Pricing European FX options by heston model calibrated with historical spot prices

Abstract

In this thesis, European type of FX call and put options are priced by two methods, Black and Scholes Model and Heston Model. Despite the fact that Black and Scholes is widely used by finance environment, the volatility of the underlying asset is ignored and assumed to be constant. However, since this assumption does not reflect the real market behavior, European options are priced by Heston model which consider that the volatility is stochastic, not constant. Heston model parameters are calibrated by using historical EUR/TL exchange rates with the Maximum Likelihood Estimation (MLE) method. The calibrated parameters are used in a simulation algorithm in order to forecast the future EUR/TL exchange rates. This is done to observe whether estimated parameters are usable in the option pricing procedure. Then, European FX call and put options are priced for given spot and strike prices, domestic and foreign interest rates and maturities. Black and Scholes model is also used for option pricing in order to compare the performances of the two models. Furthermore, model prices are compared to the real market prices. The deviations between the model prices and real prices are tried to be explained by a Root Mean Square Error and Average Relative Percentage Error analysis. The computational results show that the Heston Model outperforms the Black and Scholes model.