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Pricing options under the non-affine stochastic volatility models: An extension of the high-order compact numerical scheme

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  • Shi, Guangping
  • Liu, Xiaoxing
  • Tang, Pan

Abstract

We consider an improvement of a high-order compact finite difference scheme for option pricing in non-affine stochastic volatility models. Upon applying a proper transformation to equate the different coefficients of second-order non-cross derivatives, a high-order compact finite difference scheme is developed to solve the partial differential equation with nonlinear coefficients that the option values satisfied. Based on the local von Neumann stability analysis, a theoretical stability result is obtained under certain restrictions. Numerical experiments are presented showing the convergence and validity of the expansion methods and the important effects of the non-affine coefficient and volatility of volatility on option values.

Suggested Citation

  • Shi, Guangping & Liu, Xiaoxing & Tang, Pan, 2016. "Pricing options under the non-affine stochastic volatility models: An extension of the high-order compact numerical scheme," Finance Research Letters, Elsevier, vol. 16(C), pages 220-229.
    • Handle: RePEc:eee:finlet:v:16:y:2016:i:c:p:220-229
    DOI: 10.1016/j.frl.2015.12.004
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    References listed on IDEAS

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    1. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 55(5), pages 1943-1978, October.
    2. Ballestra, Luca Vincenzo & Cecere, Liliana, 2015. "Pricing American options under the constant elasticity of variance model: An extension of the method by Barone-Adesi and Whaley," Finance Research Letters, Elsevier, vol. 14(C), pages 45-55.
    3. Chourdakis, Kyriakos & Dotsis, George, 2011. "Maximum likelihood estimation of non-affine volatility processes," Journal of Empirical Finance, Elsevier, vol. 18(3), pages 533-545, June.
    4. Kaeck, Andreas & Alexander, Carol, 2012. "Volatility dynamics for the S&P 500: Further evidence from non-affine, multi-factor jump diffusions," Journal of Banking & Finance, Elsevier, vol. 36(11), pages 3110-3121.
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    6. David S. Bates, 2006. "Maximum Likelihood Estimation of Latent Affine Processes," The Review of Financial Studies, Society for Financial Studies, vol. 19(3), pages 909-965.
    7. Hu, Jun & Kanniainen, Juho, 2015. "Asymptotic expansion of European options with mean-reverting stochastic volatility dynamics," Finance Research Letters, Elsevier, vol. 14(C), pages 1-10.
    8. Jones, Christopher S., 2003. "The dynamics of stochastic volatility: evidence from underlying and options markets," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 181-224.
    9. Jun Liu, 2007. "Portfolio Selection in Stochastic Environments," The Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 1-39, January.
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    Cited by:

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    More about this item

    Keywords

    Non-affine stochastic volatility; Option pricing; High-order compact finite difference method; Variable mixed derivatives; Nonlinear coefficients;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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