Εμπειρική μελέτη μοντέλων αποτίμησης δικαιωμάτων που υπόκεινται σε φράγμα
Κασιμάτης, Νικόλαος Α.
This thesis presents several models for the price of the underlying asset in valuation of barrier options, Black-Scholes, Constant elasticity of variance, Stochastic Volatility of Heston, Merton’s Jump Diffusion and Variance Gamma, and compares their performance. The underlying asset of these options is the foreign exchange rate of the US dollar to euro and they refer to the specific time period of the year 2004. Firstly we display the theoretical framework which is needed for the completion of the empirical study. Thereafter we translate the data for the plain vanilla options from implied volatilities of investing strategies, as the options are usually valuated in the exchange market, in 12 market plain vanilla prices. Based on these prices for 254 days we estimate the model parameters with the iterative algorithm of Levenberg-Marquardt as well as we examine the performance of the models, out of the valuation sample. Finally we proceed to the pricing of barrier options with these estimated models in order to examine their behavior in a ‘tough environment’ as the one designated by such exotic options. On the one hand, the main difficulty comes from the lack of data, since barrier options are not contracts that take place in organized stock markets, but they are direct deals between the parties. On the other hand, another difficulty that is pointed out is the simulation of the exchange rate path, which is needed for the actual valuation.