CALL OPTION VALUATION FOR DISCRETE NORMAL MIXTURES

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Abstract
In this study a mixture call option pricing model is derived to examine the impact of non‐normal underlying returns densities. Observed fat‐tailed and skewed distributions are assumed to be the result of independent Gaussian processes with nonstationary parameters, modeled by discrete k‐component independent normal mixtures. The mixture model provides an exact solution with intuitive appeal using weighted sums of Black‐Scholes (B‐S) solutions. Simulating returns densities representative of equity securities, significant mispricing by B‐S is found in low‐priced at‐ and out‐of‐the‐money near‐term options. The lower the variance and the higher the leptokurtosis and positive skewness of the underlying returns, the more pronounced is this mispricing. Values of in‐the‐money options and options with several weeks or more to expiration are closely approximated by B‐S.

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