Pricing and Risk Analysis of Maturity Guarantees Embedded in the Retirement Investment Products

Numerous insurance and investment products offered by the private financial industry contain embedded investment guarantees. In these products the contributions are invested on the capital market, which involves investment risk for the client. To protect the contribution payers against this risk the modern pension frames include performance guarantees. It is important that these guarantees are priced correctly because improper pricing and provision policy may lead to bankruptcy. This paper proposes a pricing model for maturity guarantees embedded in retirement saving plans. A deterministic guaranteed rate of return and periodic contributions are considered. Since maturity guarantees have long-term character, an approach is needed that models the long-run behaviour of the market prices of securities. For this reason this paper uses the geometric Brownian motion with Markov switching. For guarantee pricing WEBB’s (2003) option pricing for Markov switching model is applied, which is based on the Esscher transform. The second part of the paper analyses the risk of shortfall in respect to three shortfall risk measures: the shortfall probability, the shortfall expectation and the mean expected loss.

Piaskowski, Wojtek (2005), Pricing and Risk Analysis of Maturity Guarantees Embedded in the Retirement Investment Products, Mannheimer Manuskripte zu Risikotheorie, Portfoliomanagement und Versicherungswirtschaft.