Testing the stability of implied probability density functions
Implied probability density functions (PDFs) estimated from cross-sections of observed option prices are gaining increasing attention amongst academics and practitioners. To date, however, little attention has been paid to the robustness of these estimates or to the confidence that users can place in the summary statistics (for example the skewness or the 99th percentile) derived from fitted PDFs. This paper begins to address these questions by examining the absolute and relative robustness of two of the most common methods for estimating implied PDFs - the double-lognormal approximating function and the smoothed implied volatility smile methods. The changes resulting from randomly perturbing quoted prices by no more than a half tick provide a lower bound on the confidence intervals of the summary statistics derived from the estimated PDFs. Tests are conducted using options contracts tied to short sterling futures and the FTSE 100 index - both trading on the London International Financial Futures and Options Exchange. The tests show that the smoothed implied volatility smile method dominates the double-lognormal as a technique for estimating implied PDFs when average goodness-of-fits for both methods are comparable.
|Date of creation:||May 2000|
|Contact details of provider:|| Postal: Bank of England, Threadneedle Street, London, EC2R 8AH|
Phone: +44 (0)171 601 4030
Fax: +44 (0)171 601 5196
Web page: http://www.bankofengland.co.uk/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Allan M. Malz, 1997. "Option-implied probability distributions and currency excess returns," Staff Reports 32, Federal Reserve Bank of New York.
- Yacine Aït-Sahalia & Andrew W. Lo, 1998.
"Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices,"
Journal of Finance,
American Finance Association, vol. 53(2), pages 499-547, 04.
- Yacine Aït-Sahalia & Andrew W. Lo, "undated". "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.
- Yacine Ait-Sahalia & Andrew W. Lo, 1995. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," NBER Working Papers 5351, National Bureau of Economic Research, Inc.
- 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.
- 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., 1996. "New Techniques to Extract Market expectations from Financial Instruments," SSE/EFI Working Paper Series in Economics and Finance 142, Stockholm School of Economics.
- 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.
- 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.
- 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.
- 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.
- 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.
- Dilip B. Madan & Frank Milne, 1994. "Contingent Claims Valued And Hedged By Pricing And Investing In A Basis," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 223-245.
- Frank Milne & Dilip Madan, 1994. "Contingent Claims Valued And Hedged By Pricing And Investing In A Basis," Working Papers 1158, Queen's University, Department of Economics.
- Jose M. Campa & P.H. Kevin Chang & Robert L. Reider, 1997. "Implied Exchange Rate Distributions: Evidence from OTC Option Markets," NBER Working Papers 6179, National Bureau of Economic Research, Inc.
- 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.
- Daniel F. Waggoner, 1997. "Spline methods for extracting interest rate curves from coupon bond prices," FRB Atlanta Working Paper 97-10, Federal Reserve Bank of Atlanta.
- 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.
- 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 19 Mar 1999.
- Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
- 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.
- Mc Manus, Des, 1999. "The Information Content of Interest Rate Futures Options," Staff Working Papers 99-15, Bank of Canada.
- 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.
- Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
- repec:dau:papers:123456789/9842 is not listed on IDEAS
- 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.
- 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.
- Bhupinder Bahra, 1997. "Implied risk-neutral probability density functions from option prices: theory and application," Bank of England working papers 66, Bank of England.
- Shiratsuka, Shigenori, 2001. "Information Content of Implied Probability Distributions: Empirical Studies of Japanese Stock Price Index Options," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 19(3), pages 143-170, November.
- Dilip B. Madan & Frank Milne, 1992. "Contingent Claims Valued and Hedged by Pricing and Investment in a Basis," Working Papers 868, Queen's University, Department of Economics.
- Michael P. Leahy & Charles P. Thomas, 1996. "The sovereignty option: the Quebec referendum and market views on the Canadian dollar," International Finance Discussion Papers 555, Board of Governors of the Federal Reserve System (U.S.).
- 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. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:boe:boeewp:114. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Digital Media Team)
If references are entirely missing, you can add them using this form.