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Derivation of Kurtosis and Option Pricing Formulas for Popular Volatility Models with Applications in Finance |
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| Authors: | A Thavaneswaran S Peiris Jagbir Singh |
| Institution: | 1. Department of Statistics , The University of Manitoba , Winnipeg, Manitoba, Canada thavane@cc.umanitoba.ca;3. School of Mathematics and Statistics, The University of Sydney , Sydney, Australia;4. Department of Statistics , Fox School of Business, Temple University , Philadelphia, Pennsylvania, USA |
| Abstract: | This article discusses some topics relevant to financial modeling. The kurtosis of a distribution plays an important role in controlling tail-behavior and is used in edgeworth expansion of the call prices. We present derivations of the kurtosis for a number of popular volatility models useful in financial applications, including the class of random coefficient GARCH models. Option pricing formulas for various classes of volatility models are also derived and a simple proof of the option pricing formula under the Black–Scholes model is given. |
| Keywords: | Kurtosis Option pricing Random coefficients Sign-switching Stochastic volatility |