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VALUING EQUITY-LINKED DEATH BENEFITS IN A REGIME-SWITCHING FRAMEWORK

Published online by Cambridge University Press:  13 January 2015

Chi Chung Siu ,
Sheung Chi Phillip Yam  and
Hailiang Yang
Chi Chung Siu
Affiliation:
Finance Discipline Group, Business School, University of Technology Sydney, Sydney, NSW, Australia
Sheung Chi Phillip Yam
Affiliation:
Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T. Hong Kong
Hailiang Yang*
Affiliation:
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Pokfulam, Hong Kong
*
E-Mail: hlyang@hku.hk
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Abstract

In this article, we consider the problem of computing the expected discounted value of a death benefit, e.g. in Gerber et al. (2012, 2013), in a regime-switching economy. Contrary to their proposed discounted density approach, we adopt the Laplace transform to value the contingent options. By this alternative approach, closed-form expressions for the Laplace transforms of the values of various contingent options, such as call/put options, lookback options, barrier options, dynamic fund protection and the dynamic withdrawal benefits, have been obtained. The value of each contingent option can then be recovered by the numerical Laplace inversion algorithm, and this efficient approach is documented by several numerical illustrations. The strength of our methodology becomes apparent when we tackle the valuations of exotic contingent options in the cases when (1) the contracts have a finite expiry date; (2) when the time-until-death variable is uniformly distributed in accordance with De Moivre's law.

Keywords

Regime-switchingjump-diffusion processequity-linked death benefitsguaranteed minimum death benefitsfirst passage probabilities
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 45 , Issue 2 , May 2015 , pp. 355 - 395
Copyright
Copyright © ASTIN Bulletin 2015 

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