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Hedging Costs for Variable Annuities Under Regime-Switching

In: Hidden Markov Models in Finance

Author

Listed:
  • Parsiad Azimzadeh

    (University of Waterloo)

  • Peter A. Forsyth

    (University of Waterloo)

  • Kenneth R. Vetzal

    (University of Waterloo)

Abstract

A general methodology is described in which policyholder behaviour is decoupled from the pricing of a variable annuity based on the cost of hedging it, yielding two weakly coupled systems of partial differential equations (PDEs): the pricing and utility systems. The utility system is used to generate policyholder withdrawal behaviour, which is in turn fed into the pricing system as a means to determine the cost of hedging the contract. This approach allows us to incorporate the effects of utility-based pricing and factors such as taxation. As a case study, we consider the Guaranteed Lifelong Withdrawal and Death Benefits (GLWDB) contract. The pricing and utility systems for the GLWDB are derived under the assumption that the underlying asset follows a Markov regime-switching process. An implicit PDE method is used to solve both systems in tandem. We show that for a large class of utility functions, the pricing and utility systems preserve homogeneity, allowing us to decrease the dimensionality of the PDEs and thus to rapidly generate numerical solutions. It is shown that for a typical contract, the fee required to fund the cost of hedging calculated under the assumption that the policyholder withdraws at the contract rate is an appropriate approximation to the fee calculated assuming optimal consumption. The costly nature of the death benefit is documented. Results are presented which demonstrate the sensitivity of the hedging expense to various parameters.

Suggested Citation

  • Parsiad Azimzadeh & Peter A. Forsyth & Kenneth R. Vetzal, 2014. "Hedging Costs for Variable Annuities Under Regime-Switching," International Series in Operations Research & Management Science, in: Rogemar S. Mamon & Robert J. Elliott (ed.), Hidden Markov Models in Finance, edition 127, chapter 0, pages 133-166, Springer.
    • Handle: RePEc:spr:isochp:978-1-4899-7442-6_6
    DOI: 10.1007/978-1-4899-7442-6_6
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    Citations

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    Cited by:

    1. Godin, Frédéric & Lai, Van Son & Trottier, Denis-Alexandre, 2019. "Option pricing under regime-switching models: Novel approaches removing path-dependence," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 130-142.
    2. Gerber, Hans U. & Shiu, Elias S.W. & Yang, Hailiang, 2015. "Geometric stopping of a random walk and its applications to valuing equity-linked death benefits," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 313-325.
    3. Frédéric Godiny & Van Son Lai & Denis-Alexandre Trottier, 2019. "Option Pricing Under Regime-Switching Models: Novel Approaches Removing Path-Dependence," Working Papers 2019-014, Department of Research, Ipag Business School.
    4. Denis-Alexandre Trottier & Frédéric Godin & Emmanuel Hamel, 2018. "On Fund Mapping Regressions Applied to Segregated Funds Hedging Under Regime-Switching Dynamics," Risks, MDPI, vol. 6(3), pages 1-15, August.

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