IDEAS home Printed from https://ideas.repec.org/a/kap/apfinm/v12y2005i2p109-141.html
   My bibliography  Save this article

Inference Methods for Discretely Observed Continuous-Time Stochastic Volatility Models: A Commented Overview

Author

Listed:
  • J. Jimenez
  • R. Biscay
  • T. Ozaki

Abstract

No abstract is available for this item.

Suggested Citation

  • J. Jimenez & R. Biscay & T. Ozaki, 2005. "Inference Methods for Discretely Observed Continuous-Time Stochastic Volatility Models: A Commented Overview," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 12(2), pages 109-141, June.
    • Handle: RePEc:kap:apfinm:v:12:y:2005:i:2:p:109-141
    DOI: 10.1007/s10690-006-9015-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10690-006-9015-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10690-006-9015-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. Jiang, George J. & Knight, John L., 1997. "A Nonparametric Approach to the Estimation of Diffusion Processes, With an Application to a Short-Term Interest Rate Model," Econometric Theory, Cambridge University Press, vol. 13(5), pages 615-645, October.
    2. Jean Jacod, 2000. "Non‐parametric Kernel Estimation of the Coefficient of a Diffusion," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(1), pages 83-96, March.
    3. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    4. Sundaresan, S.M., 2000. "Continuous-Time Methods in Finance: A Review and an Assessment," Papers 00-03, Columbia - Graduate School of Business.
    5. Ghysels, E. & Gourieroux, C. & Jasiak, J., 1995. "Market Time and Asset Price Movements: Theory and Estimation," Cahiers de recherche 9536, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    6. Fan J. & Zhang C., 2003. "A Reexamination of Diffusion Estimators With Applications to Financial Model Validation," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 118-134, January.
    7. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    8. Hansen, Lars Peter & Scheinkman, Jose Alexandre, 1995. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," Econometrica, Econometric Society, vol. 63(4), pages 767-804, July.
    9. Isao Shoji & Tohru Ozaki, 1997. "Comparative study of estimation methods for continuous time stochastic processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(5), pages 485-506, September.
    10. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," The Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    11. Yacine Aït-Sahalia, 2001. "Transition Densities For Interest Rate And Other Nonlinear Diffusions," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume II), chapter 1, pages 1-34, World Scientific Publishing Co. Pte. Ltd..
    12. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(4), pages 657-681, October.
    13. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    14. David A. Chapman & Neil D. Pearson, 2000. "Is the Short Rate Drift Actually Nonlinear?," Journal of Finance, American Finance Association, vol. 55(1), pages 355-388, February.
    15. Tauchen, George, 1986. "Statistical Properties of Generalized Method-of-Moments Estimators of Structural Parameters Obtained from Financial Market Data: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(4), pages 423-425, October.
    16. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    17. Durham, Garland B & Gallant, A Ronald, 2002. "Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 335-338, July.
    18. Wiggins, James B., 1987. "Option values under stochastic volatility: Theory and empirical estimates," Journal of Financial Economics, Elsevier, vol. 19(2), pages 351-372, December.
    19. Isao Shoji, 2002. "Nonparametric state estimation of diffusion processes," Biometrika, Biometrika Trust, vol. 89(2), pages 451-456, June.
    20. French, Kenneth R., 1980. "Stock returns and the weekend effect," Journal of Financial Economics, Elsevier, vol. 8(1), pages 55-69, March.
    21. A. S. Hurn & K. A. Lindsay & V. L. Martin, 2003. "On the efficacy of simulated maximum likelihood for estimating the parameters of stochastic differential Equations," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 45-63, January.
    22. Helle Sørensen, 2003. "Simulated Likelihood Approximations for Stochastic Volatility Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(2), pages 257-276, June.
    23. Elerain, Ola & Chib, Siddhartha & Shephard, Neil, 2001. "Likelihood Inference for Discretely Observed Nonlinear Diffusions," Econometrica, Econometric Society, vol. 69(4), pages 959-993, July.
    24. Bo Martin Bibby & Michael Sørensen, 2001. "Simplified Estimating Functions for Diffusion Models with a High‐dimensional Parameter," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(1), pages 99-112, March.
    25. A. Ronald Gallant & George Tauchen, "undated". "Reproducing Partial Observed Systems with Application to Interest Rate Diffusions," Computing in Economics and Finance 1997 114, Society for Computational Economics.
    26. Egorov, Alexei V. & Li, Haitao & Xu, Yuewu, 2003. "Maximum likelihood estimation of time-inhomogeneous diffusions," Journal of Econometrics, Elsevier, vol. 114(1), pages 107-139, May.
    27. Mathieu Kessler, 2000. "Simple and Explicit Estimating Functions for a Discretely Observed Diffusion Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(1), pages 65-82, March.
    28. Hull, John & White, Alan, 1987. "Hedging the risks from writing foreign currency options," Journal of International Money and Finance, Elsevier, vol. 6(2), pages 131-152, June.
    29. Chan, K C, et al, 1992. "An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
    30. Mathieu Kessler & Silvestre Paredes, 2002. "Computational Aspects Related to Martingale Estimating Functions for a Discretely Observed Diffusion," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 425-440, September.
    31. Gallant, A. Ronald & Tauchen, George, 1997. "Estimation Of Continuous-Time Models For Stock Returns And Interest Rates," Macroeconomic Dynamics, Cambridge University Press, vol. 1(1), pages 135-168, January.
    32. Hoffmann, Marc, 1999. "Adaptive estimation in diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 135-163, January.
    33. Jiang, George J., 1998. "Nonparametric Modeling of U.S. Interest Rate Term Structure Dynamics and Implications on the Prices of Derivative Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(4), pages 465-497, December.
    34. 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.
    35. Johnson, Herb & Shanno, David, 1987. "Option Pricing when the Variance Is Changing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(2), pages 143-151, June.
    36. Jean-Philippe Bouchaud & Rama Cont, 1998. "A Langevin approach to stock market fluctuations and crashes," Science & Finance (CFM) working paper archive 500027, Science & Finance, Capital Fund Management.
    37. T. Ozaki & J. C. Jimenez & V. Haggan‐Ozaki, 2000. "The Role of the Likelihood Function in the Estimation of Chaos Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(4), pages 363-387, July.
    38. Chiarella, Carl & Hung, Hing & T, Thuy-Duong, 2009. "The volatility structure of the fixed income market under the HJM framework: A nonlinear filtering approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2075-2088, April.
    39. Gallant, A. Ronald & Tauchen, George, 1997. "Reprojecting Partially Observed Systems with Application to Interest Rate Diffusions," Working Papers 97-09, Duke University, Department of Economics.
    40. 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.
    41. Ferson, Wayne E. & Foerster, Stephen R., 1994. "Finite sample properties of the generalized method of moments in tests of conditional asset pricing models," Journal of Financial Economics, Elsevier, vol. 36(1), pages 29-55, August.
    42. Durham, Garland B & Gallant, A Ronald, 2002. "Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 297-316, July.
    43. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-280, July.
    44. Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
    45. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
    46. J. C. Jimenez & T. Ozaki, 2006. "An Approximate Innovation Method For The Estimation Of Diffusion Processes From Discrete Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 77-97, January.
    47. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(4), pages 419-438, December.
    48. Martin Jacobsen, 2001. "Discretely Observed Diffusions: Classes of Estimating Functions and Small Δ‐optimality," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(1), pages 123-149, March.
    49. Carl Chiarella & Thuy-Duong To, 2005. "The Multifactor Nature of the Volatility of the Eurodollar Futures Market," Research Paper Series 150, Quantitative Finance Research Centre, University of Technology, Sydney.
    50. Durham, Garland B., 2003. "Likelihood-based specification analysis of continuous-time models of the short-term interest rate," Journal of Financial Economics, Elsevier, vol. 70(3), pages 463-487, December.
    51. Yacine Ait-Sahalia, 2002. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach," Econometrica, Econometric Society, vol. 70(1), pages 223-262, January.
    52. Tauchen, George, 1986. "Statistical Properties of Generalized Method-of-Moments Estimators of Structural Parameters Obtained from Financial Market Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(4), pages 397-416, October.
    53. Chen, Ren-Raw & Scott, Louis, 2003. "Multi-factor Cox-Ingersoll-Ross Models of the Term Structure: Estimates and Tests from a Kalman Filter Model," The Journal of Real Estate Finance and Economics, Springer, vol. 27(2), pages 143-172, September.
    54. Geyer, Alois L J & Pichler, Stefan, 1999. "A State-Space Approach to Estimate and Test Multifactor Cox-Ingersoll-Ross Models of the Term Structure," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 22(1), pages 107-130, Spring.
    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. Sun, Libo & Lee, Chihoon & Hoeting, Jennifer A., 2015. "A penalized simulated maximum likelihood approach in parameter estimation for stochastic differential equations," Computational Statistics & Data Analysis, Elsevier, vol. 84(C), pages 54-67.

    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. A. S. Hurn & J. I. Jeisman & K. A. Lindsay, 0. "Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations," Journal of Financial Econometrics, Oxford University Press, vol. 5(3), pages 390-455.
    2. Stan Hurn & J.Jeisman & K.A. Lindsay, 2006. "Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations. Working paper #2," NCER Working Paper Series 2, National Centre for Econometric Research.
    3. Zongwu Cai & Yongmiao Hong, 2013. "Some Recent Developments in Nonparametric Finance," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    4. repec:wyi:journl:002108 is not listed on IDEAS
    5. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    6. 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.
    7. Czellar, Veronika & Karolyi, G. Andrew & Ronchetti, Elvezio, 2007. "Indirect robust estimation of the short-term interest rate process," Journal of Empirical Finance, Elsevier, vol. 14(4), pages 546-563, September.
    8. Cai, Zongwu & Hong, Yongmiao, 2003. "Nonparametric Methods in Continuous-Time Finance: A Selective Review," SFB 373 Discussion Papers 2003,15, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    9. Fornari, Fabio & Mele, Antonio, 2006. "Approximating volatility diffusions with CEV-ARCH models," Journal of Economic Dynamics and Control, Elsevier, vol. 30(6), pages 931-966, June.
    10. Stan Hurn & J.Jeisman & K.A. Lindsay, 2006. "Teaching an old dog new tricks: Improved estimation of the parameters of SDEs by numerical solution of the Fokker-Planck equation," Stan Hurn Discussion Papers 2006-01, School of Economics and Finance, Queensland University of Technology.
    11. Cai, Lili & Swanson, Norman R., 2011. "In- and out-of-sample specification analysis of spot rate models: Further evidence for the period 1982-2008," Journal of Empirical Finance, Elsevier, vol. 18(4), pages 743-764, September.
    12. Michael Sørensen, 2008. "Parametric inference for discretely sampled stochastic differential equations," CREATES Research Papers 2008-18, Department of Economics and Business Economics, Aarhus University.
    13. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    14. Helle Sørensen, 2002. "Parametric Inference for Diffusion Processes Observed at Discrete Points in Time: a Survey," Discussion Papers 02-08, University of Copenhagen. Department of Economics.
    15. Jun Yu & Peter C. B. Phillips, 2001. "A Gaussian approach for continuous time models of the short-term interest rate," Econometrics Journal, Royal Economic Society, vol. 4(2), pages 1-3.
    16. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    17. 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.
    18. Jianqing Fan, 2004. "A selective overview of nonparametric methods in financial econometrics," Papers math/0411034, arXiv.org.
    19. Torben G. Andersen & Luca Benzoni & Jesper Lund, 2002. "An Empirical Investigation of Continuous‐Time Equity Return Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1239-1284, June.
    20. Peter C. B. Phillips & Jun Yu, 2009. "Simulation-Based Estimation of Contingent-Claims Prices," The Review of Financial Studies, Society for Financial Studies, vol. 22(9), pages 3669-3705, September.
    21. Yu, Jun & Yang, Zhenlin & Zhang, Xibin, 2006. "A class of nonlinear stochastic volatility models and its implications for pricing currency options," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2218-2231, December.

    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:kap:apfinm:v:12:y:2005:i:2:p:109-141. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.