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A New Framework to Estimate the Risk-Neutral Probability Density Functions Embedded in Options Prices

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  • Mr. Kevin C Cheng

Abstract

Building on the widely-used double-lognormal approach by Bahra (1997), this paper presents a multi-lognormal approach with restrictions to extract risk-neutral probability density functions (RNPs) for various asset classes. The contributions are twofold: first, on the technical side, the paper proposes useful transformation/restrictions to Bahra’s original formulation for achieving economically sensible outcomes. In addition, the paper compares the statistical properties of the estimated RNPs among major asset classes, including commodities, the S&P 500, the dollar/euro exchange rate, and the US 10-year Treasury Note. Finally, a Monte Carlo study suggests that the multi-lognormal approach outperforms the double-lognormal approach.

Suggested Citation

  • Mr. Kevin C Cheng, 2010. "A New Framework to Estimate the Risk-Neutral Probability Density Functions Embedded in Options Prices," IMF Working Papers 2010/181, International Monetary Fund.
    • Handle: RePEc:imf:imfwpa:2010/181
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    References listed on IDEAS

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    1. Bates, David S, 1991. "The Crash of '87: Was It Expected? The Evidence from Options Markets," Journal of Finance, American Finance Association, vol. 46(3), pages 1009-1044, July.
    2. Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
    3. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    4. 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 621-651, October.
    5. 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. Sonalika Sinha & Bandi Kamaiah, 2017. "Estimating Option-implied Risk Aversion for Indian Markets," IIM Kozhikode Society & Management Review, , vol. 6(1), pages 90-97, January.
    2. Datta, Deepa Dhume & Londono, Juan M. & Ross, Landon J., 2017. "Generating options-implied probability densities to understand oil market events," Energy Economics, Elsevier, vol. 64(C), pages 440-457.
    3. Fabien Le Floc’h & Cornelis W. Oosterlee, 2019. "Model-Free Stochastic Collocation for an Arbitrage-Free Implied Volatility, Part II," Risks, MDPI, vol. 7(1), pages 1-21, March.
    4. Carlos Caceres & Leandro Medina, 2012. "Measures of Fiscal Risk in Hydrocarbon-Exporting Countries," IMF Working Papers 2012/260, International Monetary Fund.
    5. José L. Vilar-Zanón & Olivia Peraita-Ezcurra, 2019. "A linear goal programming method to recover risk neutral probabilities from options prices by maximum entropy," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 259-276, June.
    6. Mr. Shaun K. Roache & Mrs. Marina V Rousset, 2013. "Unconventional Monetary Policy and Asset Price Risk," IMF Working Papers 2013/190, International Monetary Fund.

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