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Variance Gamma Process and the Correction of Volatility Skew in Stock Option Pricing

Xi Wei

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Abstract

This paper introduces a modification of Black-Scholes Option Pricing Model to correct the volatility skew of Black-Scholes Option Pricing Model on stock option. The modification is replacing the Brownian motion process in the Black-Scholes Option Pricing Model by the variance gamma process. An empirical test for the corresponding option pricing performance basing the close form solution is gived.

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What this paper is about

This paper introduces a modification of Black-Scholes Option Pricing Model to correct the volatility skew of Black-Scholes Option Pricing Model on stock option. The modification is replacing the Brownian motion process in the Black-Scholes Option Pricing Model by the variance gamma process. An empirical test for the corresponding option pricing performance basing the close form solution is gived.

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Available abstract

This paper introduces a modification of Black-Scholes Option Pricing Model to correct the volatility skew of Black-Scholes Option Pricing Model on stock option. The modification is replacing the Brownian motion process in the Black-Scholes Option Pricing Model by the variance gamma process. An empirical test for the corresponding option pricing performance basing the close form solution is gived.

Key concepts: Valuation of options, Black–Scholes model, Skew, Econometrics, Finite difference methods for option pricing, Volatility (finance), Volatility smile, Implied volatility

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