An Analysis on the Minimum Guarantee Reserves in Variable Annuities Using Different Stock Return Models

김융희; Kim， Changki

Journal of Insurance and Finance

2012, 23(4), pp.99-131
Publisher : Korea Insurance Research Institute
Research Area : Business Management

김융희 ¹ , Kim， Changki ²

¹ 고려대학교
² 고려대학교

ABSTRACT

This research studied the effects of stock return estimation model on the minimum guarantee reserves. Investigating KOSPI log return data since Jan 1990 and onwards, we were able to observe heteroscedasticity such as volatility clustering and leverage effects. To identify models which most clearly reflect these properties, we used GBM, GARCH(1,1)and EGARCH(1,1) models of which EGARCH(1,1) was found to be the optimal one. Under market incompleteness assumption, we used the conditional Esscher transform to find an appropriate risk neutral measure and the Monte-Carlo simulation method to compute the minimum guarantee reserves. Computation of the minimum guarantee reserves using GBM, GARCH(1,1) and EGARCH(1,1) models demonstrated that GBM and GARCH(1,1) models resulted in lower minimum guarantee reserves than when using EGARCH(1,1) model. In other words, we proved through this study that for sound computation of minimum guarantee reserves, one must thoroughly analyze the properties of returns of underlying assets in question prior to computation. Without such analysis, the computation may lead to underestimation of the minimum guarantee reserves.
KEYWORDS

GARCH-type model , geometric brownian motion , conditional Esscher transform , variable annuity , GMAB
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