Το μοντέλο Black-Scholes υπό στοχαστική μερισματική απόδοση
This thesis refers to the pricing of the European type options in the frame of the Black-Scholes model which incorporates the stochastic dividend yield under constant or/and stochastic market price of risk, as it is presented from Lioui Abraham (2006). To begin with, we describe the options on theoretical level, while we mention some historical incidents which are considered as benchmarks throughout the option’s evolution from ancient Greece until today. It is essential for this thesis to analyze the theoretical frame of the model, which is the pillar of the completion of the empirical study. Regarding the latter, we valuate the parameters of our model by applying the Levenberg-Marquardt algorithm with the use of Excel and then we compare our results with those of the Black-Scholes model under constant dividend yield. According to the results of our empirical study, the Black-Scholes model under stochastic dividend yield when the market price of risk is stochastic, approaches more effectively the market option prices. In addition, we test the forecasting ability of our valuations and we perform a numerical analysis. Regarding the forecasting ability of the models, the results of the empirical study show us that the time to maturity is way more important than what we initially expected in respect of the efficiency of each model. To conclude, we analyze the Greeks of the options that we use in our empirical study for all models. The results are simulated in order to assess the economic impact of assuming that the dividend yield is deterministic when it is actually stochastic.