Nonparametric option pricing under shape restrictions
AbstractFrequently, economic theory places shape restrictions on functional relationships between economic variables. This paper develops a method to constrain the values of the first and second derivatives of nonparametric locally polynomial estimators. We apply this technique to estimate the state price density (SPD), or risk-neutral density, implicit in the market prices of options. The option pricing function must be monotonic and convex. Simulations demonstrate that nonparametric estimates can be quite feasible in the small samples relevant for day-to-day option pricing, once appropriate theory-motivated shape restrictions are imposed. Using S&P500 option prices, we show that unconstrained nonparametric estimators violate the constraints during more than half the trading days in 1999, unlike the constrained estimator we propose.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 116 (2003)
Issue (Month): 1-2 ()
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Web page: http://www.elsevier.com/locate/jeconom
Other versions of this item:
- Yacine Ait-Sahalia & Jefferson Duarte, 2002. "Nonparametric Option Pricing under Shape Restrictions," NBER Working Papers 8944, National Bureau of Economic Research, Inc.
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
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- 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.
- 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.
- Matzkin, Rosa L. & Richter, Marcel K., 1991.
"Testing strictly concave rationality,"
Journal of Economic Theory,
Elsevier, vol. 53(2), pages 287-303, April.
- Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, vol. 10(3), pages 347-369, November.
- Andreas Gottschling & Christian Haefke & Halbert White, 2000.
"Closed Form Integration of Artificial Neural Networks with Some Applications to Finance,"
Econometric Society World Congress 2000 Contributed Papers
1080, Econometric Society.
- Christian Haefke & Halbert White & Andreas Gottschling, 2000. "Closed Form Integration Of Artificial Neural Networks With Some Applications To Finance," Computing in Economics and Finance 2000 366, Society for Computational Economics.
- Gottschling, Andreas & Haefke, Christian & White, Halbert, 1999. "Closed Form Integration of Artificial Neural Networks with Some Applications to Finance," University of California at San Diego, Economics Working Paper Series qt0wz7n7nm, Department of Economics, UC San Diego.
- Varian, Hal R, 1984. "The Nonparametric Approach to Production Analysis," Econometrica, Econometric Society, vol. 52(3), pages 579-97, May.
- René Garcia & Ramazan Gençay, 1998.
"Pricing and Hedging Derivative Securities with Neural Networks and a Homogeneity Hint,"
CIRANO Working Papers
- Garcia, Rene & Gencay, Ramazan, 2000. "Pricing and hedging derivative securities with neural networks and a homogeneity hint," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 93-115.
- Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. " Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-32, December.
- Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
- Ait-Sahalia, Yacine, 1996.
"Nonparametric Pricing of Interest Rate Derivative Securities,"
Econometric Society, vol. 64(3), pages 527-60, May.
- Yacine Ait-Sahalia, 1995. "Nonparametric Pricing of Interest Rate Derivative Securities," NBER Working Papers 5345, National Bureau of Economic Research, Inc.
- Varian, Hal R., 1983. "Nonparametric Tests of Models of Investor Behavior," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(03), pages 269-278, September.
- Diewert, W. E., 1973. "Functional forms for profit and transformation functions," Journal of Economic Theory, Elsevier, vol. 6(3), pages 284-316, June.
- Matzkin, Rosa L., 1986. "Restrictions of economic theory in nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 42, pages 2523-2558 Elsevier.
- 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.
- Rosa L. Matzkin, 1988. "Nonparametric and Distribution-Free Estimation of the Binary Choice and the Threshold-Crossing Models," Cowles Foundation Discussion Papers 889, Cowles Foundation for Research in Economics, Yale University.
- 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.
- Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
- 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.
- Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
- Peter Christoffersen & Kris Jacobs, 2001. "The Importance of the Loss Function in Option Pricing," CIRANO Working Papers 2001s-45, CIRANO.
- Diewert, W. E. & Parkan, C., 1985. "Tests for the consistency of consumer data," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 127-147.
- Dole, David, 1999. "CoSmo: A Constrained Scatterplot Smoother for Estimating Convex, Monotonic Transformations," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(4), pages 444-55, October.
- 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.
- Enno MAMMEN & C. THOMAS-AGNAN, 1996. "Smoothing Splines And Shape Restrictions," SFB 373 Discussion Papers 1996,87, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Matzkin, Rosa L, 1991. "Semiparametric Estimation of Monotone and Concave Utility Functions for Polychotomous Choice Models," Econometrica, Econometric Society, vol. 59(5), pages 1315-27, September.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Goldman, Steven M., 1993.
"Nonparametric Multivariate Regression Subject to Constraint,"
Department of Economics, Working Paper Series
qt7r623607, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
- S. M. Goldman & P. A. Ruud, 1993. "Nonparametric Multivariate Regression Subject to Constraint," Econometrics 9311001, EconWPA.
- Karim Abadir & Michael Rockinger, . "Density-Embedding Functions," Discussion Papers 97/16, Department of Economics, University of York.
- Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
- E. Mammen, 1999. "Smoothing Splines and Shape Restrictions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 26(2), pages 239-252.
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