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Nonparametric Estimation of American Options Exercise Boundaries and Call Prices

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  • Mark Broadie
  • Jérôme Detemple
  • Eric Ghysels
  • Olivier Torrès

Abstract

Unlike European-type derivative securities, there are no simple analytic valuation formulas for American options, even when the underlying asset price has constant volatility. The early exercise feature considerably complicates the valuation of American contracts. The strategy taken in this paper is to rely on nonparametric statistical methods using market data to estimate the call prices and the exercise boundaries. The paper focuses on the daily market option prices and exercise data on the S&P100 contract. A comparison is made with parametric constant volatility model-based prices and exercise boundaries. We find large discrepancies between the parametric and nonparametric call prices and exercise boundaries. Contrairement à ce qu'il est possible d'obtenir dans un contexte d'évaluation de titres dérivés de type européen, il n'existe pas de formule analytique simple pour évaluer les options américaines, même si la volatilité de l'actif sous-jacent est supposée constante. La possibilité d'exercice prématuré qu'offre ce type de contrat complique considérablement son évaluation. La démarche adoptée dans cette étude consiste à dériver les prix d'option et les frontières d'exercice à partir de données financières, utilisées dans un cadre d'analyse statistique non-paramétrique. Plus particulièrement, l'étude utilise les observations quotidiennes du prix du contrat sur l'indice S&P100 ainsi que les observations sur l'exercice de ce contrat. Les résultats sont comparés à ceux obtenus à l'aide de techniques paramétriques dans un modèle où la volatilité est supposée constante. La conclusion est qu'il existe des différences stratégiques entre les prédictions des deux modèles, aussi bien en ce qui concerne le prix de l'option que la politique d'exercice qui lui est associée.
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  • Mark Broadie & Jérôme Detemple & Eric Ghysels & Olivier Torrès, 1996. "Nonparametric Estimation of American Options Exercise Boundaries and Call Prices," CIRANO Working Papers 96s-24, CIRANO.
  • Handle: RePEc:cir:cirwor:96s-24
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    1. Singh, Radhey S. & Ullah, Aman, 1985. "Nonparametric Time-Series Estimation of Joint DGP, Conditional DGP, and Vector Autoregression," Econometric Theory, Cambridge University Press, vol. 1(1), pages 27-52, April.
    2. 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.
    3. Boyle, Phelim P., 1988. "A Lattice Framework for Option Pricing with Two State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(1), pages 1-12, March.
    4. Mikhail Chernov & Eric Ghysels, 1998. "What Data Should Be Used to Price Options?," CIRANO Working Papers 98s-22, CIRANO.
    5. Jing-Zhi Huang & Marti G. Subrahmanyam & G. George Yu, 1999. "Pricing And Hedging American Options: A Recursive Integration Method," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 8, pages 219-239, World Scientific Publishing Co. Pte. Ltd..
    6. Duffie, Darrell & Singleton, Kenneth J, 1993. "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, Econometric Society, vol. 61(4), pages 929-952, July.
    7. Horowitz, Joel L., 1993. "Semiparametric estimation of a work-trip mode choice model," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 49-70, July.
    8. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 85-118, Suppl. De.
    9. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
    10. 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.
    11. Bates, David S, 1991. "The Crash of '87: Was It Expected? The Evidence from Options Markets," Journal of Finance, American Finance Association, vol. 46(3), pages 1009-1044, July.
    12. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    13. 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 851-889, July.
    14. Karim Abadir & Michael Rockinger, "undated". "Density-Embedding Functions," Discussion Papers 97/16, Department of Economics, University of York.
    15. Guy Barles & Julien Burdeau & Marc Romano & Nicolas Samsoen, 1995. "Critical Stock Price Near Expiration," Mathematical Finance, Wiley Blackwell, vol. 5(2), pages 77-95, April.
    16. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. "Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-320, June.
    17. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
    18. Brennan, Michael J & Schwartz, Eduardo S, 1977. "The Valuation of American Put Options," Journal of Finance, American Finance Association, vol. 32(2), pages 449-462, May.
    19. Wolfgang Härdle & Philippe Vieu, 1992. "Kernel Regression Smoothing Of Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(3), pages 209-232, May.
    20. Ingersoll, Jonathan E, Jr, 1977. "An Examination of Corporate Call Policies on Convertible Securities," Journal of Finance, American Finance Association, vol. 32(2), pages 463-478, May.
    21. Renault, E., 1996. "Econometric Models of Option Pricing Errors," Papers 96.407, Toulouse - GREMAQ.
    22. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(4), pages 657-681, October.
    23. Kim, In Joon, 1990. "The Analytic Valuation of American Options," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 547-572.
    24. Gay, Gerald D. & Kolb, Robert W. & Yung, Kenneth, 1989. "Trader rationality in the exercise of futures options," Journal of Financial Economics, Elsevier, vol. 23(2), pages 339-361, August.
    25. Michael J. P. Selby & Stewart D. Hodges, 1987. "On the Evaluation of Compound Options," Management Science, INFORMS, vol. 33(3), pages 347-355, March.
    26. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    27. Bodurtha, James N, Jr & Courtadon, Georges R, 1986. "Efficiency Tests of the Foreign Currency Options Market," Journal of Finance, American Finance Association, vol. 41(1), pages 151-162, March.
    28. Breen, Richard, 1991. "The Accelerated Binomial Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(2), pages 153-164, June.
    29. Dan W. French & Edwin D. Maberly, 1992. "Early Exercise Of American Index Options," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 15(2), pages 127-137, June.
    30. Peter Carr & Robert Jarrow & Ravi Myneni, 2008. "Alternative Characterizations Of American Put Options," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 5, pages 85-103, World Scientific Publishing Co. Pte. Ltd..
    31. Whaley, Robert E., 1981. "On the valuation of American call options on stocks with known dividends," Journal of Financial Economics, Elsevier, vol. 9(2), pages 207-211, June.
    32. Overdahl, James A., 1988. "The Early Exercise of Options on Treasury Bond Futures," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(4), pages 437-449, December.
    33. Dunn, Kenneth B. & Eades, Kenneth M., 1989. "Voluntary conversion of convertible securities and the optimal call strategy," Journal of Financial Economics, Elsevier, vol. 23(2), pages 273-301, August.
    34. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-1250.
    35. Broadie, Mark & Detemple, Jerome & Ghysels, Eric & Torres, Olivier, 2000. "American options with stochastic dividends and volatility: A nonparametric investigation," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 53-92.
    36. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
    37. Stutzer, Michael, 1996. "A Simple Nonparametric Approach to Derivative Security Valuation," Journal of Finance, American Finance Association, vol. 51(5), pages 1633-1652, December.
    38. 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, April.
    39. Hans‐Jürg Büttler & Jorg Waldvogel, 1996. "Pricing Callable Bonds By Means Of Green'S Function1," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 53-88, January.
    40. Dan W. French & Edwin D. Maberly, 1992. "Early Exercise Of American Index Options," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 15(2), pages 127-137, June.
    41. 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.
    42. Marek Rutkowski, 1994. "The Early Exercise Premium Representation Of Foreign Market American Options1," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 313-325, October.
    43. Geske, Robert, 1979. "A note on an analytical valuation formula for unprotected American call options on stocks with known dividends," Journal of Financial Economics, Elsevier, vol. 7(4), pages 375-380, December.
    44. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    45. Andrews, Donald W. K., 1991. "Asymptotic optimality of generalized CL, cross-validation, and generalized cross-validation in regression with heteroskedastic errors," Journal of Econometrics, Elsevier, vol. 47(2-3), pages 359-377, February.
    46. Zivney, Terry L., 1991. "The Value of Early Exercise in Option Prices: An Empirical Investigation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(1), pages 129-138, March.
    47. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14, April.
    48. Diz, Fernando & Finucane, Thomas J, 1993. "The Rationality of Early Exercise Decisions: Evidence from the S&P 100 Index Options Market," Review of Financial Studies, Society for Financial Studies, vol. 6(4), pages 765-797.
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    1. 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.
    2. 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.
    3. Shively, Thomas S. & Walker, Stephen G. & Damien, Paul, 2011. "Nonparametric function estimation subject to monotonicity, convexity and other shape constraints," Journal of Econometrics, Elsevier, vol. 161(2), pages 166-181, April.
    4. Li, Gang & Zhang, Chu, 2013. "Diagnosing affine models of options pricing: Evidence from VIX," Journal of Financial Economics, Elsevier, vol. 107(1), pages 199-219.
    5. 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.
    6. Yu, Xisheng & Xie, Xiaoke, 2015. "Pricing American options: RNMs-constrained entropic least-squares approach," The North American Journal of Economics and Finance, Elsevier, vol. 31(C), pages 155-173.
    7. Broadie, Mark & Detemple, Jerome & Ghysels, Eric & Torres, Olivier, 2000. "American options with stochastic dividends and volatility: A nonparametric investigation," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 53-92.
    8. Weiping Li & Su Chen, 2018. "The Early Exercise Premium In American Options By Using Nonparametric Regressions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(07), pages 1-29, November.
    9. Yuji Yamada, 2012. "Properties of Optimal Smooth Functions in Additive Models for Hedging Multivariate Derivatives," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 19(2), pages 149-179, May.
    10. Teresa Corzo Santamaría & Javier Gómez Biscarri, 2005. "Nonparametric estimation of convergence of interest rates: Effects on bond pricing," Spanish Economic Review, Springer;Spanish Economic Association, vol. 7(3), pages 167-190, September.
    11. Tze Leung Lai & Samuel Po-Shing Wong, 2007. "Combining domain knowledge and statistical models in time series analysis," Papers math/0702814, arXiv.org.
    12. J Lu & H Ohta, 2003. "Digital contracts-driven method for pricing complex derivatives," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(9), pages 1002-1010, September.
    13. Jun Lu & Hiroshi Ohta, 2003. "A data and digital-contracts driven method for pricing complex derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 3(3), pages 212-219.
    14. Eric Ghysels & Valentin Patilea & Eric Renault & Olivier Torrès, 1997. "Nonparametric Methods and Option Pricing," CIRANO Working Papers 97s-19, CIRANO.
    15. Li, Gang & Zhang, Chu, 2016. "On the relationship between conditional jump intensity and diffusive volatility," Journal of Empirical Finance, Elsevier, vol. 37(C), pages 196-213.
    16. René Garcia & Eric Ghysels & Eric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.
    17. Gagliardini, Patrick & Ronchetti, Diego, 2013. "Semi-parametric estimation of American option prices," Journal of Econometrics, Elsevier, vol. 173(1), pages 57-82.
    18. 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.

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    More about this item

    Keywords

    Option Pricing; Derivative Securities; OEX Contract; Kernel Estimation; Prix d'options; titres dérivés; contrat OEX; estimation par méthode de noyau;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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