Bayesian analysis of equity-linked savings contracts with American-style options

Abstract

In this paper, a full Bayesian procedure is developed and implemented for the market consistent valuation of a fairly general class of equity-linked savings contracts. The developed procedure allows several combinations of contract properties. For example, the contract returns may include a guaranteed interest rate and a bonus depending on the yield of a total return equity index. Especially, the contract may include an American-style path-dependent surrender option. The underlying asset and interest rate processes are estimated using the Markov chain Monte Carlo method, and their simulation is based on their posterior predictive distribution, which is, however, adjusted to give risk-neutral dynamics. Financial guarantees and equity-linked components are common in many life insurance products. From the insurance company’s viewpoint, this paper provides a realistic and flexible modelling tool for product design and risk analysis. The focus is on a novel application of advanced theoretical and computational methods, which enable us to deal with a fairly realistic valuation framework and to address model and parameter error issues. Our empirical results support the use of elaborated instead of stylized models for asset dynamics in practical applications.