Variance Gamma process in the option pricing model

Jakub Drahokoupil

No 3.002, FFA Working Papers from Prague University of Economics and Business

Abstract: Aim of this paper is to use Variance Gamma process in the option pricing model and compare it with the well-known and the most widely used option pricing model, the Black-Scholes model. The Variance Gamma model is, in contrast to the one-parameter Black-Scholes model, a three-parameter model. In addition, these two parameters, which are included in the Variance Gamma model, serve to model the skewness and kurtosis of the empirical distribution of the logarithmic returns of the underlying asset. An important part of this work is also a comparison of suitable valuation algorithms for calculation of the option price using the Variance Gamma model. The comparison of both models will be performed primarily on historical empirical distributions of logarithmic returns of selected stocks. Then, performance and pricing error of both models will be tested when estimating implied coefficients based on market data of the option. The performance of both models will be measured by traditional statistical-econometric methods such as RMSE, Likelihood ratio, Akaike information criterion and last but not least by the Natural spline regression model, which estimates the effect of the variable "Moneyness" (distance between the strike price and the current asset value) on the pricing error. All tests performed in this work suggest that the Variance Gamma model is a more accurate model for calculating the price of options.

JEL-codes: C10 G13 (search for similar items in EconPapers)
Pages: 29 pages
Date: 2020-12-14, Revised 2021-01-31
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