On the Calculation of Price Sensitivities with a Jump-Diffusion Structure

An integral part of successful risk management in modern financial markets is the accurate calculation of the price sensitivities of the underlying asset. There are a number of recent research papers that have focused on this important issue. A strand of literature has applied the finite difference method which is biased. Another strand of literature has made use of the Malliavin calculus within a jump diffusion framework. However, the existing papers have provided the price sensitivities by conditioning on some of the stochastic part of the complicated random process. The current paper provides price sensitivities in jump diffusion model without conditioning on any stochastic part in the model. These estimates are shown to be unbiased. Thus, the solution that is provided in this paper is expected to induce decision making under uncertainty more precise.