In the thesis we describe methods for valuation of discrete Asian options based on Lévy processes. Methods described are based on article . In models, which we use, the price of the underlying was modelled as exponential Lévy process. Applied numerical methods are Monte Carlo simulations, quadrature method for arithmetic Asian options and Fourier inversion method for geometric Asian options. For greater accuracy of MC simulations we use control variate. We also present method for
calibration of the model to data. In Chapter 2 we describe main results of financial mathematics in continuous time. Black-Scholes model and its shortcomings are described in Chapter 3. Lévy processes and their properties are described in Chapter 4. In Chapter 5 Lévy market model is described together with the calibration of the model. Monte Carlo methods and control variate method are described in Chapter 6. In Chapters 7 and 8, valuation methods of discrete geometric and arithmetic Asian options are described. In Chapter 9 we describe results of model calibration and option valuation. The conclusion is given in Chapter 10.