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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. Fouque,Jean-Pierre & Papanicolaou,George & Sircar,Ronnie & Sølna,Knut, 2011. "Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives," Cambridge Books, Cambridge University Press, number 9780521843584, October.
    2. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    3. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," The Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    4. 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.
    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. R. F. Engle & A. J. Patton, 2001. "What good is a volatility model?," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 237-245.
    7. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
    8. Ball, Clifford A. & Roma, Antonio, 1994. "Stochastic Volatility Option Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(4), pages 589-607, December.
    9. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    10. Lorella Fatone & Francesca Mariani & Maria Cristina Recchioni & Francesco Zirilli, 2009. "An explicitly solvable multi‐scale stochastic volatility model: Option pricing and calibration problems," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 29(9), pages 862-893, September.
    11. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
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    Cited by:

    1. 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.
    2. 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.
    3. Gifty Malhotra & R. Srivastava & H. C. Taneja, 2019. "Comparative Study of Two Extensions of Heston Stochastic Volatility Model," Papers 1912.10237, arXiv.org.

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