Calibration and pricing Foreign Exchange Options under the Double Heston - Jump Diffusion - CIR Model

Speaker: Rehez Ahlip¹, Ante Prodan²

Affiliation: University of Western Sydney¹, University of Western Sydney²

Time: Monday 19/10/2015 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:

The theoretical work was completed as a result of work at the Baruch Volatility Workshop and generous and detailed comments by Jim Gatheral (Meryl Lynch, City University New York).

The aim of this project is to derive a semi-analytical expression for pricing Foreign Exchange options under a jump diffusion version of The Double Heston Volatility Model and calibration to market. The two factor structure for the volatility was first considered by Christofferson(2009) to address the inadequacies of the original model due to Heston. Although the Heston model is widely used in practice is not always able to fit implied volatility smile very well, especially for options with shorter maturities. The idea behind the two factor structure for the volatility was to enrich the variance process and at the same time add greater flexibility. However, empirical research indicates that stochastic volatility models alone do not offer reliable prices for close expiration derivatives. Further the addition of jumps to the dynamics of the underlying is not sufficient to capture the sudden increase in volatility due to market turbulence . Since the overall volatility in financial markets consists of a highly persistent slow moving and rapid moving components, as such we propose a Double heston Jump Diffusion for the exchange rate dynamics and a jump process to one component of the two factor volatility structure, where, as the second component is simply the Heston volatility to add extra flexibility to fit the implied volatility smile with short maturities.

Biography¹: 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.

Biography²: Ante Prodan is a Lecturer and Director of Online Programs with the School of Computing, Engineering and Mathematics. His research interest is in applying computer simulation in diverse areas of research such as networking and healthcare. For the last 5 years, Ante has been participating in a number of research projects on modelling and simulating cancer treatment related healthcare processes funded by Hunter New England Local Health District.