Jump-diffusion processes and affine term structure models: additional closed-form approximate solutions, distributional assumptions for jumps, and parameter estimates
Affine term structure models in which the short rate follows a jump-diffusion process are difficult to solve, and the parameters of such models are hard to estimate. Without analytical answers to the partial difference differential equation (PDDE) for bond prices implied by jump-diffusion processes, one must find a numerical solution to the PDDE or exactly solve an approximate PDDE. Although the literature focuses on a single linearization technique to estimate the PDDE, this paper outlines alternative methods that seem to improve accuracy. Also, closed-form solutions, numerical estimates, and closed-form approximations of the PDDE each ultimately depend on the presumed distribution of jump sizes, and this paper explores a broader set of possible densities that may be more consistent with intuition, including a bi-modal Gaussian mixture. GMM and MLE of one- and two-factor jump-diffusion models produce some evidence for jumps, but sensitivity analyses suggest sizeable confidence intervals around the parameters.
|Date of creation:||2005|
|Contact details of provider:|| Postal: 20th Street and Constitution Avenue, NW, Washington, DC 20551|
Web page: http://www.federalreserve.gov/
More information through EDIRC
|Order Information:||Web: http://www.federalreserve.gov/pubs/feds/fedsorder.html|
References listed on IDEAS
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.:
- Sanjiv R. Das, 1998. "Poisson-Guassian Processes and the Bond Markets," NBER Working Papers 6631, National Bureau of Economic Research, Inc.
- 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.
- Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
- Ahn, Chang Mo & Thompson, Howard E, 1988. " Jump-Diffusion Processes and the Term Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 43(1), pages 155-174, March.
- Pierluigi Balduzzi & Sanjiv Das & Silverio Foresi, 1996.
"The Central Tendency: A Second Factor in Bond Yields,"
New York University, Leonard N. Stern School Finance Department Working Paper Seires
96-12, New York University, Leonard N. Stern School of Business-.
- Pierluigi Balduzzi & Sanjiv Ranjan Das & Silverio Foresi, 1998. "The Central Tendency: A Second Factor In Bond Yields," The Review of Economics and Statistics, MIT Press, vol. 80(1), pages 62-72, February.
- Pierluigi Balduzzi & Sanjiv Ranjan Das & Silverio Foresi, 1997. "The Central Tendency: A Second Factor in Bond Yields," NBER Working Papers 6325, National Bureau of Economic Research, Inc.
- Ait-Sahalia, Yacine, 2004. "Disentangling diffusion from jumps," Journal of Financial Economics, Elsevier, vol. 74(3), pages 487-528, December.
- Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
- Pearson, Neil D & Sun, Tong-Sheng, 1994. " Exploiting the Conditional Density in Estimating the Term Structure: An Application to the Cox, Ingersoll, and Ross Model," Journal of Finance, American Finance Association, vol. 49(4), pages 1279-1304, September.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985.
"A Theory of the Term Structure of Interest Rates,"
Econometric Society, vol. 53(2), pages 385-407, March.
- Monika Piazzesi, 2005. "Bond Yields and the Federal Reserve," Journal of Political Economy, University of Chicago Press, vol. 113(2), pages 311-344, April.
- Ball, Clifford A. & Torous, Walter N., 1983. "A Simplified Jump Process for Common Stock Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(01), pages 53-65, March.
- Michael Johannes, 2004. "The Statistical and Economic Role of Jumps in Continuous-Time Interest Rate Models," Journal of Finance, American Finance Association, vol. 59(1), pages 227-260, 02.
- Merton, Robert C., 1975.
"Option pricing when underlying stock returns are discontinuous,"
787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
- Beckers, Stan, 1981. "A Note on Estimating the Parameters of the Diffusion-Jump Model of Stock Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 16(01), pages 127-140, March.
- Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
- Hamilton, James D, 1996. "The Daily Market for Federal Funds," Journal of Political Economy, University of Chicago Press, vol. 104(1), pages 26-56, February.
When requesting a correction, please mention this item's handle: RePEc:fip:fedgfe:2005-53. 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: (Franz Osorio)
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 references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.