Προσομοίωση στοχαστικών ανελίξεων με εφαρμογές στη χρηματοοικονομική μηχανική
Simulation of stochastic processes with applications in financial engineering
Χαριτάκης, Νικόλαος Κ.
SubjectΣτοχαστικές ανελίξεις -- Μαθηματικά υποδείγματα ; Stochastic processes -- Mathematical models ; Προσομοίωση ; Simulation methods ; Στατιστική ; Statistics
The main aim of this thesis is the presentation and implementation of methods and techniques for the simulation of continuous time stochastic processes with applications in stochastic finance. This thesis begins with the description of basic financial terms, securities and markets and then analyses the types of derivatives (forwards, futures, repos, options) and market traders (hedgers, speculators, arbitrageurs). Following it presents techniques for generating random numbers from several distributions. Using these random numbers, various models and techniques are presented for simulating specific stochastic processes: Brownian Motion, Geometric Brownian Motion in one or multiple dimensions, simulation with time-varying rate, simulation with deterministic volatility, Gaussian short-term rate models, square root diffusion, processes with Jumps and pure-jumps, Gamma processes, inverse Gaussian processes. The associated sample paths are simulated in order to assess, through Monte Carlo approach, a derivative's fair value. Finally, methods are presented for calculating the sensitivity parameters of financial derivatives prices, with a view to an approximate construction of a hedging portfolio.