Pricing of RCLA contract in incomplete market: PIDE approach

Purpose: The purpose of this project is to implement the finite difference method into the pricing of the equity-linked insurance product in the incomplete market. Besides the Brownian motion, I included two extra risk terms, namely jumps and stochastic volatilities. Accordingly, the general two dimensional finite difference method for solving pricing PDE is extended to three-dimensions, and extra integral component is added to capture the possible jump in the process of risky asset. Originality: It is the first study to use the three dimensional PIDE as the tool for pricing RCLA contract in the incomplete market. Design/methodology/approach: By introducing the concept of RCLA contact, then I derive the risky asset process in the equivalent martingale measure, and further compute the corresponding PIDE in the Matlab. Findings: By expanding the number of sources of risks in the asset process which will lead to more accuracy price of RCLA contract. Research limitations/implications: The limitation is that using PIDE may sometimes lead to convergence problem. Practical and Social implications: Providing the guidance to insurance companies or investment banks that are looking for the general pricing formula for the equity-linked securities.