In this paper, we provide Laplace transform-based analytical solutions to pricing problems of various occupation-time-related derivatives such as step options, corridor options, and quantile options under Kou's double exponential jump diffusion model. These transforms can be inverted numerically via the Euler Laplace inversion algorithm, and the numerical results illustrate that our pricing methods are accurate and efficient. The analytical solutions can be obtained primarily because we derive the closed-form Laplace transform of the joint distribution of the occupation time and the terminal value of the double exponential jump diffusion process. Beyond financial applications, the mathematical results about occupation times of a jump diffusion process are of more general interest in applied probability.
['Ning Cai', 'Nan Chen', 'Xiangwei Wan']
Occupation Times of Jump-Diffusion Processes with Double Exponential Jumps and the Pricing of Options