Pricing Ruin Contingent Life Annuity Under Stochastic Volatility

Abstract

Purpose of this paper: In this paper we consider the dynamics of the risky portfolio follows jump diffusion process, and the Ruin contingent life annuity (RCLA) contract under the Heston stochastic volatility framework is priced. By comparison to the literatures, we aim to illustrate that, by using jump diffusion processes for both asset price and stochastic volatility process, a more realistic generating process mechanism for the purpose of RCLA contract pricing can be implied.Design/methodology/approach: Under the assumption of the deterministic withdrawals, we develop the pricing scheme for the fair value of the lump sum charges of RCLA contract. In particular, we use the finite difference method for solving underlying PIDEs under both asset and volatility risks, the different pricing behaviours of the RCLA contracts under the different model parameters is obtained.Findings: Ruin contingent life annuity pricing in the complete market often underestimate the jump risk and the persistent factor in the volatility process. By our generalization, we show how these two random sources of risks can be precisely characterized.Research limitations/implications: The parameter values used in our numerical analysis are lack of supports by the empirical evidence, in order for the more precise pricing practise, the calibration from real- data is needed.Practical implications: The model as we adopt in this study for pricing of RCLA contract should provide a general guideline for the commercialization of this product by insurance companies.Social implication: The demand for RCLA contract as an alternative of annuitization option among the soon-to-retire baby boomers becomes increasingly high recently, this paper investigates the fair value of this particular product, and this might help the interested readers for a better understanding of the product design.What is original/value of Paper: It is the first research paper that aim to price the RCLA contract in the incomplete market. The gap between RCLA contract pricing and studies of jump diffusion models for derivative pricing in the literature, is therefore filled..