A Maximum Likelihood Approach to Estimation of Heath-Jarrow-Morton Models
AbstractResearch on the Heath-Jarrow-Morton (1992) term structure models so far has focused on the class having time-deterministic instantaneous forward rate volatility. In this case the forward rate is Markovian, even if the spot rate process is not. However, this Markovian feature can only be used under the historical measure, involving two unsatisfactory assumptions: one on market price risk, usually made for pure mathematical tractability, the other to use futures yields as a proxy for the instantaneous forward rate, which may result in estimation bias. This paper circumvents both of these assumptions. First, the bias is quantified and shown to be non-negligible. Then futures contracts are treated as derivative instruments written on forward rates to derive the full information maximum likelihood estimator for observable futures prices, using both time series and cross-sectional data, without the need to assume and estimate any functional forms for the market price of interest rate risk. The derivation involves the likelihood transformation method of Duan (1994). The method is then applied to the estimation of a humped forward rate volatility model for Eurodollar futures series traded on the Chicago Mercantile Exchange.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 80.
Date of creation: 01 May 2002
Date of revision:
Contact details of provider:
Postal: PO Box 123, Broadway, NSW 2007, Australia
Phone: +61 2 9514 7777
Fax: +61 2 9514 7711
Web page: http://www.business.uts.edu.au/qfrc/index.html
More information through EDIRC
term structure; heath-jarrow-morton; time-deterministic forward volatility; humped forward volatility model; full information maximum likelihood;
Find related papers by JEL classification:
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
- E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Carl Chiarella & Oh-Kang Kwon, 1999.
"Forward Rate Dependent Markovian Transformations of the Heath-Jarrow-Morton Term Structure Model,"
Research Paper Series
5, Quantitative Finance Research Centre, University of Technology, Sydney.
- Carl Chiarella & Oh Kang Kwon, 2001. "Forward rate dependent Markovian transformations of the Heath-Jarrow-Morton term structure model," Finance and Stochastics, Springer, vol. 5(2), pages 237-257.
- Brennan, Michael J. & Schwartz, Eduardo S., 1982. "An Equilibrium Model of Bond Pricing and a Test of Market Efficiency," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(03), pages 301-329, September.
- R. Bhar & C. Chiarella, 1997.
"Transformation of Heath?Jarrow?Morton models to Markovian systems,"
The European Journal of Finance,
Taylor & Francis Journals, vol. 3(1), pages 1-26.
- Ram Bhar & Carl Chiarella, 1995. "Transformation of Heath-Jarrow-Morton Models to Markovian Systems," Working Paper Series 53, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
- Cox, John C. & Ingersoll, Jonathan Jr. & Ross, Stephen A., 1981. "The relation between forward prices and futures prices," Journal of Financial Economics, Elsevier, vol. 9(4), pages 321-346, December.
- Amin, Kaushik I & Ng, Victor K, 1997. "Inferring Future Volatility from the Information in Implied Volatility in Eurodollar Options: A New Approach," Review of Financial Studies, Society for Financial Studies, vol. 10(2), pages 333-67.
- Ram Bhar & Carl Chiarella, 1995.
"Interest Rate Futures: Estimation of Volatility Parameters in an Arbitrage-Free Framework,"
Working Paper Series
55, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
- Ramaprasad Bhar & Carl Chiarella, 1997. "Interest rate futures: estimation of volatility parameters in an arbitrage-free framework," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(4), pages 181-199.
- 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.
- Lo, Andrew W., 1988. "Maximum Likelihood Estimation of Generalized Itô Processes with Discretely Sampled Data," Econometric Theory, Cambridge University Press, vol. 4(02), pages 231-247, August.
- Andrew W. Lo, . "Maximum Likelihood Estimation of Generalized Ito Processes with Discretely Sampled Data," Rodney L. White Center for Financial Research Working Papers 15-86, Wharton School Rodney L. White Center for Financial Research.
- David A. Chapman & John B. Long Jr. & Neil D. Pearson, 1998.
"Using Proxies for the Short Rate: When are Three Months Like an Instant?,"
9808004, EconWPA, revised 07 Oct 1998.
- Chapman, David A & Long, John B, Jr & Pearson, Neil D, 1999. "Using Proxies for the Short Rate: When Are Three Months Like an Instant?," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 763-806.
- 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.
- Ho, Thomas S Y & Lee, Sang-bin, 1986. " Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-29, December.
- Brennan, Michael J. & Schwartz, Eduardo S., 1979. "A continuous time approach to the pricing of bonds," Journal of Banking & Finance, Elsevier, vol. 3(2), pages 133-155, July.
- Jurgen A. Doornik & Henrik Hansen, 2008.
"An Omnibus Test for Univariate and Multivariate Normality,"
Oxford Bulletin of Economics and Statistics,
Department of Economics, University of Oxford, vol. 70(s1), pages 927-939, December.
- Jurgen A Doornik & Henrik Hansen, . "An omnibus test for univariate and multivariate normalit," Economics Papers W4&91., Economics Group, Nuffield College, University of Oxford.
- Raj, Mahendra & Sim, Ah Boon & Thurston, David C., 1997. "A generalized method of moments comparison of the cox-ingersoll-ross and heath-jarrow-morton models," Journal of Economics and Business, Elsevier, vol. 49(2), pages 169-192.
- Amin, Kaushik I. & Morton, Andrew J., 1994. "Implied volatility functions in arbitrage-free term structure models," Journal of Financial Economics, Elsevier, vol. 35(2), pages 141-180, April.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Michael J. Brennan and Eduardo S. Schwartz., 1979. "A Continuous-Time Approach to the Pricing of Bonds," Research Program in Finance Working Papers 85, University of California at Berkeley.
- Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
- Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
- Yassine El Qalli, 2010. "Recursive Bayesian Estimation In Forward Price Models Implied By Fair Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(02), pages 301-333.
- Lee, Kiseop & Xu, Mingxin, 2007. "Parameter estimation from multinomial trees to jump diffusions with k means clustering," MPRA Paper 3307, University Library of Munich, Germany, revised 26 Apr 2007.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Duncan Ford).
If references are entirely missing, you can add them using this form.