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Valuation and Hedging of Limited Price Indexed Liabilities

Published online by Cambridge University Press:  10 June 2011

H.-C. Huang  and
A. J. G. Cairns
H.-C. Huang
Affiliation:
Department of Risk Management and Insurance, National Chengchi University, Taipei, Taiwan 116, ROC.
A. J. G. Cairns
Affiliation:
Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh EH14 4AS, U.K.
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Abstract

This paper considers the market or economic valuation and the hedging of Limited Price Indexed (LPI) liabilities. This involves finding optimal static and dynamic hedging strategies which minimise the riskiness of the investment portfolio relative to the liability.

In this paper we do not aim to find the perfect hedge in a perfect world. Instead, it is assumed that optimisation is restricted to three commonly used asset classes in pension funds: cash; long-term (or irredeemable) fixed-interest bonds; and long-dated index-linked bonds. The economic value of the liability is then defined as the value of the best matching portfolio using a mean/variance type of loss function. Specifically, we adopt the risk minimising approach of Föllmer & Sondermann (1986) and Schweizer & Föllmer (1988). Even with such a simple loss function, establishing the theoretically optimal solution can be difficult. We propose that a practical solution close to the theoretical optimum can be found using two approximations. First, we approximate the ‘true’ stochastic economic model by a vector autoregressive model of order one. Second, we use a sequence of linearisations to approximate non-linear by straightforward quadratic minimisation problems.

The proposed approach is illustrated with various numerical examples, and we compare the results of the approximately optimal hedging strategy with static strategies.

Keywords

LPI LiabilityStatic HedgingRegular RebalancingDynamic HedgingRisk Minimising Hedging
Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 10 , Issue 3 , 01 August 2004 , pp. 627 - 663
Copyright
Copyright © Institute and Faculty of Actuaries 2004

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