Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-13T11:28:36.379Z Has data issue: false hasContentIssue false

Fair Valuation of Life Insurance Contracts Under a Correlated Jump Diffusion Model

Published online by Cambridge University Press:  09 August 2013

Yinghui Dong*
Affiliation:
Department of Mathematics and The Center for Financial Engineering, Soochow University, Suzhou, P.R.China, Department of Mathematics, Suzhou Science and Technology University, Suzhou, P.R.China, Email: [email protected]

Abstract

In this paper, we study the fair valuation of participating life insurance contract, which is one of the most common life insurance products, under the jump diffusion model with the consideration of default risk. The participating life insurance contracts considered here can be expressed as portfolios of options as shown by Grosen and Jørgensen (1997). We use the Laplace transforms methods to price these options.

Type
Research Article
Copyright
Copyright © International Actuarial Association 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abate, J. and Whitt, W. (1992) The Fourier-series method for inverting transforms of probability distributions. Queueing Systems 10, 588.Google Scholar
Bacinello, A.R. (2001) Fair pricing of life insurance participating contracts with a minimum interest rate guarantees. Astin Bulletin 31, 275297.CrossRefGoogle Scholar
Bacinello, A.R. (2003) Pricing guaranteed life insurance participating policies with annual premiums and surrender option. North American Actuarial Journal 7(3), 117.CrossRefGoogle Scholar
Ballotta, L. (2005) A Lévy Process-Based Framework for the Fair Valuation of Participating Life Insurance Contracts. Special Issue of Insurance: Mathematics and Economics 37(2), 173196.Google Scholar
Ballotta, L., Haberman, S. and Wang, N. (2006) Guarantees in with-profit and unitized with profit life insurance contracts: fair valuation problem in presence of the default option. Journal of Risk and Insurance 73(1), 97121.Google Scholar
Brennan, M.J. and Schwartz, E.S. (1976) The pricing of equity-linked life insurance policies with an asset value guarantee. Journal of Financial Economics 3, 195213.Google Scholar
Briys, E. and de Varenne, F. (1994) Life insurance in a contingent claim framework: pricing and regulatory implications. The Geneva Papers on Risk and Insurance Theory 19(1), 5372.CrossRefGoogle Scholar
Briys, E. and de Varenne, F. (1997) On the risk of life insurance liabilities: debunking some common pitfalls. Journal of Risk Insurance 64(4), 673694.CrossRefGoogle Scholar
Briys, E. and de Varenne, F. (1997) Valuing risky fixed rate debt: an extension. Journal of Financial and Quantitative Analysis 32(2), 239248.Google Scholar
Bernard, C., Le Courtois, O. and Quittard-Pinon, F. (2005) Market value of life insurance contracts under stochastic interest rates and default risk. Insurance: Mathematics and Economics 36(3), 499516.Google Scholar
Cai, N. and Kou, S.G. (2007) Option pricing under a hyper-exponential jump diffusion model. Working paper.Google Scholar
Cai, N. (2009) On first passage times of a hyper-exponential jump diffusion process. Operations Research Letters 37, 127134.CrossRefGoogle Scholar
Chen, A. and Suchanechi, M. (2007) Default risk, bankruptcy procedures and the market value of life insurance liabilities. Insurance: Mathematics and Economics 40, 231255.Google Scholar
Chi, Y.C. (2010) Analysis of Expected Discounted Penalty Function for a General Jump-Diffusion Risk Model and Applications in Finance Insurance: Mathematics and Economics 46(2), 385396.Google Scholar
Cossette, H. and Marceau, E. (2000) The discrete-time model with correlated classes of businesses. Insurance: Mathematics and Economics 26, 133149.Google Scholar
Gerber, H.U. and Shiu, E.S.W. (2005) The time value of ruin in a Sparre Andersen model. North American Actuarial Journal 9(2), 4984.Google Scholar
Grosen, A. and Jørgensen, P. (1997) Valuation of early exercisable interest rate guarantees. Journal of Risk Insurance 64(3), 481503.Google Scholar
Grosen, A. and Jørgensen, P. (2002) Life insurance liabilities at market value: an analysis of insolvency risk, bonus policy, and regulatory intervention rules in a barrier option framework. Journal of Risk Insurance 69(1), 6391.Google Scholar
Huang, J.Z. and Huang, M. (2003) How much of the corporate-treasury yield spread is due to credit risk? SSRN elibrary, http://ssrn.com/abstract=307360. Google Scholar
Kou, S.G. (2002) A Jump Diffusion Model for Option Pricing. Management Science 48, 10861101.Google Scholar
Kou, S.G. and Wang, H. (2004) Option pricing under a double exponential jump diffusion model. Management Science 50, 11781192.CrossRefGoogle Scholar
Kou, S.G. and Wang, H. (2003) First passage times of a jump diffusion process. Advances in Applied Probability 35, 427445.Google Scholar
Kou, S.G., Petrella, G. and Wang, H. (2005) Pricing path-dependent options with jump risk via Laplace transforms. Kyoto Economic Review 74(1), 123.Google Scholar
Le Courtois, O. and Quittard-Pinon, F. (2008) Fair Valuation of Participating Life Insurance Contracts with Jump Risk. The Geneva Risk and Insurance Review 33(2), 106136.CrossRefGoogle Scholar
Pelsser, A. (2000) Pricing double barrier options using Laplace transforms. Finance and Stochastics 4, 95104.Google Scholar
Petrella, G. (2004) An extension of the Euler Laplace transform inversion algorithm with applications in option pricing. Operations Research Letters 32, 380389.Google Scholar
Riesner, M. (2006) Hedging Life Insurance Contracts in a Lévy Process Financial Market. Insurance: Mathematics and Economics 38(3), 599608.Google Scholar
Wang, G.J. and Yuen, K.C. (2005) On a correlated aggregate claims model with thinning-dependence structure. Insurance: Mathematics and Economics 36, 456468.Google Scholar
Zhang, Z.M., Yang, H. and Li, S.M. (2010). The perturbed compound Poisson risk model with two-sided jumps. Journal of Computational and Applied Mathematics 233, 17731784.Google Scholar