Simulations for Hedging Financial Contracts with Optimal Decisions
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.
Keywordsstochastic simulation mutual fund guarantees hedging segregated funds variable annuities investor behaviour modelling.
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- Broadie, M. and Glasserman, P. (1998). A stochastic mesh method for pricing high dimensional American options. Eighth Annual Derivative Securities Conference, Boston.Google Scholar
- Falloon, W. (1999). Canada’s option nightmare. Risk, 12 (8): 60.Google Scholar
- 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
- Wilmott, P., Howison, S., and Dewynne, J. (1993). Option Pricing: Mathematical Models and Computation. Oxford Financial Press.Google Scholar
- 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