Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-28T22:59:13.607Z Has data issue: false hasContentIssue false
  • English
  • Français

Market Consistent Valuation of Life Assurance Business

Published online by Cambridge University Press:  10 June 2011

T. J. Sheldon  and
A. D. Smith
T. J. Sheldon
Affiliation:
Deloitte, Horizon House, 28, Upper High Street, Epsom, Surrey KT17 4RS, U.K. Email: [email protected]
A. D. Smith
Affiliation:
Deloitte, Horizon House, 28, Upper High Street, Epsom, Surrey KT17 4RS, U.K. Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In recent years there has been a trend towards market consistent valuation in those institutions for which actuaries have responsibilities. The larger United Kingdom with-profits insurance companies are now preparing realistic balance sheets, both for internal purposes and also at the request of the Financial Services Authority. International accounting standards have been moving to a fair value approach. Pension fund accounting under FRS 17 has also moved in this direction.

In this paper we examine the reasons for the adoption of market consistent valuation and discuss some of the commercial implications and corporate valuation. We consider the methods and assumptions which can be used to develop market consistent valuations of cash flows typically encountered in the liabilities of financial institutions, together with some of the problems inherent in the calibration of models used for the valuation of these cash flows. The volatility assumption is crucial to the valuation of options and guarantees, and we discuss the relationship between historical and implied volatility.

While most insurance companies initially adopted formulae to value their with-profits guarantees, several offices are now using a Monte Carlo simulation approach for their realistic balance sheets. The Monte Carlo approach enables allowance to be made for management discretion in bonus and investment policy, as well as policyholder actions. However, in many cases it is possible to develop analytical formulae for cash flows approximating those payable under insurance contracts.

The valuation formulae have implications for the hedging of embedded guarantees. The authors discuss the construction of hedges for financial risks in with-profits funds, the separate perspectives of policyholders and shareholders, possible funds in which to hold hedging instruments, limitations of capital market hedging tools and the effect of taxation on hedge effectiveness.

Keywords

Market Consistent ValuationRealistic Balance SheetGuaranteesOptionsOption PricingBlack Scholes FormulaArbitrageHistorical and Implied VolatilityVolatility SmileExotic GuaranteesCredit RiskCalibrationMarket DataTaxationMonte Carlo SimulationHedging
Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 10 , Issue 3 , 01 August 2004 , pp. 543 - 605
Copyright
Copyright © Institute and Faculty of Actuaries 2004

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

Abbink, M. & Saker, M. (2002). Getting to grips with fair value. Paper presented to the Staple Inn Actuarial Society.Google Scholar
Altmann, E. & Vanderhoof, I.T. (1998). The fair value of insurance liabilities. Kluwer.Google Scholar
Anderson, N., Breedon, F., Deacon, M., Derry, A. & Murphy, G. (1996). Estimating and interpreting the yield curve. Wiley, Chichester.Google Scholar
Ballotta, L. & Haberman, S. (2003). Guaranteed annuity conversion options and their valuation. Working paper, Cass Business School.CrossRefGoogle Scholar
Bacinello, A.R. & Ortu, F. (1993). Pricing equity-linked life insurance with endogenous minimum guarantees. Insurance: Mathematics and Economics, 12, 245–247.Google Scholar
van Bezooyen, J.T.S., Exley, C.J. & Mehta, S.J.B. (1998). Valuing and hedging guaranteed annuity options. Paper presented to the Institute and Faculty of Actuaries Investment Conference, September 1998, University of Cambridge.Google Scholar
van Bezooyen, J.T.S., Mehta, S.J.B. & Smith, A.D. (2000). Investment strategy and valuation of with profits products. Investment Conference, Institute of Actuaries.Google Scholar
Blight, P., Kapel, A. & Bice, A. (2003). Market-consistent economic valuations for the wealth management industry. Institute of Actuaries of Australia.Google Scholar
Bouwknegt, P. & Pelsser, A. (2001). Market value of insurance contracts with profit sharing. AFIR Colloquium, Toronto.CrossRefGoogle Scholar
Briys, E., Bellelah, M., Mai, M.H. & de Varenne, F. (1998). Options, futures and exotic derivatives. Wiley.Google Scholar
Buhlmann, H.F.F., Delbaen, F., Embrechts, P. & Shiryaev, A.N. (1998). On Esscher transforms in discrete finance models. ASTINBulletin, 28(2), 171–186.Google Scholar
Dempster, M.A.H., Germano, M., Medova, E.A. & Villaverde, M. (2003). Global asset liablity management. British Actuarial Journal, 9, 137–195.CrossRefGoogle Scholar
Dodhia, M. & Sheldon, T.J. (1994). Guaranteed equity products. Paper presented to the Staple Inn Actuarial Society.Google Scholar
Dullaway, D. & Needleman, P. (2004). Realistic liabilities and risk capital margins for with-profits business. A discussion paper, British Actuarial Journal, (to appear).CrossRefGoogle Scholar
Exley, C.J. & Smith, A.D. (2003). The cost of capital for financial firms. Discussion paper presented to the Finance and Investment Conference.Google Scholar
Feldman, K.S., Bergman, B., Cairns, A.J.G., Chaplin, G.B., Gwilt, G.D., Lockyer, P.R. & Turley, F.B. (1998). Report of the fixed-interest working group. British Actuarial Journal, 4, 213–384.CrossRefGoogle Scholar
Financial Services Authority (2003). CP195.Google Scholar
Geske, R. (1979). The valuation of compound options. Journal of Financial Economics, 7, 63–81.CrossRefGoogle Scholar
Goldman, B., Sosin, H. & Gatto, M. (1979). Path dependent options. Journal of Finance, 34, 111.Google Scholar
Griffiths, J., Imam-Sadeque, F., Ong, A. & Smith, A.D. (1997). Actuaries take note - the yield curve is not flat. Investment Conference, Institute of Actuaries.Google Scholar
Grosen, A. & Jorgensen, P.L. (2000). Fair valuation of life insurance liabilities: the impact of interest rate guarantees, surrender options and bonus policies. Insurance: Mathematics and Economics, 26, 37–57.Google Scholar
Hairs, C.J., Belsham, D.J., Bryson, N.M., George, C.M., Hare, D.J.P., Smith, D.A. & Thompson, S. (2001). Fair valuation of liabilities. British Actuarial Journal, 8, 203–299.CrossRefGoogle Scholar
Hancock, J., Huber, P. & Koch, P. (2001). The economics of insurance — how insurers create value for shareholders. Swiss Re Publishing.Google Scholar
Hardy, M.R. (2003). Investment guarantees: modelling and risk management for equity-linked life insurance. Wiley.Google Scholar
Hare, D.J.P., Dickson, J.A., McDade, P.A.P., Morrison, D., Priestley, R.P. & Wilson, G.J. (1999). A market-based approach to pricing with-profits guarantees. British Actuarial Journal, 6, 143–196.Google Scholar
Hibbert, A.J. & Turnbull, C.J. (2003). Measuring and managing the economic risks and costs of with-profits business. British Actuarial Journal, 9, 725–786 and 1141-1154.Google Scholar
Hull, J.C. (2003). Options, futures and other derivative securities. Prentice-Hall, Fifth edition.Google Scholar
Hull, J.C. & White, A. (1990). Pricing interest rate derivative securities. Review of Financial Studies, 3, 573–592.Google Scholar
Jamshidian, F. (1989). An exact bond option formula. Journal of Finance, 44, 205–209.Google Scholar
Jarvis, S., Southall, F. & Varnell, E. (2001). Modern valuation techniques. Paper presented to the Staple Inn Actuarial Society. Market Co nsistent Valuation of L ife Assurance Business 605Google Scholar
Jensen, J.L. (1995). Saddlepoint approximations. Oxford.Google Scholar
Kemp, M.H.M. (1997). Actuaries and derivatives. British ActuarialJournal, 3, 51–162.CrossRefGoogle Scholar
Kipling, M. & Moran, I. (2003). Realistic balance sheets. Presentation to Current Issues in Life Assurance seminar.Google Scholar
Mehta, S.J.B. (1992). Taxation in the assessment of profitability of life assurance products and of life office appraisal values. Transactions of the Faculty of Actuaries, 43, 484–553.CrossRefGoogle Scholar
Mehta, S.J.B. (1999). Supply and demand imbalances in the government bond market. Investment Conference, Institute of Actuaries.Google Scholar
Moran, I., Smith, A.D. & Walczak, . (2003). Why can financial firms charge for diversifiable risk? Discussion paper presented to Bowles Symposium, Society of Actuaries (USA).Google Scholar
Muir, M. & Waller, R. (2003). Twin peaks - the enhanced capital requirements for realistic basis life firms. Paper presented to the Staple Inn Actuarial Society.Google Scholar
Ng, H.M. & Varnell, E. (2003). Frictional Costs. Paper presented to the Staple Inn Actuarial Society.Google Scholar
Ranson, R.H. & Headdon, C.P. (1989). With profits without mystery. Journal of the Institute of Actuaries, 116, 301–325.CrossRefGoogle Scholar
Rogers, L.C.M. & Zane, O. (1999). Saddle-point approximations to option prices. Ann. Appl. Probability, 9, 493–503.Google Scholar
Smith, A.D. (2003). Option pricing with deflators. In Asset and liability management tools, edited by Bernd Scherer, Risk Publications. Smith, A.D. & Speed, C. (1998). Gauge transforms in stochastic models. AFIR Colloquium, Cambridge.Google Scholar
Smith, A.D. & Wilson, T. (2000). Fitting yield curves with long constraints. Financial Options Research Centre, Warwick.Google Scholar
Wilkie, A.D. (1987). An option pricing approach to bonus policy. Journal of the Institute of Actuaries, 114, 21–77.CrossRefGoogle Scholar
Wilkie, A.D., Waters, H.R. & Yang, S. (2003). Reserving, pricing and hedging for policies with guaranteed annuity options. British Actuarial Journal, 9, 263–391 and 10, 101-150.CrossRefGoogle Scholar