisfied in almost all applications. We study the impact of nonnormality on exchange options by using a bivariate Gram-Charlier approximation. For near-the-money exchange options, skewness and coskewness induce price corrections which are linear in moneyness, while kurtosis and cokurtosis induce quadratic price corrections. The nonnormality helps to explain the implied correlation smile observed in practice.

Keywords: multivariate Gram-Charlier approximation, nonnormality, exchange option, Margrabe formula

JEL Classification: C14, G12, G13

Suggested Citation

Li, Minqiang, The Impact of Return Nonnormality on Exchange Options (March 2007). Available at SSRN: or

Minqiang Li (Contact Author)

Bloomberg LP ( email )

731 Lexington Avenue
New York, NY 10022
United States

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