(This abstract was borrowed from another version of this item.)"> (This abstract was borrowed from another version of this item.)">
[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v24y2000i11-12p1829-1857.html
   My bibliography  Save this article

Nonparametric estimation of American options' exercise boundaries and call prices

Author

Listed:
  • Broadie, Mark
  • Detemple, Jerome
  • Ghysels, Eric
  • Torres, Olivier
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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Broadie, Mark & Detemple, Jerome & Ghysels, Eric & Torres, Olivier, 2000. "Nonparametric estimation of American options' exercise boundaries and call prices," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1829-1857, October.
    • Handle: RePEc:eee:dyncon:v:24:y:2000:i:11-12:p:1829-1857
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-1889(99)00094-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Mikhail Chernov & Eric Ghysels, 1998. "What Data Should Be Used to Price Options?," CIRANO Working Papers 98s-22, CIRANO.
    3. 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..
    4. 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.
    5. 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.
    6. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    7. 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.
    8. Karim Abadir & Michael Rockinger, "undated". "Density-Embedding Functions," Discussion Papers 97/16, Department of Economics, University of York.
    9. 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.
    10. Renault, E., 1996. "Econometric Models of Option Pricing Errors," Papers 96.407, Toulouse - GREMAQ.
    11. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(4), pages 657-681, October.
    12. 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..
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
    18. Stutzer, Michael, 1996. "A Simple Nonparametric Approach to Derivative Security Valuation," Journal of Finance, American Finance Association, vol. 51(5), pages 1633-1652, December.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. Diz, Fernando & Finucane, Thomas J, 1993. "The Rationality of Early Exercise Decisions: Evidence from the S&P 100 Index Options Market," The Review of Financial Studies, Society for Financial Studies, vol. 6(4), pages 765-797.
    24. 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.
    25. 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.
    26. 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.
    27. 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.
    28. 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.
    29. 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.
    30. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
    31. 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.
    32. 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.
    33. 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.
    34. Kim, In Joon, 1990. "The Analytic Valuation of American Options," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 547-572.
    35. 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.
    36. Michael J. P. Selby & Stewart D. Hodges, 1987. "On the Evaluation of Compound Options," Management Science, INFORMS, vol. 33(3), pages 347-355, March.
    37. 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.
    38. 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..
    39. 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.
    40. 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.
    41. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," The Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-1250.
    42. 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.
    43. repec:bla:jfinan:v:53:y:1998:i:2:p:499-547 is not listed on IDEAS
    44. 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.
    45. Marek Rutkowski, 1994. "The Early Exercise Premium Representation Of Foreign Market American Options1," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 313-325, October.
    46. 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.
    47. 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.
    48. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    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. Eric Ghysels & Valentin Patilea & Eric Renault & Olivier Torrès, 1997. "Nonparametric Methods and Option Pricing," CIRANO Working Papers 97s-19, CIRANO.
    9. René Garcia & Eric Ghysels & Eric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.
    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. repec:hum:wpaper:sfb649dp2005-020 is not listed on IDEAS
    12. Gagliardini, Patrick & Ronchetti, Diego, 2013. "Semi-parametric estimation of American option prices," Journal of Econometrics, Elsevier, vol. 173(1), pages 57-82.
    13. 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.
    14. Fengler, Matthias R. & Härdle, Wolfgang Karl & Mammen, Enno, 2005. "A dynamic semiparametric factor model for implied volatility string dynamics," SFB 649 Discussion Papers 2005-020, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    15. Tze Leung Lai & Samuel Po-Shing Wong, 2007. "Combining domain knowledge and statistical models in time series analysis," Papers math/0702814, arXiv.org.
    16. 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.
    17. 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.
    18. 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.
    19. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    3. Manuel Moreno & Javier Navas, 2003. "On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives," Review of Derivatives Research, Springer, vol. 6(2), pages 107-128, May.
    4. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    5. Mark Broadie & Jérôme Detemple, 1996. "Recent Advances in Numerical Methods for Pricing Derivative Securities," CIRANO Working Papers 96s-17, CIRANO.
    6. René Garcia & Eric Ghysels & Eric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.
    7. Weihan Li & Jin E. Zhang & Xinfeng Ruan & Pakorn Aschakulporn, 2024. "An empirical study on the early exercise premium of American options: Evidence from OEX and XEO options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(7), pages 1117-1153, July.
    8. Minqiang Li, 2010. "A quasi-analytical interpolation method for pricing American options under general multi-dimensional diffusion processes," Review of Derivatives Research, Springer, vol. 13(2), pages 177-217, July.
    9. Gao, Bin & Huang, Jing-zhi & Subrahmanyam, Marti, 2000. "The valuation of American barrier options using the decomposition technique," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1783-1827, October.
    10. Ruas, João Pedro & Dias, José Carlos & Vidal Nunes, João Pedro, 2013. "Pricing and static hedging of American-style options under the jump to default extended CEV model," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4059-4072.
    11. Barone-Adesi, Giovanni, 2005. "The saga of the American put," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2909-2918, November.
    12. Cosma, Antonio & Galluccio, Stefano & Pederzoli, Paola & Scaillet, Olivier, 2020. "Early Exercise Decision in American Options with Dividends, Stochastic Volatility, and Jumps," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(1), pages 331-356, February.
    13. Cosma, Antonio & Galluccio, Stefano & Scaillet, Olivier, 2012. "Valuing American options using fast recursive projections," Working Papers unige:41856, University of Geneva, Geneva School of Economics and Management.
    14. Aricson Cruz & José Carlos Dias, 2020. "Valuing American-style options under the CEV model: an integral representation based method," Review of Derivatives Research, Springer, vol. 23(1), pages 63-83, April.
    15. Zhongkai Liu & Tao Pang, 2016. "An efficient grid lattice algorithm for pricing American-style options," International Journal of Financial Markets and Derivatives, Inderscience Enterprises Ltd, vol. 5(1), pages 36-55.
    16. Roland Mallier & Ghada Alobaidi, 2000. "Laplace transforms and American options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(4), pages 241-256.
    17. B. Gao J. Huang, "undated". "The Valuation of American Barrier Options Using the Decomposition Technique," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-002, New York University, Leonard N. Stern School of Business-.
    18. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    19. In oon Kim & Bong-Gyu Jang & Kyeong Tae Kim, 2013. "A simple iterative method for the valuation of American options," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 885-895, May.
    20. repec:wyi:journl:002108 is not listed on IDEAS
    21. Gagliardini, Patrick & Ronchetti, Diego, 2013. "Semi-parametric estimation of American option prices," Journal of Econometrics, Elsevier, vol. 173(1), pages 57-82.

    More about this item

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:24:y:2000:i:11-12:p:1829-1857. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jedc .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.