주가수익률 추정 모델 선택에 따른 변액 연금 최저보증준비금 분석
An Analysis on the Minimum Guarantee Reserves in Variable Annuities Using Different Stock Return Models
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초록
이 연구는 주식수익률 추정 모델의 선택이 변액연금의 최저보증준비금에 미치는영향을 분석하였다. 1990년 1월 이후 KOSPI 로그수익률을 분석한 결과 우리는이분산성과 변동성의 군집현상 그리고 레버리지 효과를 관찰하였으며 이러한 특성을가장 잘 반영하는 모델을 찾기 위해 GBM, GARCH(1,1) 그리고 EGARCH(1,1) 모델들을 이용한 결과 EGARCH(1,1)이 최적의 모델이라는 것을 발견하였다. 시장의불완전성 가정하에서 우리는 conditional Esscher transform을 이용해 GARCH-type 모델 사용 시 적합한 risk neutral measure를 구하고 몬테카를로 시뮬레이션을 이용해최저보증준비금을 산출하였다. 그 결과 GBM과 GARCH(1,1)을 사용하면 EGARCH(1,1)을사용 하는 것보다 낮은 수준의 최저보증준비금이 산출되었다. 즉 이 연구를 통해 우리는적절한 최저보증준비금 산출을 위해서는 대상이 되는 기초자산의 수익률의 특성에 대한분석이 선행되어야 하며 만일 이를 제대로 반영하지 않고 최저보증준비금을산출한다면 과소추정의 문제가 발생될 수 있다는 점을 보였다.
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.
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