On the analysis and design of pension contracts from the customer's perspective

Abstract

This thesis aims to design new long term investment structured products that can be used by insurance companies to smooth investment returns for their customers. These products are widely known as pension contracts as they are mainly used in the accumulation part of a pension scheme. Two popular pension schemes in UK are the Defined Benefit (DB) scheme and the Defined Contribution (DC) scheme. Recently, with the transition from the DB scheme to the DC scheme, more individuals must provide for their own retirement without the security of an employer-backed pension promise. Thus, it is of importance to provide the customer with suitable long term investment products. The thesis, consisting of three research papers, aims to show how to design a new pension contract that best meet the demand from the customers. In order to better understand the pension contracts, our first paper (Chapter 3) care fully examines a traditional with-profits contract in the market. This paper gives a closed form solution for the pricing of this contract and shows that it is overvalued to the customers because of its embedded guarantees. In addition, the smoothing method of this contract exposes the insurer to a risk that cannot be hedged. More over, the inter-generation risk sharing has been studied for this contract. The smoothing method, which is a typical feature of the with-profits products, is examined in detail in the second paper (Chapter 4). This paper compares three common smoothing methods of with-profits contracts in UK and see how the smoothing method performs. We not only compare the absolute terminal smoothed value, but also take the interim utility, customers’ satisfaction within the investment horizons, in to account. This has been done by using Multi-Cumulative Prospect theory (MCPT). The third paper (Chapter 5) propose a new pension contract with the features of guarantees and bonuses. It has transparent structure and clear distribution rule. Under Cumulative Prospect thoery (CPT), the new contract generates higher utility than the contract introduced in Guill´en et al. (2006). The result provides the evidence why the guarantees should be included in the pension contract. In addition, our result shows with the increase of policyholder’s investment horizons, the proportion of risky asset in the underlying investment portfolio increases while the proportion of risk free asset decreases. This result conforms to the traditional life cycle pension investment advice.