Hedging in a discontinuous market: the barrier option

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and Economics

In principle, the Black-Scholes equation assumes log-normal underlying prices, but market dynamics do not empirically fit these assumptions, and the related scale invariance and continuity properties fail at shorter time spans. The aim of this study is to analyze how the pricing-hedging model may be adjusted when prices are assumed to have discontinuous paths resulting in heavy tails distribution of returns. Numerically, the model seems to work for vanilla contracts but not for exotic options. Some explanations and alternatives are therefore provided. Finally, a further interesting question arises from the results achieved: is it possible to smooth the smile effect?