Hostname: page-component-6b989bf9dc-6f5p8 Total loading time: 0.001 Render date: 2024-04-14T15:04:53.496Z Has data issue: false hasContentIssue false

PRICING AND SOLVENCY OF VALUE-MAXIMIZING LIFE ANNUITY PROVIDERS

Published online by Cambridge University Press:  08 October 2013

Maathumai Nirmalendran
Affiliation:
Finity Consulting, Level 7, 155 George St, Sydney, Australia E-Mail: Maathu.Nirmalendran@finity.com.au
Michael Sherris*
Affiliation:
Risk and Actuarial Studies and ARC Centre of Excellence in Population Ageing Research (CEPAR), Australian School of Business, University of New South Wales, New South Wales, Australia
Katja Hanewald
Affiliation:
Risk and Actuarial Studies and ARC Centre of Excellence in Population Ageing Research (CEPAR), Australian School of Business, University of New South Wales, New South Wales, Australia E-Mail: k.hanewald@unsw.edu.au

Abstract

This paper provides a detailed quantitative assessment of the impact of capital and default probability on product pricing and shareholder value for a life insurer providing life annuities. A multi-period cash flow model, allowing for stochastic mortality and asset returns, imperfectly elastic product demand, as well as frictional costs, is used to derive value-maximizing capital and pricing strategies for a range of one-year default probability levels reflecting differences in regulatory regimes including Solvency II. The model is calibrated using realistic assumptions. The sensitivity of results is assessed. The results show that value-maximizing life insurers should target higher solvency levels than the Solvency II regulatory one-year 99.5% probability under assumptions of reasonable levels of policyholder's aversion to insolvency risk. Even in the case of less restrictive solvency probabilities, policyholder price elasticity and solvency preferences are shown to be important factors for a life insurer's value-maximizing strategy.

Type
Research Article
Copyright
Copyright © ASTIN Bulletin 2013 

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

[1]AM Best (2007) Best's idealized default matrix. www.ambest.com, accessed September 2011.Google Scholar
[2]Australian Bureau of Statistics (2010) Australian demographic statistics. www.abs.gov.au, accessed September 2011.Google Scholar
[3]Australian Prudential Regulatory Authority (APRA) (2010). Half Yearly Life Insurance Bulletin June 2010. www.apra.gov.au, accessed July 2011.Google Scholar
[4]Australian Prudential Regulatory Authority (APRA) (2011). Life insurance industry consolidation. APRA Insight Issue One 2011. www.apra.gov.au, accessed December 2011.Google Scholar
[5]Australian Tax Office (2011) Simplified imputation — Overview of the imputation system. www.ato.gov.au, accessed September 2011.Google Scholar
[6]Babbel, D.F. and Merrill, C.B. (2006) Rational decumulation. Wharton Financial Institutions Center Working Paper No. 06-14, Wharton School, University of Pennsylvania, Philadelphia.CrossRefGoogle Scholar
[7]Challenger Life Company Limited (2011) Challenger guaranteed annuity (liquid lifetime). Product Disclosure Statement, dated 21 October 2011.Google Scholar
[8]Ganegoda, A. and Bateman, H. (2008) Australia's disappearing market for life annuities. Centre for Pensions and Superannuation Discussion Paper 01/08, Australian School of Business, University of New South Wales, Sydney.Google Scholar
[9]Gründl, H., Post, T. and Schulze, R. (2006) To hedge or not to hedge: Managing demographic risk in life insurance companies. Journal of Risk and Insurance, 73 (1), 1941.CrossRefGoogle Scholar
[10]Hull, J.C. (2009) Options, Futures and Other Derivatives, 7th ed.Upper Saddle River, NJ: Prentice Hall.Google Scholar
[11]Human Mortality Database (2011) University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany). www.mortality.org or www.humanmortality.de, accessed March 2011.Google Scholar
[12]Lee, R. D. and Carter, L. (1992) Modeling and forecasting U.S. mortality. Journal of the American Statistical Association, 87 (419), 659671.Google Scholar
[13]Munch, P. and Smallwood, D. (1981) Theory of solvency regulation in the property and casualty insurance industry. In Studies in Public Regulation (ed. Fromm, G.), pp. 119167. Cambridge: MIT Press.Google Scholar
[14]Rees, R., Gravelle, H. and Wambach, A. (1999) Regulation of insurance markets. Geneva Papers on Risk and Insurance, 24 (1), 5568.CrossRefGoogle Scholar
[15]Schade, C., Kunreuther, H., Koellinger, P. and Kaas, K.P. (2009) Protecting against low probability disasters: A large stakes experiment. Wharton Risk Center Working Paper. Wharton School, University of Pennsylvania, Philadelphia.Google Scholar
[16]Swiss, Re (2005) Insurer's cost of capital and economic value creation: Principles and practical implications. Swiss Re Technical Publishing Sigma No 3.Google Scholar
[17]Van Deventer, D.R., Imai, K. and Mesler, M. (2005) Advanced Financial Risk Management: Tools & Techniques for Integrated Credit Risk and Interest Rate Risk Managements. Singapore: John Wiley.Google Scholar
[18]Vasicek, O. (1977) An equilibrium characterisation of the term structure. Journal of Financial Economics, 5 (2), 177188.CrossRefGoogle Scholar
[19]Wills, S. and Sherris, M. (2010) Securitization, structuring and pricing of longevity risk. Insurance: Mathematics and Economics, 46 (1), 173185.Google Scholar
[20]Yow, S. and Sherris, M. (2008) Enterprise risk management, insurer value maximisation, and market frictions. ASTIN Bulletin 38 (1), 293339.CrossRefGoogle Scholar
[21]Zanjani, G. (2002) Pricing and capital allocation in catastrophe insurance. Journal of Financial Economics, 65 (2), 283305.CrossRefGoogle Scholar
[22]Zimmer, A., Gründl, H. and Schade, C. (2011) Price-default risk-demand-curves and the optimal corporate risk strategy of insurers: A behavioral approach, Working paper. School of Business and Economics, Humboldt-Universität zu Berlin, Berlin.Google Scholar
[23]Zimmer, A., Schade, C. and Gründl, H. (2009) Is default risk acceptable when purchasing insurance? Experimental evidence for different probability representations, reasons for default, and framings. Journal of Economic Psychology, 30 (1), 1123.CrossRefGoogle Scholar