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Numerical Methods and Volatility Models for Valuing Cliquet Options

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  • H. A. Windcliff
  • P. A. Forsyth
  • K. R. Vetzal

Abstract

Several numerical issues for valuing cliquet options using PDE methods are investigated. The use of a running sum of returns formulation is compared to an average return formulation. Methods for grid construction, interpolation of jump conditions, and application of boundary conditions are compared. The effect of various volatility modelling assumptions on the value of cliquet options is also studied. Numerical results are reported for jump diffusion models, calibrated volatility surface models, and uncertain volatility models.

Suggested Citation

  • H. A. Windcliff & P. A. Forsyth & K. R. Vetzal, 2006. "Numerical Methods and Volatility Models for Valuing Cliquet Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(4), pages 353-386.
    • Handle: RePEc:taf:apmtfi:v:13:y:2006:i:4:p:353-386
    DOI: 10.1080/13504860600839964
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    References listed on IDEAS

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    1. Windcliff, H. & Forsyth, P.A. & Vetzal, K.R., 2006. "Pricing methods and hedging strategies for volatility derivatives," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 409-431, February.
    2. Leif Andersen & Jesper Andreasen, 2000. "Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing," Review of Derivatives Research, Springer, vol. 4(3), pages 231-262, October.
    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    4. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
    5. P. Forsyth & K. Vetzal & R. Zvan, 2002. "Convergence of numerical methods for valuing path-dependent options using interpolation," Review of Derivatives Research, Springer, vol. 5(3), pages 273-314, October.
    6. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    7. T. J. Lyons, 1995. "Uncertain volatility and the risk-free synthesis of derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 117-133.
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    Cited by:

    1. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2017. "Equity-linked annuity pricing with cliquet-style guarantees in regime-switching and stochastic volatility models with jumps," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 46-62.
    2. Marcellino Gaudenzi & Antonino Zanette, 2011. "Pricing cliquet options by tree methods," Computational Management Science, Springer, vol. 8(1), pages 125-135, April.
    3. Alain François-Heude & Ouidad Yousfi, 2014. "On the liquidity of CAC 40 index options market," Post-Print hal-02050806, HAL.
    4. Ludovic Goudenege & Andrea Molent & Antonino Zanette, 2024. "Leveraging Machine Learning for High-Dimensional Option Pricing within the Uncertain Volatility Model," Papers 2407.13213, arXiv.org.
    5. Feng, Yaqin & Wang, Min & Zhang, Yuanqing, 2019. "CVA for Cliquet options under Heston model," The North American Journal of Economics and Finance, Elsevier, vol. 48(C), pages 272-282.

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