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Simulations for Hedging Financial Contracts with Optimal Decisions

Case Study: Segregated Fund Guarantees
  • H. Windcliff
  • P. A. Forsyth
  • K. R. Vetzal
  • W. J. Morland
Part of the Applied Optimization book series (APOP, volume 74)

Abstract

Simulation is a powerful technique for quantifying risk exposure. We present here a methodology for simulating the performance of hedging strategies for financial contracts with embedded optimization features. As a case study, we provide simulations of mutual fund guarantees offering a reset provision. In Canada, these types of contracts are known as segregated funds. The optimization component of these contracts allows the holder to lock in market gains, typically up to two or four times per calendar year. Recently, Canadian regulators have imposed new capital requirements for firms selling these contracts. However, these requirements can be reduced if hedging strategies are put in place. The techniques presented here would allow companies to evaluate their proposed hedging strategies and quantify their remaining risk exposure. We study the effect of non-optimal investor behaviour on the hedging of these contracts. In particular, we present results for the heuristic use of the reset feature; for example, locking in whenever the underlying asset value has risen by 15% as recently suggested by a Canadian Institute of Actuaries task force on segregated funds.

Keywords

stochastic simulation mutual fund guarantees hedging segregated funds variable annuities investor behaviour modelling. 

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References

  1. Boyle, P. P. and Emanuel, D. (1980). Discretely adjusted option hedges. Journal of Financial Economics, 8: 259–282.CrossRefGoogle Scholar
  2. Boyle, P. P. and Hardy, M. R. (1997). Reserving for maturity guarantees: Two approaches. Insurance: Mathematics & Economics, 21: 113–127.CrossRefGoogle Scholar
  3. Boyle, P. P., Kolkiewicz, A. W., and Tan, K. S. (2001). Valuation of the reset options embedded in some equity-linked insurance products. NorthAmerican Actuarial Journal, 5 (3): 1–18.CrossRefGoogle Scholar
  4. Broadie, M. and Glasserman, P. (1998). A stochastic mesh method for pricing high dimensional American options. Eighth Annual Derivative Securities Conference, Boston.Google Scholar
  5. Duffle, D. and Pan, J. (1997). An overview of value at risk. Journal of Derivatives, 4 (3): 7–49.CrossRefGoogle Scholar
  6. Falloon, W. (1999). Canada’s option nightmare. Risk, 12 (8): 60.Google Scholar
  7. Joy, C., Boyle, P. P., and Tan, K. S. (1996). Quasi-Monte Carlo methods in numerical finance. Management Science, 42: 926–938.CrossRefGoogle Scholar
  8. Merton, R. (1973). The theory of rational option pricing. Bell Journal of Economics and Management Science, 4: 141–183.CrossRefGoogle Scholar
  9. Milevsky, M. and Posner, S. E. (2001). The Titanic option: Valuation of the guaranteed minimum death benefit in variable annuities and mutual funds. Journal of Risk and Insurance, 68: 55–79.Google Scholar
  10. Wilmott, P., Howison, S., and Dewynne, J. (1993). Option Pricing: Mathematical Models and Computation. Oxford Financial Press.Google Scholar
  11. Windcliff, H., Forsyth, R A., and Vetzal, K. R. (2001a). Valuation of segregated funds: Shout options with maturity extensions. Insurance: Mathematics & Economics, 29: 1–21.CrossRefGoogle Scholar
  12. Windcliff, H., Forsyth, P. A., and Vetzal, K. R. (2001b). Shout options: A framework for pricing contracts which can be modified by the investor. Journal of Computational and Applied Mathematics, 134: 213–241.CrossRefGoogle Scholar
  13. Windcliff, H., Le Roux, M., Forsyth, P. A., and Vetzal, K. R. (2002). Understanding the behaviour and hedging of segregated funds offering the reset feature. North American Actuarial Journal, forthcoming.Google Scholar
  14. Wirch, J. L. and Hardy, M. R. (1999). A synthesis of risk measures for capital adequacy. Insurance: Mathematics & Economics, 25: 337–347.CrossRefGoogle Scholar
  15. Zvan, R., Forsyth, P. A., and Vetzal, K. R. (1998). Penalty methods for American options with stochastic volatility. Journal of Computational and Applied Mathematics, 91: 119–218.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • H. Windcliff
    • 1
  • P. A. Forsyth
    • 1
  • K. R. Vetzal
    • 2
  • W. J. Morland
    • 3
  1. 1.Department of Computer ScienceUniversity of WaterlooWaterlooCanada
  2. 2.Centre for Advanced Studies in FinanceUniversity of WaterlooWaterlooCanada
  3. 3.Algorithmics IncorporatedTorontoCanada

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