Pricing Asian options

Absztrakt (kivonat)

The pricing of Asian options is a notably difficult problem in finance as it involves calculations with the arithmetic average of stock prices, which follows an unknown probability distribution in most price models. Nonetheless, Geman and Yor [1993] showed that it is possible to derive the Laplace transform of the \normalized price" of Asian options and thus the valuation problem is reduced to the inversion of this transform. In my thesis, I present two numerical methods by which the mentioned Laplace transform could be efficiently inverted and compare these with Monte Carlo simulation methods for a wide range of parameter inputs. Also, I investigate how variance reduction methods could be employed in order to cut down on the uctuation inherent in simulation methods. Explaining the logic of risk-neutral derivative valuation in the Black-Scholes framework in the first section, I make a distinction between the pricing problem of geometric- and arithmetic-average Asian options in the second section. Then, I present the MATLAB implementation of the inversion and simulation algorithms and compare the results of the different approaches. Finally, I investigate the limitations and the speed of convergence of both approachesas well as make suggestions on the appropriate of parameters for each method