A Study of Option Pricing Using Variance Gamma Process

- Journal title : Korean Journal of Applied Statistics
- Volume 25, Issue 1, 2012, pp.55-66
- Publisher : The Korean Statistical Society
- DOI : 10.5351/KJAS.2012.25.1.055

Title & Authors

A Study of Option Pricing Using Variance Gamma Process

Lee, Hyun-Eui; Song, Seong-Joo;

Lee, Hyun-Eui; Song, Seong-Joo;

Abstract

Option pricing models using Levy processes are suggested as an alternative to the Black-Scholes model since empirical studies showed that the Black-Sholes model could not reflect the movement of underlying assets. In this paper, we investigate whether the Variance Gamma model can reflect the movement of underlying assets in the Korean stock market better than the Black-Scholes model. For this purpose, we estimate parameters and perform likelihood ratio tests using KOSPI 200 data based on the density for the log return and the option pricing formula proposed in Madan et al. (1998). We also calculate some statistics to compare the models and examine if the volatility smile is corrected through regression analysis. The results show that the option price estimated under the Variance Gamma process is closer to the market price than the Black-Scholes price; however, the Variance Gamma model still cannot solve the volatility smile phenomenon.

Keywords

Black-Scholes model;Lvy processes;Variance Gamma process;option pricing model;

Language

Korean

Cited by

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