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Revealing the implied risk-neutral MGF from options: The wavelet method

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  • Haven, Emmanuel
  • Liu, Xiaoquan
  • Ma, Chenghu
  • Shen, Liya
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    Abstract

    Options are believed to contain unique information on the risk-neutral moment generating function (MGF) or the risk-neutral probability density function (PDF) of the underlying asset. This paper applies the wavelet method to approximate the implied risk-neutral MGF from option prices. Monte Carlo simulations are carried out to show how the risk-neutral MGF can be obtained using the wavelet method. With the Black-Scholes model as the benchmark, we offer a novel method to reveal the implied MGF, and to price in-sample options and forecast out-of-sample option prices with the estimated MGF.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0165-1889(08)00163-2
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    Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

    Volume (Year): 33 (2009)
    Issue (Month): 3 (March)
    Pages: 692-709

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    Handle: RePEc:eee:dyncon:v:33:y:2009:i:3:p:692-709
    Contact details of provider: Web page: http://www.elsevier.com/locate/jedc

    Keywords: Wavelet analysis Option pricing Laplace transform;

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    1. Bliss, Robert R. & Panigirtzoglou, Nikolaos, 2002. "Testing the stability of implied probability density functions," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 381-422, March.
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    11. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October.
    12. Antoniou, Antonios & Vorlow, Constantinos E., 2005. "Price clustering and discreteness: is there chaos behind the noise?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 348(C), pages 389-403.
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    14. Melick, William R. & Thomas, Charles P., 1997. "Recovering an Asset's Implied PDF from Option Prices: An Application to Crude Oil during the Gulf Crisis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 32(01), pages 91-115, March.
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    Cited by:

    1. Schlögl, Erik, 2013. "Option pricing where the underlying assets follow a Gram/Charlier density of arbitrary order," Journal of Economic Dynamics and Control, Elsevier, vol. 37(3), pages 611-632.
    2. Fabozzi, Frank J. & Leccadito, Arturo & Tunaru, Radu S., 2014. "Extracting market information from equity options with exponential Lévy processes," Journal of Economic Dynamics and Control, Elsevier, vol. 38(C), pages 125-141.
    3. Haven, Emmanuel & Liu, Xiaoquan & Shen, Liya, 2012. "De-noising option prices with the wavelet method," European Journal of Operational Research, Elsevier, vol. 222(1), pages 104-112.

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