HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.41, no.5, pp.767-783, 2012 (SCI-Expanded)
We consider a geometric Levy market model. Since these markets are generally incomplete, we cannot find a unique martingale measure. There are many ways to handle this problem. In this paper, we choose the completion technique, firstly introduced in J. M. Corcuera, D. Nualart and W. Schoutens (Completion of a Levy market by power-jump assets, Journal of Computational Finance, 7, 1-49, 2004), which employs special artificial assets called power-jump assets. The price processes of power-jump assets are based on an orthogonalized family of Teugel martingales. By using the Gram-Schmidt process and obtaining the coefficients we express the price process of the power-jump assets in terms of Teugel martingales. Afterwards, we derive pricing formulas for European call options by using two methods: the martingale pricing approach and the characteristic formula approach which is performed via the fast Fourier transform (FFT). Throughout the pricing and application to real market price data, jump sizes are assumed to have a particular distribution.