Pricing Foreign Currency Options Under Levy Processes and Stochastic Interest Rates

Speaker: Rehez Ahlip

Affiliation: University of Western Sydney

Time: Monday 13/05/2013 from 14:00 to 15:00

Venue: Access Grid UWS. Presented from Parramatta (EB.1.32), accessible from Campbelltown (26.1.50) and Penrith (Y239).

Abstract:

Foreign exchange options are studied in the Heston stochastic volatility model for the exchange rate which includes jumps in both the spot exchange rate and volatility dynamics combined with the Cox et al. dynamics for the domestic and foreign stochastic interest rates. The instantaneous volatility is correlated with the dynamics of the exchange rate return, whereas the domestic and foreign short-term rates are assumed to be independent of the dynamics of the exchange rate. The main result furnishes a semi-analytical formula for the price of the foreign exchange European call option. The FX options pricing formula is derived using the probabilistic approach, which leads to explicit expressions for conditional characteristic functions. We argue that the model examined in this paper is the only analytically tractable version of the foreign exchange market model that combines the Heston stochastic volatility model with jumps for the exchange rate with the CIR dynamics for interest rates.

This work is jointly with Marek Rutkowski (Professor of Financial Mathematics, School of Mathematics, University of Sydney).

Biography: Rehez Ahlip is a Senior Lecturer with the School of Computing, Engineering and Mathematics and a member of the UWS Centre for Research in Mathematics. His research is in the area of financial mathematics that defines pricing and hedging of derivatives. For the last 7 years Rehez has been collaborating with Professor Marek Rutkowski from The University of Sydney on developing mathematical models for pricing of foreign exchange options of increasing sophistication. As the result of this research Rehez has published a number of well received journal papers.