Estimating the Risk Neutral Probability Density Functions Natural Spline versus Hypergeometric Approach Using European Style Options
This paper examines the ability of two recent approaches to estimate implied risk neutral probability density functions (RNDs) - the smoothed implied volatility smile method (SML) and the density functionals based on the confluent hypergeometric functions (DFCH) from the prices of European-style options. A Monte Carlo experiment is conducted to compare the capability of the two techniques to recover simulated distributions based on Heston's (1993) stochastic volatility model. The paper investigates the accuracy and stability of the two methods via two categories of estimated summary statistics. We find that while the SML method outperforms the DFCH method for the summary statistics which are sensitive to the tails of the distribution, the DFCH method dominates the SML method for the summary statistics that are less sensitive to outliers. Due to the lack of observations in the tails when estimating RNDs, we feel that the most appropriate measures for comparing the two methods are the ones less sensitive to extreme values. In this sense, the DFCH method seems to be more appealing. We also apply the two methods via an empirical application.
|Date of creation:||2005|
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- 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(01), pages 143-159, March.
- 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.
- Söderlind, Paul & Svensson, Lars E.O., 1996.
"New Techniques to Extract Market expectations from Financial Instruments,"
SSE/EFI Working Paper Series in Economics and Finance
142, Stockholm School of Economics.
- Soderlind, Paul & Svensson, Lars, 1997. "New techniques to extract market expectations from financial instruments," Journal of Monetary Economics, Elsevier, vol. 40(2), pages 383-429, October.
- Paul Soderlind & Lars E. O. Svensson, 1997. "New Techniques to Extract Market Expectations from Financial Instruments," NBER Working Papers 5877, National Bureau of Economic Research, Inc.
- Soderlind, P & Svensson, L-E-O, 1996. "New Techniques to Extract Market Expectations from Financial Instruments," Papers 621, Stockholm - International Economic Studies.
- Söderlind, Paul & Svensson, Lars E O, 1997. "New Techniques to Extract Market Expectations from Financial Instruments," CEPR Discussion Papers 1556, C.E.P.R. Discussion Papers.
- Söderlind, Paul & Svensson, Lars E.O., 1997. "New Techniques to Extract Market Expectations from Financial Instruments," Seminar Papers 621, Stockholm University, Institute for International Economic Studies.
- Bhupinder Bahra, 1997. "Implied risk-neutral probability density functions from option prices: theory and application," Bank of England working papers 66, Bank of England.
- Mc Manus, Des, 1999. "The Information Content of Interest Rate Futures Options," Staff Working Papers 99-15, Bank of Canada.
- Michael Rockinger & Eric Jondeau, 1997.
"Reading the Smile: The Message Conveyed by Methods which Infer Risk Neutral Densities,"
- Jondeau, Eric & Rockinger, Michael, 2000. "Reading the smile: the message conveyed by methods which infer risk neutral densities," Journal of International Money and Finance, Elsevier, vol. 19(6), pages 885-915, December.
- Jondeau, Eric & Rockinger, Michael, 1998. "Reading the Smile: The Message Conveyed by Methods which Infer Risk Neutral Densities," CEPR Discussion Papers 2009, C.E.P.R. Discussion Papers.
- 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.
- Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
- María C. Manzano & Isabel Sánchez, 1998. "Indicators of Short-Term Interest Rate Expectations. The Information Contained in the Options Market," Working Papers 9816, Banco de España;Working Papers Homepage.
- Söderlind, Paul, 1997.
"Market Expectations in the UK Before and After the ERM Crisis,"
SSE/EFI Working Paper Series in Economics and Finance
210, Stockholm School of Economics, revised 01 Sep 1998.
- Soderlind, Paul, 2000. "Market Expectations in the UK before and after the ERM Crisis," Economica, London School of Economics and Political Science, vol. 67(265), pages 1-18, February.
- Panigirtzoglou, Nikolaos & Skiadopoulos, George, 2004. "A new approach to modeling the dynamics of implied distributions: Theory and evidence from the S&P 500 options," Journal of Banking & Finance, Elsevier, vol. 28(7), pages 1499-1520, July.
- Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
- Peter A. Abken & Dilip B. Madan & Buddhavarapu Sailesh Ramamurtie, 1996. "Estimation of risk-neutral and statistical densities by Hermite polynomial approximation: with an application to Eurodollar futures options," FRB Atlanta Working Paper 96-5, Federal Reserve Bank of Atlanta.
- Allan M. Malz, 1997. "Option-implied probability distributions and currency excess returns," Staff Reports 32, Federal Reserve Bank of New York.
- Robert R. Bliss & Nikolaos Panigirtzoglou, 2004. "Option-Implied Risk Aversion Estimates," Journal of Finance, American Finance Association, vol. 59(1), pages 407-446, 02.
- 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.
- 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.
- Neuhaus, Holger, 1995. "The information content of derivatives for monetary policy: Implied volatilities and probabilities," Discussion Paper Series 1: Economic Studies 1995,03e, Deutsche Bundesbank, Research Centre.
- Abadir, Karim, 1995.
"An Introduction to Hypergeometric Functions for Economists,"
9510, Exeter University, Department of Economics.
- Karim Abadir, 1999. "An introduction to hypergeometric functions for economists," Econometric Reviews, Taylor & Francis Journals, vol. 18(3), pages 287-330.
- 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.
- Campa, Jose M. & Chang, P. H. Kevin & Reider, Robert L., 1998. "Implied exchange rate distributions: evidence from OTC option markets1," Journal of International Money and Finance, Elsevier, vol. 17(1), pages 117-160, February.
- Malz, Allan M., 1996. "Using option prices to estimate realignment probabilities in the European Monetary System: the case of sterling-mark," Journal of International Money and Finance, Elsevier, vol. 15(5), pages 717-748, October.
- Abadir, Karim M. & Rockinger, Michael, 2003. "Density Functionals, With An Option-Pricing Application," Econometric Theory, Cambridge University Press, vol. 19(05), pages 778-811, October.
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