MULTI-ASSET OPTIONS AND THEIR ANALYSIS - Beja, Ana Beatriz Ferreira (2024)
This thesis is divided into two main parts: the first part consists of the theoretical part of the multi-asset options dealt with in this thesis, i.e. basket options, outperformance options and best and worst of options; the second part presents and analyzes the results obtained for option prices and Greeks, with all outcomes derived from fictitious data. In general, the main Greeks are studied for all multi-asset options, but the most important for this thesis is Cega, the Greek related to the correlation coefficient, since this parameter only exists when studying options on more than one asset. To study the effects of correlation and other parameters that influence the price of an option, Python programming was used. The Python programming language can be used to program the pricing formulas for options that have them and their respective derivatives. For options that do not have explicit formulas to calculate their price, Monte Carlo simulation and other numerical methods were utilized to calculate their price and derivatives. To analyse the results obtained for the price and the Greeks of the options, graphs were made in Python. The graphs made the analysis easier and it was possible to conclude that the different multi-asset options behave differently with respect to the correlation parameter. Additionally, it was observed that other methods for approximating the price and Greeks of options that do not have an explicit formula are more viable than Monte Carlo simulation, due to the latter’s longer computational time.