Προσομοίωση ανελίξεων Levy με εφαρμογές στην αποτίμηση παραγώγων χρηματοοικονομικών προϊόντων
Simulation of Levy processes with applications in financial derivatives pricing
Σφακιανάκης, Θεόδωρος Μ.
SubjectLevy processes ; Derivative securities -- Prices -- Mathematics ; Finance -- Statistical methods ; Στοχαστικές ανελίξεις -- Μαθηματικά υποδείγματα ; Παράγωγα (Χρηματοοικονομική)
During the last decades, the effort of financial mathematics scientific community on market models creation is continuous and uninterrupted. The contribution of Levy processes theory is quite important in achieving this effort. Under this point of view, the aim of this master thesis is to present various Levy processes simulation methods and the use of them in option pricing. Specifically, initially we conduct a comprehensive review of the necessary mathematical tools for the study of stochastic processes. We continue by introducing the family of Levy processes and present its basic characteristics. After gaining an overall view of Levy processes theory, we proceed to the presentation of Levy processes simulation methods. In particular, we present and implement (via Mathematica software package) algorithms for simulating well-known members of Levy processes family. Finally, we describe the basic principles of derivatives pricing, introduce the stochastic volatility exponential Levy market model and (Monte Carlo) estimate call option prices of Lookback, Barrier and Asian type under specific assumptions.