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Evaluating Quantile Reserve for Equity-Linked Insurance in a Stochastic Volatility Model: Long vs. Short Memory

Published online by Cambridge University Press:  09 August 2013

Hwai-Chung Ho ,
Sharon S. Yang  and
Fang-I Liu
Hwai-Chung Ho
Affiliation:
Institute of Statistical Science, Academia Sinica and Department of Finance, National Taiwan University, Taipei 115, Taiwan, E-mail: hcho@stat.sinica.edu.tw
Sharon S. Yang
Affiliation:
Department of Finance, National Central University, Taoyuan, 320, Taiwan, E-mail: syang@ncu.edu.tw
Fang-I Liu
Affiliation:
Department of Finance, National Taiwan University, Taipei 106, Taiwan Email: d93723006@ntu.edu.tw
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Abstract

This paper evaluates the long-term risk for equity-linked insurance products. We consider a specific type of equity-linked insurance product with guaranteed minimum maturity benefits (GMMBs), and assume that the underlying equity follows the stochastic volatility model which allows the return's latent volatility component to be short- or long-memory. The explicit form of the quantile reserve or the Value at Risk and its confidence intervals are derived for both the long-memory and short-memory stochastic volatility models. To illustrate the effect of long-memory volatility, we use the S&P 500 index as an example of linked equity. Simulation studies are performed to examine the accuracy of the quantile reserve and to demonstrate the consequence of low coverage probability if model misspecification takes place. The empirical results show that the confidence interval of quantile reserve could be severely underestimated if the long-memory effect in equity volatility is ignored.

Keywords

Equity-linked InsuranceValue at RiskStochastic Volatility ModelLong-memory Stochastic Volatility Model
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 2 , November 2010 , pp. 669 - 698
Copyright
Copyright © International Actuarial Association 2010

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