Pricing currency derivatives when the foreign exchange rate and the interest rates follow jump -diffusion processes.

摘要

In this dissertation, I propose a joint dynamics of exchange rate process, domestic interest rate process, and foreign interest rate process. The underlying processes are assumed to follow jump-diffusion process with the diffusion being driven by multi-dimensional Wiener process and the jump process modeled by marked point process which has time-dependent functional parameters. This formulation captures the fat.-tailed distribution of the exchange rates and allows for discontinuities in the interest rates that arises due to certain events or news. By modeling the exchange rate and interest rates jointly with specific shocks I am allowing for some correlation among the processes. I also formulate a tractable subclass of the model in order to price certain cross-currency derivatives. The formulae highlights the effects of jumps having time-dependent functional parameters.