Pricing and Risk Analysis of Maturity Guarantees Embedded in the Retirement Investment Products - Markov Switching Approach

Piaskowski, Wojtek

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URN: urn:nbn:de:bsz:180-madoc-12494
Document Type: Working paper
Year of publication: 2005
The title of a journal, publication series: Mannheimer Manuskripte zu Risikotheorie, Portfolio Management und Versicherungswirtschaft
Volume: 162
Place of publication: Mannheim
Publication language: English
Institution: Business School > Sonstige - Fakultät für Betriebswirtschaftslehre
MADOC publication series: Lehrstuhl für ABWL, Risikotheorie, Portfolio Management und Versicherungswirtschaft (Albrecht) > Mannheimer Manuskripte zu Risikotheorie, Portfolio Management und Versicherungswirtschaft
Subject: 330 Economics
Subject headings (SWD): Markov-Ketten-Monte-Carlo-Verfahren , Risikoanalyse , Kapitalmarkt
Abstract: 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 proced correctly because improper pricing and provision policy may lead to bankruptcy. This paper proposes a pricing model for maturityguarantees 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 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.
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