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

김융희; Kim， Changki

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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REFERENCES (34)
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* 2021년 이후 발행 논문의 참고문헌은 현재 구축 중입니다.

[journal] 권용재 / 2010 / Determination of Required Capital for Guaranteed Minimum Accumulation Benefits Embedded in Variable Annuities Via a Method Based on Stochastic Scenarios / 보험학회지 / 한국보험학회 (87) : 1~33

[journal] 김삼용 / 2006 / Comparison of a Class of Nonlinear Time Series models(GARCH, IGARCH, EGARCH) / 응용통계연구 / 한국통계학회 19(1) : 33~41

[journal] 김융희 / 2011 / Analyzing Guarantees in Variable Annuities / 보험금융연구 / 보험연구원 22(2) : 3~25

[journal] 노건엽 / 2012 / Evaluating the Guarantee Reserves in Variable Insurance by Stock Return Scenarios with Stochastic Volatility / 보험금융연구 / 보험연구원 23(1) : 3~34

[journal] 엄영호 / 2009 / Variable Annuity Pricing and Risk Analysis / 보험학회지 / 한국보험학회 (84) : 105~138

[journal] 옥기율 / 2009 / KOSPI200의 변동성 추정방법에 따른 VaR 비교연구 / 보험학회지 / 보험학회 (84) : 105~137

[journal] 황진태 / 2010 / Impact of Macroeconomic Variables on Initial Premiums in Variable Life Insurance with a Vector Error Correction Model / 보험금융연구 / 보험연구원 21(3) : 3~32

[confproc] Black, F. / Studies of Stock Price Volatility Changes / Proceedings of the 1976 Meetings of the Business and Economics Statistics Section / American Statistical Association : 177~181

[journal] Black, F. / 1973 / The Pricing of Options and Corporate Liabilities / Journal of Political Economy 81 : 637~654

[journal] Bollerslev, T. / 1986 / Generalized Autoregressive Conditional Heteroskedasticity / Journal of Econometrics 31 : 307~327

[report] Bolton, M. J. / 1997 / Reserving for Annuity Guarantees, The Report of the Annuity Guaranteed Working Party

[journal] Boyle, P.P. / 1997 / Reserving for Maturity Guarantees: Two Approaches / Insurnace: Mathematics and Economics 21(2) : 113~127

[journal] Boyle, P.P. / 1977 / Equilibrium Prices of Guarantees under Equity-Linked Contracts / Journal of Risk and Insurance 44(4) : 639~660

[journal] Brandt, M. W. / 2006 / Volatility Forecasting with Range-Based EGARCH Models / Journal of Business and Economic Statistics 24(4) : 470~486

[journal] Buhlman, H. / 1996 / No-Arbitrage, Change of Measure and Conditional Esscher Transforms / CWI Quarterly 9 : 291~317

[journal] Christie, A.A. / 1982 / The Stochastic Behavior of Common Stock Variances: Value, Leverage and Interest Rate Effects / The Journal of Financial Economics 10 : 407~432

[journal] Cumby, R. / 1993 / Forecasting Volatilities and Correlation with EGARCH Models / The Journal of Derivatives 1(2) : 51~63

[book] Davis, M. A. / 1997 / Option Pricing in Incomplete Markets, In Mathematics of Derivative Securities / Cambridge University Press : 216~226

[journal] Engle, R. F. / 1982 / Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of Unites KingdomInflation / Econometrica 50 : 987~1006

[journal] Engle, R.F. / 1993 / Measuring and testing the impact of news on volatility / Journal of Finance 48 : 1749~1778

[journal] Esscher, F. / 1932 / On the Probability Function in the Collective Theory of Risk / Skandinavisk Aktuarietidskrift 15 : 175~195

[journal] French, K. R. / 1987 / Expected Stock Returns and Volatility / The Journal of Financial Economics 19 : 3~29

[book] Hardy, M. R. / 1999 / Stock Return Models for Segregated Fund Investment Guarantees / University of Waterloo, Institute for Insurance and Pensions Research

[journal] Hardy, M. R. / 2001 / A Regime Switching Model of Long Term Stock Returns / North American Actuarial Journal 5(2) : 41~53

[book] Hardy, M / 2003 / Investment Guarnatees: Modeling and Risk Management for Equity-Linked Life Insurance / Jhon Wiley & Sons

[journal] Hardy, M.R. / 2006 / Validation of Long-Term Equity Return Models for Equity-Linked Guarantees / North American Actuarial Journal 10(4) : 28~47

[journal] Merton, R. C. / 1973 / Theory of Rational Option Pricing / Bell Journal of Economics and Management Science 4 : 141~183

[report] Nelson, D. B. / 1988 / Conditional Heteroskedasticity in Asset Returns: A New Approach / University of Chicago

[journal] Nq, A. C. / 2011 / Modeling Investment Quarantees in Japan: A Risk Neutral GARCH Approach / International Review of Financial Analysis 20 : 20~26

[journal] Schweizer, M. / 1996 / Approximation Pricing and the Variance-Optimal Martin-gale Measure / Annals of Probability 24 : 206~236

[journal] Schwert, G. W. / 1990 / Stock Volatility and the Crush of ‘87” / Review of Financial Studies 3(1) : 77~102

[journal] Siu, T. K. / 2004 / On Pricing Derivatives Under GARCH Models: A Dynamic Gerber-Shiu Approach / North American Actuarial Journal 8 : 17~31

[journal] Wilkie, A. D. / 1986 / A Stochastic Investment Model for Actuarial Use / Transaction of the Faculty of Actuaries 39 : 341~381

[journal] Wilkie, A. D / 1995 / More on a Stochastic Asset Model for Actuarial Use / British Actuarial Journal 1 : 777~964

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