Pricing Dynamic Fund Protections With A Stochastic Barrier

Dynamic fund protection(DFP)provides a guarantee that the account value of the investor never drops below a barrier over the investment period.This paper considers the pricing of the dynamic fund protection under a jump-diffusion model with a stochastic barrier.In general,under a jump-diffusion model,it is difficult to give the explicit formula for the price of dynamic fund protection.However,when the jump sizes follow a hyper-exponential distribution,we can give the formula for the Laplace transform of the price of dynamic fund protection.By inverting the Laplace transform,we give numerical results for the price of dynamic fund protection.This paper includes three parts: Firstly,we consider the valuation of the dynamic fund protection under a jump-diffusion model with a stochastic protection level,the explicit formula for the Laplace transform of the price of dynamic fund protection is obtained under a hyper-exponential jump-diffusion process.Secondly,we investigate the valuation of dynamic fund protection under the assumption that the market value of the basic fund and the protection level follow regime-switching processes with jumps.In particular,we give the explicit formula for the Laplace transform of the price of dynamic fund protection when the jump sizes follow a regime-switching,hyper-exponential jump-diffusion process.Thirdly,by using the Gaver-Stehfest algorithm,we perform some sensitivity tests and present some numerical results for the price of dynamic fund protection.