Analytical solutions to Barrier Options and Compound Options on Jump-Diffusion Processes

trinity · October 14th, 2004, 7:20 am

Does anyone know where I can see an analytical solution to a barrier option. a knock-out call, on a jump-diffusion process ? Also, an option on such a barrier option ?Thanks

Anton · October 14th, 2004, 7:27 am

The price of a barrier call of an asset modeled by a jump-diffusion process exists in close form only for the double-exponential jump-diffusion model, also known as Steven Kou's model. Have a look at his hompage. There is also a paper by Alex Lipton at "Risk" (Jan 2002) on the same topic.A.

trinity · October 14th, 2004, 7:46 am

Many thanks Anton, looking at it now. On a related topic, I have another question: assume the jump is a simple jump to ruin, i.e. k=-1 where the asset value jumps to zero. A la Merton's model of default. Couldn't one simply price a compound option, say a put option on a call option, replacing the interest rate, r, with a shifted interest rate, i.e. r+h, where h is the hazard rate for the jump process, and then using Geske's formula ?Thanks