Dynamics of State Price Densities
State price densities (SPD) are an important element in applied quantitative finance. In a Black-Scholes model they are lognormal distributions with constant volatility parameter. In practice volatility changes and the distribution deviates from log-normality. We estimate SPDs using EUREX option data on the DAX index via a nonparametric estimator of the second derivative of the (European) call price function. The estimator is constrained so as to satisfy no-arbitrage constraints and it corrects for intraday covariance structure. Given a low dimensional representation of this SPD we study its dynamic for the years 1995–2003. We calculate a prediction corridor for the DAX for a 45 day forecast. The proposed algorithm is simple, it allows calculation of future volatility and can be applied to hedging exotic options.
|Date of creation:||Apr 2005|
|Date of revision:|
|Contact details of provider:|| Postal: Spandauer Str. 1,10178 Berlin|
Web page: http://sfb649.wiwi.hu-berlin.de
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.:
- Stoll, Hans R, 1969. "The Relationship between Put and Call Option Prices," Journal of Finance, American Finance Association, vol. 24(5), pages 801-24, December.
- Yacine Ait-Sahalia & Jefferson Duarte, 2002.
"Nonparametric Option Pricing under Shape Restrictions,"
NBER Working Papers
8944, National Bureau of Economic Research, Inc.
- Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
- Hans Buehler, 2006. "Expensive martingales," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 207-218.
- Fengler, Matthias R. & Härdle, Wolfgang & Mammen, Enno, 2003. "Implied volatility string dynamics," SFB 373 Discussion Papers 2003,54, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Yatchew, Adonis & Hardle, Wolfgang, 2006. "Nonparametric state price density estimation using constrained least squares and the bootstrap," Journal of Econometrics, Elsevier, vol. 133(2), pages 579-599, August.
- 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.
- Yacine Ait-Sahalia & Andrew W. Lo, 2000. "Nonparametric Risk Management and Implied Risk Aversion," NBER Working Papers 6130, National Bureau of Economic Research, Inc.
- 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.
- 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 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.
- Matthias Fengler, 2009.
"Arbitrage-free smoothing of the implied volatility surface,"
Taylor & Francis Journals, vol. 9(4), pages 417-428.
- Matthias R. Fengler, 2005. "Arbitrage-Free Smoothing of the Implied Volatility Surface," SFB 649 Discussion Papers SFB649DP2005-019, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-83, November.
- Jackwerth, Jens Carsten, 1999. "Option Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review," MPRA Paper 11634, University Library of Munich, Germany.
- L. Randall Wray & Stephanie Bell, 2004. "Introduction," Chapters, in: Credit and State Theories of Money, chapter 1 Edward Elgar Publishing.
- Bondarenko, Oleg, 2003. "Estimation of risk-neutral densities using positive convolution approximation," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 85-112.
- Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
- Philippe Robert-Demontrond & R. Ringoot, 2004. "Introduction," Post-Print halshs-00081823, HAL.
- Ait-Sahalia, Yacine & Wang, Yubo & Yared, Francis, 2001. "Do option markets correctly price the probabilities of movement of the underlying asset?," Journal of Econometrics, Elsevier, vol. 102(1), pages 67-110, May.
- Huynh, Kim & Kervella, Pierre & Zheng, Jun, 2002. "Estimating state-price densities with nonparametric regression," SFB 373 Discussion Papers 2002,40, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Matthias Fengler & Wolfgang Härdle & Enno Mammen, 2005. "A Dynamic Semiparametric Factor Model for Implied Volatility String Dynamics," SFB 649 Discussion Papers SFB649DP2005-020, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- 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.
When requesting a correction, please mention this item's handle: RePEc:hum:wpaper:sfb649dp2005-021. 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: (RDC-Team)
If references are entirely missing, you can add them using this form.