State price density estimation via nonparametric mixtures
We consider nonparametric estimation of the state price density encapsulated in option prices. Unlike usual density estimation problems, we only observe option prices and their corresponding strike prices rather than samples from the state price density. We propose to model the state price density directly with a nonparametric mixture and estimate it using least squares. We show that although the minimization is taken over an infinitely dimensional function space, the minimizer always admits a finite dimensional representation and can be computed efficiently. We also prove that the proposed estimate of the state price density function converges to the truth at a ``nearly parametric'' rate.
|Date of creation:||Oct 2009|
|Date of revision:|
|Publication status:||Published in Annals of Applied Statistics 2009, Vol. 3, No. 3, 963-984|
|Contact details of provider:|| Web page: http://arxiv.org/|
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- Joshua Rosenberg & Robert F. Engle, 2000.
"Empirical Pricing Kernels,"
New York University, Leonard N. Stern School Finance Department Working Paper Seires
99-014, New York University, Leonard N. Stern School of Business-.
- Jackwerth, Jens Carsten, 2000.
"Recovering Risk Aversion from Option Prices and Realized Returns,"
Review of Financial Studies,
Society for Financial Studies, vol. 13(2), pages 433-51.
- Jens Carsten Jackwerth., 1996. "Recovering Risk Aversion from Option Prices and Realized Returns," Research Program in Finance Working Papers RPF-265, University of California at Berkeley.
- Jens Carsten Jackwerth, 1998. "Recovering Risk Aversion from Option Prices and Realized Returns," Finance 9803002, EconWPA.
- James M. Hutchinson & Andrew W. Lo & Tomaso Poggio, 1994.
"A Nonparametric Approach to Pricing and Hedging Derivative Securities Via Learning Networks,"
NBER Working Papers
4718, National Bureau of Economic Research, Inc.
- Hutchinson, James M & Lo, Andrew W & Poggio, Tomaso, 1994. " A Nonparametric Approach to Pricing and Hedging Derivative Securities via Learning Networks," Journal of Finance, American Finance Association, vol. 49(3), pages 851-89, July.
- Yacine Ait-Sahalia & Andrew W. Lo, 2000.
"Nonparametric Risk Management and Implied Risk Aversion,"
NBER Working Papers
6130, National Bureau of Economic Research, Inc.
- 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.
- Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
- 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.
- 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.
- 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.
- Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
- René Garcia & Eric Ghysels & Éric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.
- Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
- 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.
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