Αποτίμηση δικαιωμάτων επί πολλαπλών περιουσιακών στοιχείων μέσω προσομοίωσης Monte-Carlo
Pricing multi-asset options using Monte-Carlo simulation
Γκόρος, Ηλίας Ν.
The multi asset options is a rather recent tool in the finance derivatives market. These options are not so widely used as the vanilla ones, mainly due to their complexity. In practice they are usually considered as single options, e.g. when the underlying asset is a stock market index. The main characteristic of these derivatives is that their final value is dependent on two or more assets that are related to each other. The increasing power of modern computing systems enable us to approximate with satisfactory accuracy the fair value of any multi-asset option (with predefined exercise date) using simulation techniques. The main purpose of this master thesis is to present and implement appropriate simulation algorithms for estimating the price of European style multi assets options. In the first chapter, we make a brief discussion regarding derivatives, derivatives markets and also concepts such as hedging, and we refer to different types of multi asset options which are the main subject of this thesis. In the second chapter we briefly discuss the theoretical background of option pricing. A reference will be made to the “fair” value of a contract, and to arbitrage pricing. The main focus will be on the stochastic processes of one-dimensional and multi-dimensional Brownian motion and Geometric Brownian motion, as well as the Black&Scholes model. In the third chapter we present pricing methods for single vanilla options and exotic options using the Monte Carlo method. In the fourth chapter we present and implement simulation algorithms in order to approximate the fair price of Basket, Exchange, Quanto and Extreme options. The practical use of these type of options is discussed and certain graphs that may lead us to useful conclusions are illustrated. Finally, the fifth chapter deals with path dependent multi asset options such as Barrier, Extreme and Asian basket options. In the Appendix of this thesis, we refer in general to the Monte Carlo method, to the generation of “random” numbers and the methods used to produce “random” numbers from the multi-dimensional normal distribution. The Wolfram Mathematica 10 software package is used in all computations.