Quantile hedging of equity-linked life insurance contracts: stochastic interest rate environment

Alexander Melnikov, Shuo Tong

Abstract


This paper studies the problem of pricing equity-linked life insurance contracts, and also focuses on the valuation of insurance contracts with stochastic guarantee. The contracts under consideration are based on two risky assets that satisfy a two-factor jump-diffusion model: one asset is responsible for future gains, and the other one is a stochastic guarantee. As most life insurance products are long-term contracts, it is more practical to consider the problem in a stochastic interest rate environment. In our setting, the stochastic interest rate behaviour is also described by a jump-diffusion model. In addition, quantile hedging technique is developed and exploited to price such finance/insurance contracts with initial capital constraints. Explicit formulas for both the price of the contracts and the survival probability are obtained. Our results are illustrated by numerical example based on financial indexes Russell 2000 and S&P 500.

 


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References


Arias E, Rostron B, Tejada-Vera B. United States life tables 2005, National Vital Statistics Reports 2010; 58:1-40.

Bacinello AR, Persson, SA. Design and pricing of equity-linked life insurance under stochastic interest rates. Journal of Risk Finance 2002; 3: 6-21.

Boers NL, Gerber GC, Hickman HU, Jones DA, Nesbit CJ. Actuarial Mathematics. Schaumburg, Illinois: The Society of Actuaries; 1997.

Boyle PP, Schwartz ES. Equilibrium prices of guarantees under equity-linked contracts. Journal of Risk and Insurance 1977; 44: 639-680.

Brennan MJ, Schwartz ES. The pricing of equity-linked life insurance policies with an asset value guarantee. J. Financial Economics 1976; 3: 195-213.

Chiarella C, Sklibosios CN. A class of jump-diffusion bond pricing models within the HJM framework. Asia-Pacific Financial Markets 2003; 10: 87-127.

Ekern S, Persson S. Exotic unit-linked life insurance contracts. Geneva Papers on Risk and Insurance Theory 1996; 21, 35-63.

Foellmer H, Leukert P. Efficient hedging: cost versus short-fall risk. Finance and Stochastic 2000; 4: 117-146.

Foellmer H, Leukert P. Quantile hedging. Finance and Stochastic 1999; 3: 251-273.

Gao QS, He T, Zhang C. Quantile hedging for equity-linked life insurance contracts in a stochastic interest rate economy. Economic Modelling 2010; 28: 147-156.

Heath D, Jarrow R, Morton A. Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation. Econometrica 1992; 60:77-105.

Kaushik A, Jarrow R. Pricing options on risky assets in a stochastic interest rate economy. Mathematical Finance 1992; 2:217-237.

Kirch M, Melnikov A. Efficient hedging and pricing of life insurance policies in a jump-diffusion model. Stochastic Analysis and Applications 2005; 23:1213-1233.

Mancini C. Estimation of the characteristics of the jumps of a general Poisson-diffusion model. Scand. Actuarial J. 2004; 1: 42-52.

Melnikov A, Romanyuk Y. Efficient hedging and pricing of equity-linked life insurance contracts on several risky assets. International Journal of Theoretical and Applied Finance 2008; 11: 295-323.

Melnikov A, Skornyakova V. Quantile hedging and its application to life insurance. Statistics and Decisions 2005; 23:301-316.

Melnikov A, Volkov SN, Nechaev ML. Mathematics of Financial Obligations.Providence, RI: American Math. Soc.; 2002.

Melnikov A. Quantile hedging of equity-linked life insurance policies. Doklady mathematics 2004; 69: 428-430.

Moeller T. Hedging equity-linked life insurance contracts. North American Actuarial Journal 2001; 5: 79-95.

Moeller T. Risk-minimizing hedging strategies for unit-linked life-insurance contracts. ASTIN Bulletin 1998; 28:17-47.

Shirakawa H. Interest rate option pricing with Poisson-Gaussion forward rate curve processes. Mathematical Finance 1991; 1, 77-94.




DOI: http://dx.doi.org/10.7434/mser.v1i1.16203

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