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Quadratic approximation of the slow factor of volatility in a multifactor stochastic volatility model

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  • Gifty Malhotra
  • R. Srivastava
  • H. C. Taneja

Abstract

A new multifactor stochastic volatility model is proposed in which the slow volatility factor is approximated by a quadratic arc. The perturbation technique is used to obtain the approximate expression for the European option price. The notion of a modified Black‐Scholes price is introduced. A simplified expression for the European option price, perturbed around the modified Black‐Scholes price, is obtained. An expression of modified price is also obtained in terms of the Black‐Scholes price. The effect of this modification on pricing is explained, the accuracy of the approximate option pricing formula established, and its computational cost discussed.

Suggested Citation

  • Gifty Malhotra & R. Srivastava & H. C. Taneja, 2018. "Quadratic approximation of the slow factor of volatility in a multifactor stochastic volatility model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(5), pages 607-624, May.
    • Handle: RePEc:wly:jfutmk:v:38:y:2018:i:5:p:607-624
    DOI: 10.1002/fut.21895
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    References listed on IDEAS

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    1. Peter Christoffersen & Steven Heston & Kris Jacobs, 2009. "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well," Management Science, INFORMS, vol. 55(12), pages 1914-1932, December.
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    Cited by:

    1. Gifty Malhotra & R. Srivastava & H. C. Taneja, 2019. "Comparative Study of Two Extensions of Heston Stochastic Volatility Model," Papers 1912.10237, arXiv.org.
    2. Malhotra, Gifty & Srivastava, R. & Taneja, H.C., 2019. "Calibration of the risk-neutral density function by maximization of a two-parameter entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 45-54.
    3. Choi, Sun-Yong, 2019. "The influence of shock signals on the change in volatility term structure," Economics Letters, Elsevier, vol. 183(C), pages 1-1.

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