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CALL OPTION VALUATION FOR DISCRETE NORMAL MIXTURES

168 citations0/0 files storedThe Journal of Financial Research

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Stochastic processes and financial applications Financial Markets and Investment Strategies Financial Risk and Volatility Modeling

Abstract

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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References

1973The Pricing of Options and Corporate Liabilities 1976Option pricing when underlying stock returns are discontinuous 1987The Pricing of Options on Assets with Stochastic Volatilities 1976The valuation of options for alternative stochastic processes 1979The valuation of compound options 1975Fact and Fantasy in the Use of Options 1985Nonparametric Tests of Alternative Option Pricing Models Using All Reported Trades and Quotes on the 30 Most Active CBOE Option Classes from August 23, 1976 Through August 31, 1978 1982Approximate option valuation for arbitrary stochastic processes

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