PRICING OF EXOTIC FOREIGN EXCHANGE RATE OPTIONS
Antti Eloranta
24th January 2008

Abstract:
The popularity of exotic foreign exchange rate options has grown rapidly during the past decade. High profit margins and rapid market growth have made the market particularly lucrative for the banks. On the other hand, the correct pricing of exotic options requires more sophisticated models than the traditional Black-Scholes. The objective of this thesis is to build, implement, and validate a pricing model for the exotic foreign exchange rate options.






Based on previous research, this thesis models the stochastic behavior of the foreign exchange rates as a stochastic volatility – jump-diffusion process with piecewise constant model parameters. The process is defined in both continuous and discrete times. The continuous time process is used for pricing European options in a semi-closed form, which enables an efficient model calibration. The discrete time model is used for pricing exotic options with Monte Carlo. The model is calibrated using a method customized specifically for the purposes of this thesis.

The model is validated by analyzing its performance with real market data from the beginning of July to the end of August 2007. The convergence of the closed-form and Monte Carlo solution option prices shows that the model is internally consistent. The comparison of the model implied and market implied option prices indicate that the model is market consistent. The analysis of the robustness suggests that the model and its calibration are mathematically meaningful.