×

Capital forbearance, ex ante life insurance guaranty schemes, and interest rate uncertainty. (English) Zbl 1414.91204

Summary: Insurance guaranty funds have been adopted in many countries to compensate policyholders for losses resulting from insurers’ insolvencies. In this article we focus on the risk-based premiums in ex ante insurance guaranty schemes since a preassessment mechanism could reduce the shareholders’ incentive to engage in risk-taking behavior. We derive the closed-form solutions of the risk-based premium charged by the insurance guaranty fund in a setting that incorporates financial leverage, asset allocation, early closure, and capital forbearance during the grace period. Most importantly, we assume that the interest rate is stochastic, and we find that the premium is underpriced if the uncertainty of the interest rate is neglected by the insurance guaranty fund. Moreover, the influence of stochastic interest rate for the premium is more significant when we consider the capital forbearance mechanism. The impacts of the key factors in our model that decide the fair premium of the guaranty fund are examined numerically. The results of our analysis could provide valuable insights for regulators in terms of revising regulatory policies and insurance guaranty schemes.

MSC:

91B30 Risk theory, insurance (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Bacinello, A. R., Fair Pricing of Life Insurance Participating Policies with a Minimum Interest Rate Guaranteed, ASTIN Bulletin, 31, 275-297, (2001) · Zbl 1098.91537
[2] Ballotta, L., A Levy Process-Based Framework for the Fair Valuation of Participating Life Insurance Contracts, Insurance Mathematics and Economics, 37, 173-196, (2005) · Zbl 1125.91060
[3] Bernard, C.; Le Courtois, O.; Quittard-Pinon, F., A Study of Mutual Insurance for Bank Deposits, Geneva Risk and Insurance Review, 30, 129-146, (2005)
[4] Bernard, C.; Le Courtois, O.; Quittard-Pinon, F., Market Value of Life Insurance Contracts under Stochastic Interest Rates and Default Risk, Insurance Mathematics and Economics, 36, 499-516, (2005) · Zbl 1242.60068
[5] Boulier, J. F.; Huang, S. J.; Taillard, G., Optimal Management under Stochastic Rates: The Case of a Protected Defined Contribution Pension Fund, Insurance Mathematics and Economics, 28, 173-189, (2001) · Zbl 0976.91034
[6] Briys, E.; de Varenne, F., Life Insurance in a Contingent Claim Framework: Pricing and Regulatory Implications, Geneva Papers on Risk and Insurance Theory, 19, 53-72, (1994)
[7] Briys, E.; de Varenne, F., On the Risk of Insurance Liabilities: Debunking Some Common Pitfalls, Journal of Risk and Insurance, 64, 673-694, (1997)
[8] Chen, A., A Risk-Based Model for the Valuation of Pension Insurance, Insurance Mathematics and Economics, 49, 401-409, (2011) · Zbl 1228.91030
[9] Chen, A.; Suchanecki, M., Default Risk, Bankruptcy Procedures and the Market Value of Life Insurance Liabilities, Insurance Mathematics and Economics, 40, 231-255, (2007) · Zbl 1141.91494
[10] Cummins, J. D., Risk-Based Premiums for Insurance Guaranty Funds, Journal of Finance, 43, 823-839, (1988)
[11] Duan, J. C.; Moreau, A. F.; Sealey, C. W., Deposit Insurance and Bank Interest Rate Risk: Pricing and Regulatory Implications, Journal of Banking and Finance, 19, 1091-1108, (1995)
[12] Duan, J. C.; Simonato, J. G., Maximum Likelihood Estimation of Deposit Insurance Value with Interest Rate Risk, Journal of Empirical Finance, 9, 109-132, (2002)
[13] Duan, J. C.; Yu, M. T., Assessing the Cost of Taiwan’s Deposit Insurance, Pacific-Basin Finance Journal, 2, 73-90, (1994)
[14] Duan, J. C.; Yu, M. T., Capital Standard, Forbearance and Deposit Insurance Pricing under GARCH, Journal of Banking and Finance, 23, 1691-1706, (1999)
[15] Duan, J. C.; Yu, M. T., Fair Insurance Guaranty Premia in the Present of Risk-Based Capital Regulations, Stochastic Interest Rate and Catastrophe Risk, Journal of Banking and Finance, 29, 2435-2454, (2005)
[16] Duncan, M. P.; Randall, E. D., Property-Liability Post-Assessment Guaranty Funds, Issues in Insurance, 19, 239-302, (1987), , Malvern, PA: American Institute for Property and Liability Underwriters, , Malvern, PA
[17] Grosen, A.; Jørgensen, P. L., 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 and Insurance, 69, 63-91, (2002)
[18] Han, L. M.; Lai, G. C.; Witt, R. C., A Financial-Economic Evaluation of Insurance Guaranty Fund System: An Agency Cost Perspective, Journal of Banking and Finance, 21, 1107-1129, (1997)
[19] Hwang, D. Y.; Shie, F. S.; Wang, K.; Lin, J. C., The Pricing of Deposit Insurance Considering Bankruptcy Costs and Closure Policies, Journal of Banking and Finance, 33, 1909-1919, (2009)
[20] Jeanblanc, M.; Yor, M.; Chesney, M., Mathematical Methods for Financial Markets, (2009), Springer Finance: Springer Finance, , London: Springer, Springer Finance: Springer Finance, , London · Zbl 1205.91003
[21] Krogh, H. C., Insurer Post-Insolvency Guaranty Funds, Journal of Risk and Insurance, 39, 431-450, (1972)
[22] Labart, C.; Lelong, J., Pricing Parisian Options Using Laplace Transforms, Bankers, Markets and Investors, 99, 29-43, (2009) · Zbl 1190.91143
[23] Le Courtois, O.; Quittard-Pinon, F., Fair Valuation of Participating Life Insurance Contracts with Jump Process, Geneva Risk and Insurance Review, 33, 106-136, (2008)
[24] Lee, S. C.; Lee, J. P.; Yu, M. T., Bank Capital Forbearance and Valuation of Deposit Insurance, Canadian Journal of Administrative Sciences, 22, 220-229, (2005)
[25] Marcus, A.; Bodie, Z.; Shoven, J. B.; Wise, D. A., Corporate Pension Policy and the Value of PBGC Insurance, Issues in Pension Economics, 49-80, (1987), , Chicago: University of Chicago Press, , Chicago
[26] Merton, R. C., An Analytic Derivation of the Cost of Deposit Insurance and Loan Guarantees, Journal of Banking and Finance, 1, 3-11, (1977)
[27] Insurance Guarantee Schemes in the EU: Comparative Analysis of Existing Schemes, Analysis of Problems and Evaluation of Options. A final report for European Commission DG Internal Market and Services, United Kingdom, (2007)
[28] Pennacchi, G. G.; Lewis, C. M., The Value of Pension Benefit Guaranty Corporation Insurance, Journal of Money, Credit and Banking, 26, 735-753, (1994)
[29] Ronn, E. I.; Verma, A. K., Pricing Risk-Adjusted Deposit Insurance: An Option-Based Model, Journal of Finance, 41, 871-895, (1986)
[30] Rutkowski, M., Self-financing Trading Strategies for Sliding, Rolling-Horizon, and Consol Bonds, Mathematical Finance, 9, 361-385, (1999) · Zbl 0996.91072
[31] Sharpe, W. F., Corporate Pension Funding Policy, Journal of Financial Economics, 3, 183-193, (1976)
[32] Tanskanen, A. J.; Lukkarinen, J., Fair Valuation of Path-Dependent Participating Life Insurance Contracts, Insurance Mathematics and Economics, 33, 595-609, (2003) · Zbl 1103.91373
[33] Vasicek, O., An Equilibrium Characterization of the Term Structure, Journal of Financial Economics, 5, 177-188, (1977) · Zbl 1372.91113
[34] Yang, S. Y.; Hwang, Y. W.; Chang, S. C., The Bankruptcy Cost of Life Insurance Industry under Regulatory Forbearance: An Embedded Option Approach, North American Actuarial Journal, 16, 513-523, (2012) · Zbl 1291.91134
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.