IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v4y1988i02p231-247_01.html
   My bibliography  Save this article

Maximum Likelihood Estimation of Generalized Itô Processes with Discretely Sampled Data

Author

Listed:
  • Lo, Andrew W.

Abstract

This paper considers the parametric estimation problem for continuous-time stochastic processes described by first-order nonlinear stochastic differential equations of the generalized Itô type (containing both jump and diffusion components). We derive a particular functional partial differential equation which characterizes the exact likelihood function of a discretely sampled Itô process. In addition, we show by a simple counterexample that the common approach of estimating parameters of an Itô process by applying maximum likelihood to a discretization of the stochastic differential equation does not yield consistent estimators.

Suggested Citation

  • Lo, Andrew W., 1988. "Maximum Likelihood Estimation of Generalized Itô Processes with Discretely Sampled Data," Econometric Theory, Cambridge University Press, vol. 4(2), pages 231-247, August.
  • Handle: RePEc:cup:etheor:v:4:y:1988:i:02:p:231-247_01
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0266466600012044/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Grossman, S J & Melino, Angelo & Shiller, Robert J, 1987. "Estimating the Continuous-Time Consumption-Based Asset-Pricing Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(3), pages 315-327, July.
    2. Sims, Christopher A, 1971. "Discrete Approximations to Continuous Time Distributed Lags in Econometrics," Econometrica, Econometric Society, vol. 39(3), pages 545-563, May.
    3. Harrison, J Michael & Pitbladdo, Richard & Schaefer, Stephen M, 1984. "Continuous Price Processes in Frictionless Markets Have Infinite Variation," The Journal of Business, University of Chicago Press, vol. 57(3), pages 353-365, July.
    4. Shiller, Robert J. & Perron, Pierre, 1985. "Testing the random walk hypothesis : Power versus frequency of observation," Economics Letters, Elsevier, vol. 18(4), pages 381-386.
    5. Chamberlain, Gary, 1988. "Asset Pricing in Multiperiod Securities Markets," Econometrica, Econometric Society, vol. 56(6), pages 1283-1300, November.
    6. Lars Peter Hansen & Thomas J. Sargent, 1982. "Formulating and estimating continuous time rational expectations models," Staff Report 75, Federal Reserve Bank of Minneapolis.
    7. Marsh, Terry A & Rosenfeld, Eric R, 1983. "Stochastic Processes for Interest Rates and Equilibrium Bond Prices," Journal of Finance, American Finance Association, vol. 38(2), pages 635-646, May.
    8. Phillips, P C B, 1972. "The Structural Estimation of a Stochastic Differential Equation System," Econometrica, Econometric Society, vol. 40(6), pages 1021-1041, November.
    9. Harvey, A. C. & Stock, James H., 1985. "The Estimation of Higher-Order Continuous Time Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 1(1), pages 97-117, April.
    10. Abel, Andrew B, 1983. "Optimal Investment under Uncertainty," American Economic Review, American Economic Association, vol. 73(1), pages 228-233, March.
    11. 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 637-654, May-June.
    12. Ball, Clifford A & Torous, Walter N, 1985. "On Jumps in Common Stock Prices and Their Impact on Call Option Pricing," Journal of Finance, American Finance Association, vol. 40(1), pages 155-173, March.
    13. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Bertsimas, Dimitris. & Kogan, Leonid, 1974- & Lo, Andrew W., 1997. "Pricing and hedging derivative securities in incomplete markets : an e-arbitrage approach," Working papers WP 3973-97., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    3. Bu, Ruijun & Cheng, Jie & Hadri, Kaddour, 2016. "Reducible diffusions with time-varying transformations with application to short-term interest rates," Economic Modelling, Elsevier, vol. 52(PA), pages 266-277.
    4. van der Wel, M., 2020. "Connecting Silos : On linking macroeconomics and finance, and the role of econometrics therein," ERIM Inaugural Address Series Research in Management 124748, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam..
    5. Dimitris Bertsimas & Leonid Kogan & Andrew W. Lo, 1997. "Pricing and Hedging Derivative Securities in Incomplete Markets: An E-Aritrage Model," NBER Working Papers 6250, National Bureau of Economic Research, Inc.
    6. Shiller, Robert J. & Huston McCulloch, J., 1990. "The term structure of interest rates," Handbook of Monetary Economics, in: B. M. Friedman & F. H. Hahn (ed.), Handbook of Monetary Economics, edition 1, volume 1, chapter 13, pages 627-722, Elsevier.
    7. Hélène Hamisultane, 2008. "Which Method for Pricing Weather Derivatives ?," Working Papers halshs-00355856, HAL.
    8. Bent Jesper Christensen & Olaf Posch & Michel van der Wel, 2014. "Estimating Dynamic Equilibrium Models Using Mixed Frequency Macro and Financial Data," CESifo Working Paper Series 5030, CESifo.
    9. repec:dau:papers:123456789/5374 is not listed on IDEAS
    10. S H Martzoukos, 2009. "Real R&D options and optimal activation of two-dimensional random controls," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(6), pages 843-858, June.
    11. Sercu, P., 1991. "Bond options and bond portfolio insurance," Insurance: Mathematics and Economics, Elsevier, vol. 10(3), pages 203-230, December.
    12. Christensen, Bent Jesper & Posch, Olaf & van der Wel, Michel, 2016. "Estimating dynamic equilibrium models using mixed frequency macro and financial data," Journal of Econometrics, Elsevier, vol. 194(1), pages 116-137.
    13. Dimitris Bertsimas & Leonid Kogan & Andrew W. Lo, 2001. "Hedging Derivative Securities and Incomplete Markets: An (epsilon)-Arbitrage Approach," Operations Research, INFORMS, vol. 49(3), pages 372-397, June.
    14. Ruijun Bu & Ludovic Giet & Kaddour Hadri & Michel Lubrano, 2009. "Modeling Multivariate Interest Rates using Time-Varying Copulas and Reducible Stochastic Differential Equations," Working Papers halshs-00408014, HAL.
    15. Thornton, Michael A. & Chambers, Marcus J., 2016. "The exact discretisation of CARMA models with applications in finance," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 739-761.
    16. Ben-Ameur, Hatem & Breton, Michele & Karoui, Lotfi & L'Ecuyer, Pierre, 2007. "A dynamic programming approach for pricing options embedded in bonds," Journal of Economic Dynamics and Control, Elsevier, vol. 31(7), pages 2212-2233, July.
    17. Eduardo Abi Jaber, 2020. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Working Papers hal-02946146, HAL.
    18. Bernard Dumas, "undated". "Pricing Physical Assets Internationally," Rodney L. White Center for Financial Research Working Papers 12-88, Wharton School Rodney L. White Center for Financial Research.
    19. Saphores, Jean-Daniel & Khalaf, Lynda & Pelletier, Denis, 2000. "On Jumps and ARCH Effects in Natural Resource Prices. An Application to Stumpage Prices from Pacific Northwest National Forests," Cahiers de recherche 0003, GREEN.
    20. Posch, Olaf, 2009. "Structural estimation of jump-diffusion processes in macroeconomics," Journal of Econometrics, Elsevier, vol. 153(2), pages 196-210, December.
    21. Bulan, Laarni & Mayer, Christopher & Somerville, C. Tsuriel, 2009. "Irreversible investment, real options, and competition: Evidence from real estate development," Journal of Urban Economics, Elsevier, vol. 65(3), pages 237-251, May.

    More about this item

    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:cup:etheor:v:4:y:1988:i:02:p:231-247_01. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://www.cambridge.org/ect .

    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: Keith Waters (email available below). General contact details of provider: https://www.cambridge.org/ect .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.