The impact of return nonnormality on exchange options

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Abstract

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 a bivariate normal distribution is not fully satisfied in almost all applications. The impact of nonnormality on exchange options is studied by using a bivariate Gram–Charlier approximation. For near-the-money exchange options, skewness and coskewness induce price corrections that are linear in moneyness, whereas kurtosis and cokurtosis induce quadratic price corrections. The nonnormality helps to explain the implied correlation smile observed in practice. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:845–870, 2008

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