Option Pricing with Bounded Expected Loss under Variance-Gamma Processes

Title & Authors
Option Pricing with Bounded Expected Loss under Variance-Gamma Processes
Song, Seong-Joo; Song, Jong-Woo;

Abstract
Exponential L$\small{\acute{e}}$evy models have become popular in modeling price processes recently in mathematical finance. Although it is a relatively simple extension of the geometric Brownian motion, it makes the market incomplete so that the option price is not uniquely determined. As a trial to find an appropriate price for an option, we suppose a situation where a hedger wants to initially invest as little as possible, but wants to have the expected squared loss at the end not exceeding a certain constant. For this, we assume that the underlying price process follows a variance-gamma model and it converges to a geometric Brownian motion as its quadratic variation converges to a constant. In the limit, we use the mean-variance approach to find the asymptotic minimum investment with the expected squared loss bounded. Some numerical results are also provided.
Keywords
Option pricing;variance-gamma processes;weak convergence;incomplete market;bounded loss;
Language
English
Cited by
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