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Matching distributions: Recovery of implied physical densities from option prices

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  • Jarno Talponen

Abstract

We introduce a non-parametric method to recover physical probability distributions of asset returns based on their European option prices and some other sparse parametric information. Thus the main problem is similar to the one considered foir instance in the Recovery Theorem by Ross (2015), except that here we consider a non-dynamical setting. The recovery of the distribution is complete, instead of estimating merely a finite number of its parameters, such as implied volatility, skew or kurtosis. The technique is based on a reverse application of recently introduced Distribution Matching by the author and is related to the ideas in Distribution Pricing by Dybvig (1988) as well as comonotonicity.

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  • Jarno Talponen, 2018. "Matching distributions: Recovery of implied physical densities from option prices," Papers 1803.03996, arXiv.org.
    • Handle: RePEc:arx:papers:1803.03996
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    References listed on IDEAS

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    1. Torben G. Andersen & Nicola Fusari & Viktor Todorov, 2015. "Parametric Inference and Dynamic State Recovery From Option Panels," Econometrica, Econometric Society, vol. 83(3), pages 1081-1145, May.
    2. Jarno Talponen, 2013. "Matching distributions: Asset pricing with density shape correction," Papers 1312.4227, arXiv.org, revised Mar 2018.
    3. C. J. Corrado & Tie Su, 1997. "Implied volatility skews and stock return skewness and kurtosis implied by stock option prices," The European Journal of Finance, Taylor & Francis Journals, vol. 3(1), pages 73-85, March.
    4. Marco Airoldi, 2005. "A moment expansion approach to option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 5(1), pages 89-104.
    5. Szakmary, Andrew & Ors, Evren & Kyoung Kim, Jin & Davidson, Wallace III, 2003. "The predictive power of implied volatility: Evidence from 35 futures markets," Journal of Banking & Finance, Elsevier, vol. 27(11), pages 2151-2175, November.
    6. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
    7. Buchen, Peter W. & Kelly, Michael, 1996. "The Maximum Entropy Distribution of an Asset Inferred from Option Prices," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(1), pages 143-159, March.
    8. 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.
    9. Longstaff, Francis A, 1995. "Option Pricing and the Martingale Restriction," The Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1091-1124.
    10. 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.
    11. Kristensen, Dennis & Mele, Antonio, 2011. "Adding and subtracting Black-Scholes: A new approach to approximating derivative prices in continuous-time models," Journal of Financial Economics, Elsevier, vol. 102(2), pages 390-415.
    12. Igor Halperin & Andrey Itkin, 2014. "Pricing options on illiquid assets with liquid proxies using utility indifference and dynamic-static hedging," Quantitative Finance, Taylor & Francis Journals, vol. 14(3), pages 427-442, March.
    13. Bakshi, Gurdip & Madan, Dilip & Panayotov, George, 2010. "Returns of claims on the upside and the viability of U-shaped pricing kernels," Journal of Financial Economics, Elsevier, vol. 97(1), pages 130-154, July.
    14. Steve Ross, 2015. "The Recovery Theorem," Journal of Finance, American Finance Association, vol. 70(2), pages 615-648, April.
    15. Jennifer Conrad & Robert F. Dittmar & Eric Ghysels, 2013. "Ex Ante Skewness and Expected Stock Returns," Journal of Finance, American Finance Association, vol. 68(1), pages 85-124, February.
    16. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    17. Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
    18. Robert Engle & Stephen Figlewski, 2015. "Modeling the Dynamics of Correlations among Implied Volatilities," Review of Finance, European Finance Association, vol. 19(3), pages 991-1018.
    19. Gurdip Bakshi & Nikunj Kapadia & Dilip Madan, 2003. "Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options," The Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 101-143.
    20. Charles Corrado, 2007. "The hidden martingale restriction in Gram‐Charlier option prices," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 27(6), pages 517-534, June.
    21. 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.
    22. 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(1), pages 91-115, March.
    23. Bollerslev, Tim & Russell, Jeffrey & Watson, Mark (ed.), 2010. "Volatility and Time Series Econometrics: Essays in Honor of Robert Engle," OUP Catalogue, Oxford University Press, number 9780199549498.
    24. Song, Zhaogang & Xiu, Dacheng, 2016. "A tale of two option markets: Pricing kernels and volatility risk," Journal of Econometrics, Elsevier, vol. 190(1), pages 176-196.
    25. Robert JARROW & Andrew RUDD, 2008. "Approximate Option Valuation For Arbitrary Stochastic Processes," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 1, pages 9-31, World Scientific Publishing Co. Pte. Ltd..
    26. Stutzer, Michael, 1996. "A Simple Nonparametric Approach to Derivative Security Valuation," Journal of Finance, American Finance Association, vol. 51(5), pages 1633-1652, December.
    27. repec:bla:jfinan:v:53:y:1998:i:2:p:499-547 is not listed on IDEAS
    28. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. "Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-1632, December.
    29. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420-420.
    30. Chalamandaris, Georgios & Rompolis, Leonidas S., 2012. "Exploring the role of the realized return distribution in the formation of the implied volatility smile," Journal of Banking & Finance, Elsevier, vol. 36(4), pages 1028-1044.
    31. repec:bla:jfinan:v:59:y:2004:i:1:p:407-446 is not listed on IDEAS
    32. Bondarenko, Oleg, 2003. "Estimation of risk-neutral densities using positive convolution approximation," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 85-112.
    33. Carr, Peter & Wu, Liuren, 2016. "Analyzing volatility risk and risk premium in option contracts: A new theory," Journal of Financial Economics, Elsevier, vol. 120(1), pages 1-20.
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