Uniform confidence bands for pricing kernels
AbstractPricing kernels implicit in option prices play a key role in assessing the risk aversion over equity returns. We deal with nonparametric estimation of the pricing kernel (Empirical Pricing Kernel) given by the ratio of the risk-neutral density estimator and the subjective density estimator. The former density can be represented as the second derivative w.r.t. the European call option price function, which we estimate by nonparametric regression. The subjective density is estimated nonparametrically too. In this framework, we develop the asymptotic distribution theory of the EPK in the L1 sense. Particularly, to evaluate the overall variation of the pricing kernel, we develop a uniform confidence band of the EPK. Furthermore, as an alternative to the asymptotic approach, we propose a bootstrap confidence band. The developed theory is helpful for testing parametric specifications of pricing kernels and has a direct extension to estimating risk aversion patterns. The established results are assessed and compared in a Monte-Carlo study. As a real application, we test risk aversion over time induced by the EPK.
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Bibliographic InfoPaper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2010-003.
Length: 30 pages
Date of creation: Jan 2010
Date of revision:
Empirical Pricing Kernel; Confidence band; Bootstrap; Kernel Smoothing; Nonparametric;
Find related papers by JEL classification:
- C00 - Mathematical and Quantitative Methods - - General - - - General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- J01 - Labor and Demographic Economics - - General - - - Labor Economics: General
- J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials
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- Ait-Sahalia, Yacine & Lo, Andrew W., 2000.
"Nonparametric risk management and implied risk aversion,"
Journal of Econometrics, Elsevier,
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 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, Elsevier, vol. 116(1-2), pages 9-47.
- Fousseni Chabi-Yo & René Garcia & Eric Renault, 2008. "State Dependence Can Explain the Risk Aversion Puzzle," Review of Financial Studies, Society for Financial Studies, vol. 21(2), pages 973-1011, April.
- 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, 1998. "Recovering Risk Aversion from Option Prices and Realized Returns," Finance, EconWPA 9803002, EconWPA.
- Jens Carsten Jackwerth., 1996. "Recovering Risk Aversion from Option Prices and Realized Returns," Research Program in Finance Working Papers, University of California at Berkeley RPF-265, University of California at Berkeley.
- Rosenberg, Joshua V. & Engle, Robert F., 2002.
"Empirical pricing kernels,"
Journal of Financial Economics, Elsevier,
Elsevier, vol. 64(3), pages 341-372, June.
- Joshua Rosenberg & Robert F. Engle, 2000. "Empirical Pricing Kernels," New York University, Leonard N. Stern School Finance Department Working Paper Seires, New York University, Leonard N. Stern School of Business- 99-014, New York University, Leonard N. Stern School of Business-.
- Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers, University of California at Berkeley RPF-232, University of California at Berkeley.
- Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. " Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, American Finance Association, vol. 51(5), pages 1611-32, December.
- Kahneman, Daniel & Tversky, Amos, 1979.
"Prospect Theory: An Analysis of Decision under Risk,"
Econometrica, Econometric Society,
Econometric Society, vol. 47(2), pages 263-91, March.
- Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
- Maria Grith & Wolfgang Härdle & Juhyun Park, 2009. "Shape invariant modelling pricing kernels and risk aversion," SFB 649 Discussion Papers SFB649DP2009-041, 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.
- Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, American Finance Association, vol. 49(3), pages 771-818, July.
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