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Pricing Financial Derivatives by Gram-Charlier Expansions

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  • Yin-Hei (Michael) Cheng

    (Department of Statistics & Actuarial Science, School of Accounting & Finance, University of Waterloo, Canada)

  • Tony S. Wirjanto

    (Department of Statistics & Actuarial Science, School of Accounting & Finance, University of Waterloo, Canada)

Abstract

In this paper we provide several applications of Gram-Charlier expansions in financial derivative pricing. We first give an exposition on how to calculate swaption prices under a two-factor Cox-Ingersoll-Ross (CIR2) model. Then we apply this method to an extended version of the model (CIR2++). We also develop a procedure to calculate European call options under Heston’s model of stochastic volatility by the Gram-Charlier Expansions.

Suggested Citation

  • Yin-Hei (Michael) Cheng & Tony S. Wirjanto, 2013. "Pricing Financial Derivatives by Gram-Charlier Expansions," Working Paper series 61_13, Rimini Centre for Economic Analysis.
  • Handle: RePEc:rim:rimwps:61_13
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    References listed on IDEAS

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    1. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    2. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    3. 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 637-654, May-June.
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