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Recovering Risk Neutral Densities from Option Prices: A New Approach

Published online by Cambridge University Press:  06 April 2009

Leonidas S. Rompolis  and
Elias Tzavalis
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Abstract

In this paper we present a new method of approximating the risk neutral density (RND) from option prices based on the C-type Gram-Charlier series expansion (GCSE) of a probability density function. The exponential form of this type of GCSE guarantees that it will always give positive values of the risk neutral probabilities, and it can allow for stronger deviations from normality, which are two drawbacks of the A-type GCSE used in practice. To evaluate the performance of the suggested expansion of the RND, the paper presents simulation and empirical evidence.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 43 , Issue 4 , December 2008 , pp. 1037 - 1053
Copyright
Copyright © School of Business Administration, University of Washington 2008

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References

Abadir, K. M., and Rockinger, M.. “Density Functionals, with an Option-Pricing Application.” Econometric Theory, 19 (2003), 778–811.CrossRefGoogle Scholar
Ait-Sahalia, Y. “Maximum Likelihood Estimation of Discretely Sampled Diffusion: A Closed-Form Approximation Approach.” Econometrica, 70 (2002), 223–262.CrossRefGoogle Scholar
Ait-Sahalia, Y., and Lo, A. W.. “Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices.” Journal of Finance, 53 (1998), 499–548.CrossRefGoogle Scholar
Ait-Sahalia, Y., and Duarte, J.. “Nonparametric Option Pricing under Shape Restrictions.” Journal of Econometrics, 116 (2003), 9–47.CrossRefGoogle Scholar
Bakshi, G.; Cao, C.; and Chen, Z.. “Empirical Performance of Alternative Option Pricing Models.” Journal of Finance, 52 (1997), 2003–2049.CrossRefGoogle Scholar
Bakshi, G.; Ju, N.; and Ou-Yang, H.. “Estimation of Continuous-Time Models with an Application to Equity Volatility Dynamics.” Journal of Financial Economics, 82 (2006), 227–249.CrossRefGoogle Scholar
Bakshi, G.; Kapadia, N.; and Madan, D.. “Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options.” Review of Financial Studies, 16 (2003), 101–143.CrossRefGoogle Scholar
Bakshi, G., and Madan, D.. “Spanning and Derivative Security Valuation.” Journal of Financial Economics, 55 (2000), 205–238.CrossRefGoogle Scholar
Bliss, R., and Panigirtzoglou, N.. “Testing the Stability of Implied Probability Density Functions.” Journal of Banking and Finance, 26 (2002), 381–422.CrossRefGoogle Scholar
Campa, J. M.; Chang, P. H. K.; and Reider, R. L.. “Implied Exchange Rate Distributions: Evidence from OTC Option Markets.” Journal of International Money and Finance, 17 (1998), 117–160.CrossRefGoogle Scholar
Charlier, C. V. L. “A New Form of the Frequency Function.” Maddalende fran Lunds Astronomiska Observatorium, Ser II (1928), 51.Google Scholar
Chernov, M., and Ghysels, E.. “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, 56 (2000), 407–458.CrossRefGoogle Scholar
Corrado, C., and Su., T. “S&P 500 Index Option Tests of Jarrow and Rudd's Approximate Option Valuation Formula.” Journal of Futures Markets, 16 (1996a), 611–629.3.0.CO;2-I>CrossRefGoogle Scholar
Corrado, C., and Su, T.. “Skewness and Kurtosis in S&P 500 Index Returns Implied by Option Prices.” Journal of Financial Research, 19 (1996b), 175–192.CrossRefGoogle Scholar
Corrado, C., and Su, T.. “Implied Volatility Skews and Stock Index Skewness and Kurtosis Implied by S&P 500 Index Option Prices.” Journal of Derivatives, 4 (1997), 8–19.CrossRefGoogle Scholar
Cox, J., and Ross, S.. “The Valuation of Options for Alternative Stochastic Processes.” Journal of Financial Economics, 3 (1976), 145–166.CrossRefGoogle Scholar
Dennis, P., and Mayhew, S.. “Risk Neutral Skewness: Evidence from Option Prices.” Journal of Financial and Quantitative Analysis, 37 (2002), 471–493.CrossRefGoogle Scholar
Flamouris, D., and Giamouridis, D.. “Estimating Implied PDF's from American Options and Futures: A New Semiparametric Approach.” Journal of Futures Markets, 22 (2002), 1–30.CrossRefGoogle Scholar
Greene, W.Econometric Analysis. London: Prentice Hall International (2003).Google Scholar
Heston, S. L. “A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options.” Review of Financial Studies, 6 (1993), 327–343.CrossRefGoogle Scholar
Heston, S. L., and Nandi, S.. “A Closed-Form GARCH Option Valuation Model.” Review of Financial Studies, 13 (2000), 585–625.CrossRefGoogle Scholar
Jackwerth, J. C., and Rubinstein, M.. “Recovering Probability Distributions from Options Prices.” Journal of Finance, 51 (1996), 1611–1631.CrossRefGoogle Scholar
Jarrow, R., and Rudd, A.. “Approximate Valuation for Arbitrary Stochastic Processes.” Journal of Financial Economics, 10 (1982), 347–369.CrossRefGoogle Scholar
Jondeau, E., and Rockinger, M.. “Gram-Charlier Densities.” Journal of Economic Dynamics and Control, 25 (2001), 1457–1483.CrossRefGoogle Scholar
Kendall, M. G., and Stuart, A.. The Advanced Theory of Statistics. New York, NY: Hafner Publishing Company (1969).Google Scholar
Knight, J., and Satchell, S.. “Pricing Derivatives Written on Assets with Arbitrary Skewness and Kurtosis.” In Return Distributions in Finance, Knight, and Satchell, (eds.). Oxford: Butterworth and Heinemann (2001), 252–275.CrossRefGoogle Scholar
Longstaff, F. A. “Option Pricing and the Martingale Restriction.” Review of Financial Studies, 8 (1995), 1091–1124.CrossRefGoogle Scholar
Madan, D. B., and Milne, F.. “Contingent Claims Valued and Hedged by Pricing and Investing in a Basis.” Mathematical Finance, 4 (1994), 223–245.CrossRefGoogle Scholar
Melick, W. R., and Thomas, C. P.. “Recovering an Asset Implied PDF from Option Prices: An Application to Crude Oil During the Gulf Crisis.” Journal of Financial and Quantitative Analysis, 32 (1997), 91–115.CrossRefGoogle Scholar
Muscolino, G., and Ricciardi, G.. “Probability Density Function of MDOF Structural Systems Under Non-Normal Delta-Correlated Inputs.” Computer Methods in Applied Mechanics and Engineering, 168 (1999), 121–133.CrossRefGoogle Scholar
Pagan, A., and Ullah, A.. Nonparametric Econometrics. Cambridge: Cambridge University Press (1999).CrossRefGoogle Scholar
Riordan, J.Combinatorial Identities. New York, NY: Robert E. Krieger Publishing Co. (1979).Google Scholar
Rompolis, L. S., and Tzavalis, E.. “Retrieving Risk Neutral Moments from Option Prices.” Mimeo, Athens University of Economics and Business (2004).Google Scholar
Rubinstein, M. “Implied Binomial Trees.” Journal of Finance, 49 (1994), 771–818.CrossRefGoogle Scholar
Shohat, J. A., and Tamarkin, J. D.. The Problem of Moments. Providence, RI: AMS Mathematical Survey (1943).CrossRefGoogle Scholar