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Efficient Pricing of European-Style Options Under Heston's Stochastic Volatility Model

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  • Zhylyevskyy, Oleksandr

Abstract

Heston's stochastic volatility model is frequently employed by finance researchers and practitioners. Fast pricing of European-style options in this setting has considerable practical significance. This paper derives a computationally efficient formula for the value of a European-style put under Heston's dynamics, by utilizing a transform approach based on inverting the characteristic function of the underlying stock's log-price and by exploiting the characteristic function's symmetry. The value of a European-style call is computed using a parity relationship. The required characteristic function is obtained as a special case of a more general solution derived in prior research. Computational advantage of the option value formula is illustrated numerically. The method can help to mitigate the time cost of algorithms that require repeated evaluation of European-style options under Heston's dynamics.

Suggested Citation

  • Zhylyevskyy, Oleksandr, 2012. "Efficient Pricing of European-Style Options Under Heston's Stochastic Volatility Model," Staff General Research Papers Archive 34827, Iowa State University, Department of Economics.
  • Handle: RePEc:isu:genres:34827
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    References listed on IDEAS

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    1. Oleksandr Zhylyevskyy, 2010. "A fast Fourier transform technique for pricing American options under stochastic volatility," Review of Derivatives Research, Springer, vol. 13(1), pages 1-24, April.
    2. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    3. Geske, Robert & Johnson, Herb E, 1984. "The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-1524, December.
    4. 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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    Cited by:

    1. Lu, Xiaoping & Putri, Endah R.M., 2020. "A semi-analytic valuation of American options under a two-state regime-switching economy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    2. Chen, Ding & Härkönen, Hannu J. & Newton, David P., 2014. "Advancing the universality of quadrature methods to any underlying process for option pricing," Journal of Financial Economics, Elsevier, vol. 114(3), pages 600-612.
    3. Zhylyevskyy, Oleksandr, 2012. "Joint Characteristic Function of Stock Log-Price and Squared Volatility in the Bates Model and Its Asset Pricing Applications," Staff General Research Papers Archive 35559, Iowa State University, Department of Economics.
    4. Mrázek, Milan & Pospíšil, Jan & Sobotka, Tomáš, 2016. "On calibration of stochastic and fractional stochastic volatility models," European Journal of Operational Research, Elsevier, vol. 254(3), pages 1036-1046.

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    More about this item

    Keywords

    characteristic function inversion; Heston's model; European-style option;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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