Pricing ruin‐contingent life annuity under stochastic volatility

Abstract

Purpose

The purpose of this paper is to propose a model for ruin‐contingent life annuity (RCLA) contracts under a jump diffusion model, where the dynamics of volatility is governed by the Heston stochastic volatility framework. The paper aims to illustrate that the proposed jump diffusion process, for both asset price and stochastic volatility, will provide a more realistic pricing model for RCLA contracts in comparison to existing models.

Design/methodology/approach

Under the assumption of the deterministic withdrawals, the authors use a partial integro differential equation (PIDE) approach to develop the pricing scheme for the fair value of the lump sum charges of RCLA contracts. Consequently, the authors employ an elegant numerical scheme, finite difference method, for solving the PIDEs for the reference portfolio, as well as the volatility. The findings show that a different pricing behaviour of the RCLA contracts under the authors' model parameters is obtained compared to that in the existing literature.

Findings

RCLA pricing in the complete market often underestimates the jump risk and the persistent factor in the volatility process. The authors' generalized model shows how these two random sources of risks can be precisely characterized.

Research limitations/implications

The parameter values used in the numerical analysis require more empirical evidence. Hence, in order for more precise pricing practice, the calibration from real data is needed.

Practical implications

The model, as adopted in this study, for pricing of RCLA contracts should provide a general guideline for the commercialization of this product by insurance companies.

Social implications

The demand for RCLA contracts as an alternative to the commonly‐practised annuitization option has recently increased, rapidly, among the soon‐to‐retire baby boomers. This paper investigates the fair value of this particular product, which could be beneficial to researchers for a better understanding of the product design.

Originality/value

This is the first research paper which prices the RCLA contracts 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.

Citation

Rong, N. and Alavi Fard, F. (2013), "Pricing ruin‐contingent life annuity under stochastic volatility", Journal of Risk Finance, Vol. 14 No. 1, pp. 35-48. https://doi.org/10.1108/15265941311288095