Aasia optsioonide hindamine

Abstract

Determining the correct value of an option is the main problem in option theory. There are several factors which determine the price of an option. In addition to these factors, Asian options also depend on the history of the underlying asset which complicates the correct pricing of an Asian option. Although the structure of an Asian option is more complex than for example European option's, many of the typical numerical methods can still be used to nd the price of an Asian option when modi ed correctly. In the rst part of this thesis some of these typical numerical methods are introduced. The basic idea of lattice method, di erential method and Monte-Carlo method are described by showing how to nd a value of a usual European option step by step. The last and main part of this thesis is dedicated to Asian options and lattice method. It is shown how to modify the lattice method so that it could be used for pricing an Asian option. The modi ed lattice method for pricing an Asian option is called forward shooting grid method (FSG) and was rst used in 1993 by Hull and White for nding the value of Asian and lookback options. The method is described thoroughly and 2 di erent approaches (Barraquand-Pudet method and modi ed Hull-White method) for choosing the average price of an underlying asset are introduced. To ensure that the FSG method can truly be used for pricing an Asian option, some results obtained by using the FSG method with di erent parameters N, and are brought out in the last section of the thesis. The prices found by Barraquand and Pudet method and modi ed Hull and White method are compared with a price of an unrealistic Asian option, which analytical value can be found. For one more realistical case of an Asian option the prices found by FSG method are compared with a price found by Monte-Carlo method. Source codes (written in Python) for FSG method and Monte-Carlo method are brought out in Appendixes (Lisad).