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Implied risk-neutral probability density functions from option prices: theory and application

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  • Bhupinder Bahra
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    Abstract

    Due to their forward-looking nature, derivative markets provide monetary authorities with a rich source of information for gauging market sentiment. For example, a futures price gives a widely used measure of the market's views about the future value of an asset, namely its mean or expected value at the maturity date of the futures contract. Moreover, the information available from futures prices can be extended by using option prices to estimate the market's entire probability distribution of the future value of an asset. This paper develops various techniques for estimating the market's probability distribution of the future value of an underlying asset from the prices of options on that asset. It discusses the relative merits and drawbacks of each approach, and shows how our preferred approach can be applied to estimate ex ante probability distributions using LIFFE equity and interest rate options, and Philadelphia Stock Exchange currency options. The paper then illustrates the potential value of this type of information to the policy-maker in assessing monetary conditions and conducting monetary operations. Finally, the paper looks at the limitations in data availability and highlights some areas for future research.

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    Bibliographic Info

    Paper provided by Bank of England in its series Bank of England working papers with number 66.

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    Date of creation: Jul 1997
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    Handle: RePEc:boe:boeewp:66

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    References

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    1. Yacine Aït-Sahalia & Andrew W. Lo, . "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," CRSP working papers 332, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
    2. 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.
    3. Jens Carsten Jackwerth and Mark Rubinstein., 1995. "Implied Probability Distributions: Empirical Analysis," Research Program in Finance Working Papers RPF-250, University of California at Berkeley.
    4. Ritchey, Robert J, 1990. "Call Option Valuation for Discrete Normal Mixtures," Journal of Financial Research, Southern Finance Association & Southwestern Finance Association, vol. 13(4), pages 285-96, Winter.
    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 637-54, May-June.
    6. Whaley, Robert E., 1982. "Valuation of American call options on dividend-paying stocks : Empirical tests," Journal of Financial Economics, Elsevier, vol. 10(1), pages 29-58, March.
    7. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    8. Ross, Stephen A, 1976. "Options and Efficiency," The Quarterly Journal of Economics, MIT Press, vol. 90(1), pages 75-89, February.
    9. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    10. King, Mervyn, 1995. "Credibility and Monetary Policy: Theory and Evidence," Scottish Journal of Political Economy, Scottish Economic Society, vol. 42(1), pages 1-19, February.
    11. 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.
    12. Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, vol. 10(3), pages 347-369, November.
    13. Allan M. Malz, 1995. "Using option prices to estimate realignment probabilities in the European Monetary System," Staff Reports 5, Federal Reserve Bank of New York.
    14. Garman, Mark B. & Kohlhagen, Steven W., 1983. "Foreign currency option values," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 231-237, December.
    15. Ball, Clifford A & Torous, Walter N, 1985. " On Jumps in Common Stock Prices and Their Impact on Call Option Pricing," Journal of Finance, American Finance Association, vol. 40(1), pages 155-73, March.
    16. Longstaff, Francis A, 1995. "Option Pricing and the Martingale Restriction," Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1091-1124.
    17. Banz, Rolf W & Miller, Merton H, 1978. "Prices for State-contingent Claims: Some Estimates and Applications," The Journal of Business, University of Chicago Press, vol. 51(4), pages 653-72, October.
    18. Ball, Clifford A. & Torous, Walter N., 1983. "A Simplified Jump Process for Common Stock Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(01), pages 53-65, March.
    19. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    20. MacBeth, James D & Merville, Larry J, 1980. " Tests of the Black-Scholes and Cox Call Option Valuation Models," Journal of Finance, American Finance Association, vol. 35(2), pages 285-301, May.
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    Citations

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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. Stephen Satchell & George Christodoulakis, 1996. "The Simulation of Option Prices with Application to LIFFE Options on Futures," Archive Working Papers 007, Birkbeck, Department of Economics, Mathematics & Statistics.
    3. Vergote, Olivier & Puigvert Gutiérrez, Josep Maria, 2012. "Interest rate expectations and uncertainty during ECB Governing Council days: Evidence from intraday implied densities of 3-month EURIBOR," Journal of Banking & Finance, Elsevier, vol. 36(10), pages 2804-2823.
    4. 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.
    5. Kang, Byung Jin & Kim, Tong Suk, 2006. "Option-implied risk preferences: An extension to wider classes of utility functions," Journal of Financial Markets, Elsevier, vol. 9(2), pages 180-198, May.
    6. Duca, Ioana Andreea & Ruxanda, Gheorghe, 2013. "A View on the Risk-Neutral Density Forecasting of the Dax30 Returns," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(2), pages 101-114, June.
    7. 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.
    8. Hisashi Nakamura & Shigenori Shiratsuka, 1999. "Extracting market expectations from option prices: case studies in Japanese option markets," Working Paper Series WP-99-1, Federal Reserve Bank of Chicago.
    9. Tapiero, Charles S., 2008. "Orders and inventory commodities with price and demand uncertainty in complete markets," International Journal of Production Economics, Elsevier, vol. 115(1), pages 12-18, September.
    10. Casillas-Olvera, Gabriel & Bessler, David A., 2006. "Probability forecasting and central bank accountability," Journal of Policy Modeling, Elsevier, vol. 28(2), pages 223-234, February.
    11. Anthony Tay & Kenneth F. Wallis, 2000. "Density Forecasting: A Survey," Econometric Society World Congress 2000 Contributed Papers 0370, Econometric Society.
    12. Andersson, Magnus & Lomakka, Magnus, 2005. "Evaluating implied RNDs by some new confidence interval estimation techniques," Journal of Banking & Finance, Elsevier, vol. 29(6), pages 1535-1557, June.
    13. Vähämaa, Sami, 2004. "Option-implied asymmetries in bond market expectations around monetary policy actions of the ECB," Working Paper Series 0315, European Central Bank.
    14. Bondarenko, Oleg, 2003. "Estimation of risk-neutral densities using positive convolution approximation," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 85-112.
    15. Halil Ibrahim Aydin & Ahmet Degerli & Pinar Ozlu, 2010. "Recovering Risk-Neutral Densities from Exchange Rate Options: Evidence in Turkey (Kur Opsiyonlarindan Riske Duyarsiz Yogunluk Fonksiyonu Cikarimi: Turkiye Ornegi)," Working Papers 1003, Research and Monetary Policy Department, Central Bank of the Republic of Turkey.
    16. Robert R Bliss & Nikolaos Panigirtzoglou, 2000. "Testing the stability of implied probability density functions," Bank of England working papers 114, Bank of England.

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