Τιμολόγηση και αντιστάθμιση κινδύνου σε μη πλήρεις αγορές: η περίπτωση των διαχύσεων με άλματα
Pricing and hedging in incomplete markets: the case of jump-diffusion processes
KeywordsΤιμολόγηση ; Αντιστάθμιση κινδύνου ; Μη πλήρεις αγορές ; Παράγωγα χρηματοοικονομικά προϊόντα ; Τιμολόγηση παραγώγων ; Pricing ; Hedging ; Incomplete markets ; Derivatives ; Financial derivatives ; Merton JD model ; Kou model
Jump-diffusion processes have been used over the past few years to model financial securities price fluctuations in order to offer alternative approaches for pricing derivative products and to manage risk more effectively. Exponential jump processes are in many cases better suited for this purpose than the Geometric Brownian Motion used in the simple Black-Scholes model. However, the downside is that the markets in which prices jump are incomplete, i.e. replicating portfolios that offer perfect hedging are not always feasible. Therefore, in such markets it is not easy to determine a “fair” price for various financial derivatives through the non-Arbitrage theory. In the present MSc thesis, we will first present the most important results of the Jump-diffusion processes and then review various known techniques for the valuation of financial derivatives in markets with price jumps (Merton and Kou methods) as well as the construction of appropriate (partial) hedging portfolios (Merton's Approach, Superhedging, Utility Maximization, Quadratic Hedging). Finally, the introduced valuation techniques will be implemented and empirically compared (through simulation) using the computational software Wolfram Mathematica.