Risk quantification of an option portfolio through the introduction of the fuzzy Black-Scholes formula

Abstract

The aim of this thesis is to quantify the market risk of an option portfolio under uncertainty. The fuzzy sets theory is introduced to model the parameters of the Black-Scholes option-pricing formula. Since the option price is calculated through the fuzzy Black-Scholes formula, we can compute the Value-at-Risk as a fuzzy number. By doing so, we aim to capture extra information that is lost in traditional models given the uncertainty derived from the fluctuations of financial markets. Finally, we want to conclude whether the introduction of the fuzzy sets theory is useful in order to improve the risk management.