Constant proportion portfolio insurance under a regime switching exponential Lévy process

The constant proportion portfolio insurance is analyzed by assuming that the risky asset price follows a regime switching exponential Lévy process. Analytical forms of the shortfall probability, expected shortfall and expected gain are derived. The characteristic function of the gap risk is also obtained for further exploration on its distribution. The specific implementation is discussed under some popular Lévy models including the Merton's jump-diffusion, Kou's jump-diffusion, variance gamma and normal inverse Gaussian models. Finally, a numerical example is presented to demonstrate the implication of the established results.