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Maximum Likelihood Estimation of Generalized Ito Processes with Discretely Sampled Data

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  • Andrew W. Lo

Abstract

In this paper, we consider the parametric estimation problem for continuous time stochastic processes described by general first-order nonlinear stochastic differential equations of the Ito type. We characterize the likelihood function of a discretely-sampled set of observations as the solution to a functional partial differential equation. The consistency and asymptotic normality of the maximum likelihood estimators are explored, and several illustrative examples are provided.

Suggested Citation

  • Andrew W. Lo, 1986. "Maximum Likelihood Estimation of Generalized Ito Processes with Discretely Sampled Data," NBER Technical Working Papers 0059, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberte:0059
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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Chamberlain, Gary, 1988. "Asset Pricing in Multiperiod Securities Markets," Econometrica, Econometric Society, vol. 56(6), pages 1283-1300, November.
    6. 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.
    7. Sims, Christopher A, 1971. "Discrete Approximations to Continuous Time Distributed Lags in Econometrics," Econometrica, Econometric Society, vol. 39(3), pages 545-563, May.
    8. Lars Peter Hansen & Thomas J. Sargent, 1982. "Formulating and estimating continuous time rational expectations models," Staff Report 75, Federal Reserve Bank of Minneapolis.
    9. 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.
    10. Phillips, P C B, 1972. "The Structural Estimation of a Stochastic Differential Equation System," Econometrica, Econometric Society, vol. 40(6), pages 1021-1041, November.
    11. Abel, Andrew B, 1983. "Optimal Investment under Uncertainty," American Economic Review, American Economic Association, vol. 73(1), pages 228-233, March.
    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.
    14. Lo, Andrew W., 1986. "Statistical tests of contingent-claims asset-pricing models : A new methodology," Journal of Financial Economics, Elsevier, vol. 17(1), pages 143-173, September.
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