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Real World Pricing of Long Term Cash-Linked Annuities and Equity-Linked Annuities with Cash-Linked Guarantees

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Abstract

This paper proposes a paradigm shift in the valuation of long term cash-linked annuities and equity-linked annuities with cash-linked guarantees, away from classical no-arbitrage pricing towards pricing under the real world probability measure. In contrast to risk neutral pricing, which is a form of relative pricing, the long term average excess return of the equity market comes into play. Instead of the savings account, the numeraire portfolio is employed as the fundamental unit of value in the analysis. The numeraire portfolio is the strictly positive, tradable portfolio that when used as benchmark makes all benchmarked nonnegative portfolios supermartingales. Intuitively, benchmarked portfolios are in the mean downward trending or trendless. The benchmarked real world price of a benchmarked contingent claim equals its real world conditional expectation. This yields the minimal possible price for its hedgeable part and minimizes the variance for its hedge error. Classical actuarial and risk neutral pricing emerge as special cases of the proposed real world pricing. In long term liability and asset valuation, the proposed real world pricing can lead to signi cantly lower prices than suggested by classical approaches. The existence of an equivalent risk neutral probability measure is not required.

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Bibliographic Info

Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 338.

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Length: 39
Date of creation: 01 Nov 2013
Date of revision:
Handle: RePEc:uts:rpaper:338

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Keywords: long term contracts; real world pricing; actuarial pricing; risk neutral pricing; numeraire portfolio; law of the minimal price; strong arbitrage; hedge error; diversi cation;

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  1. Grosen, Anders & Lochte Jorgensen, Peter, 2000. "Fair valuation of life insurance liabilities: The impact of interest rate guarantees, surrender options, and bonus policies," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 37-57, February.
  2. Bacinello, Anna Rita & Ortu, Fulvio, 1993. "Pricing equity-linked life insurance with endogenous minimum guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 12(3), pages 245-257, June.
  3. Platen, Eckhard, 2000. "A minimal financial market model," SFB 373 Discussion Papers 2000,91, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  4. Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 443-468, December.
  5. Aase Nielsen, J. & Sandmann, Klaus, 1995. "Equity-linked life insurance: A model with stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 16(3), pages 225-253, July.
  6. Bacinello, Anna Rita & Ortu, Fulvio, 1996. "Fixed income linked life insurance policies with minimum guarantees: Pricing models and numerical results," European Journal of Operational Research, Elsevier, vol. 91(2), pages 235-249, June.
  7. Bacinello, Anna Rita, 2005. "Endogenous model of surrender conditions in equity-linked life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 270-296, October.
  8. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Research Paper Series 129, Quantitative Finance Research Centre, University of Technology, Sydney.
  9. Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.
  10. Truc Le & Eckhard Platen, 2006. "Approximating the growth optimal portfolio with a diversified world stock index," Journal of Risk Finance, Emerald Group Publishing, vol. 7(5), pages 559-574, November.
  11. Alexander Melnikov & Yuliya Romanyuk, 2008. "Efficient Hedging And Pricing Of Equity-Linked Life Insurance Contracts On Several Risky Assets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(03), pages 295-323.
  12. OECD & Nuclear Energy Agency, 2008. "Summary Notes," Nuclear Law Bulletin, OECD Publishing, vol. 2008(2), pages 27-28.
  13. Eckhard Platen, 2004. "A Benchmark Approach to Finance," Research Paper Series 138, Quantitative Finance Research Centre, University of Technology, Sydney.
  14. David F. Babbel & Craig Merrill, 1997. "Economic Valuation Models for Insurers," Center for Financial Institutions Working Papers 97-44, Wharton School Center for Financial Institutions, University of Pennsylvania.
  15. Michael J. Brennan and Eduardo S. Schwartz., 1979. "A Continuous-Time Approach to the Pricing of Bonds," Research Program in Finance Working Papers 85, University of California at Berkeley.
  16. Grosen, Anders & Løchte Jørgensen, Peter, 2001. "Life Insurance Liabilities at Market Value," Finance Working Papers 01-4, University of Aarhus, Aarhus School of Business, Department of Business Studies.
  17. Richard D. Phillips & J. David Cummins & Franklin Allen, 1996. "Financial Pricing of Insurance in the Multiple Line Insurance Company," Center for Financial Institutions Working Papers 96-09, Wharton School Center for Financial Institutions, University of Pennsylvania.
  18. OECD & Nuclear Energy Agency, 2008. "Notes sommaires," Bulletin de droit nucléaire, OECD Publishing, vol. 2008(2), pages 29-31.
  19. Eckhard Platen & Renata Rendek, 2010. "Approximating the Numeraire Portfolio by Naive Diversification," Research Paper Series 281, Quantitative Finance Research Centre, University of Technology, Sydney.
  20. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  21. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
  22. Nielsen, J. Aase & Klaus Sandmann, 1995. "Uniqueness of the Fair Premium for Equity-Linked Life Insurance Contracts," Discussion Paper Serie B 327, University of Bonn, Germany, revised Mar 1996.
  23. Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992. "Option Pricing Under Incompleteness and Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 153-187.
  24. Bilodeau, Claire, 1997. "Better late than never: The case of the rollover option," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 103-111, November.
  25. Tanskanen, Antti Juho & Lukkarinen, Jani, 2003. "Fair valuation of path-dependent participating life insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 595-609, December.
  26. Brennan, Michael J. & Schwartz, Eduardo S., 1979. "A continuous time approach to the pricing of bonds," Journal of Banking & Finance, Elsevier, vol. 3(2), pages 133-155, July.
  27. Melnikov, Alexander & Romaniuk, Yulia, 2006. "Evaluating the performance of Gompertz, Makeham and Lee-Carter mortality models for risk management with unit-linked contracts," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 310-329, December.
  28. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
  29. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
  30. Moore, Kristen S. & Young, Virginia R., 2003. "Pricing equity-linked pure endowments via the principle of equivalent utility," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 497-516, December.
  31. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
  32. Jaimungal, Sebastian & Young, Virginia R., 2005. "Pricing equity-linked pure endowments with risky assets that follow Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 329-346, June.
  33. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
  34. Costabile, Massimo & Massabó, Ivar & Russo, Emilio, 2008. "A binomial model for valuing equity-linked policies embedding surrender options," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 873-886, June.
  35. Milevsky, Moshe A. & David Promislow, S., 2001. "Mortality derivatives and the option to annuitise," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 299-318, December.
  36. Chi Chiu Chu & Yue Kuen Kwok, 2007. "Valuation Of Guaranteed Annuity Options In Affine Term Structure Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 363-387.
  37. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  38. Constantinos Kardaras & Eckhard Platen, 2008. "Multiplicative Approximation of Wealth Processes Involving No-Short-Sale Strategies," Research Paper Series 240, Quantitative Finance Research Centre, University of Technology, Sydney.
  39. Hans Buhlmann & Eckhard Platen, 2002. "A Discrete Time Benchmark Approach for Finance and Insurance," Research Paper Series 74, Quantitative Finance Research Centre, University of Technology, Sydney.
  40. Brennan, Michael J. & Schwartz, Eduardo S., 1976. "The pricing of equity-linked life insurance policies with an asset value guarantee," Journal of Financial Economics, Elsevier, vol. 3(3), pages 195-213, June.
  41. Adair Turner, 2006. "Pensions, Risks, and Capital Markets," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 559-574.
  42. Siu, Tak Kuen, 2005. "Fair valuation of participating policies with surrender options and regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 533-552, December.
  43. Windcliff, H. & Forsyth, P. A. & Vetzal, K. R., 2001. "Valuation of segregated funds: shout options with maturity extensions," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 1-21, August.
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