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Poisson-Guassian Processes and the Bond Markets

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  • Sanjiv R. Das

Abstract

That interest rates move in a discontinuous manner is no surprise to participants in the bond markets. This paper proposes and estimates a class of Poisson-Gaussian processes that allow for jumps in interest rates. Estimation is undertaken using exact continuous-time and discrete-time estimators. Analytical derivations of the characteristic functions, moments and density functions of jump-diffusion stochastic process are developed and employed in empirical estimation. These derivations are general enough to accommodate any jump distribution. We find that jump processes capture empirical features of the data which would not be captured by diffusion models. The models in the paper enable an assessment of the impact of Fed activity and day-of-week effects on the stochastic process for interest rates. There is strong evidence that existing diffusion models would be well-enhanced by jump processes.

Suggested Citation

  • Sanjiv R. Das, 1998. "Poisson-Guassian Processes and the Bond Markets," NBER Working Papers 6631, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:6631 Note: AP
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    References listed on IDEAS

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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. David Backus & Silverio Foresi & Liuren Wu, 1997. "Macroeconomic Foundations of Higher Moments in Bond Yields," New York University, Leonard N. Stern School Finance Department Working Paper Seires 96-10, New York University, Leonard N. Stern School of Business-.
    3. Heath, David & Jarrow, Robert & Morton, Andrew, 1990. "Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(04), pages 419-440, December.
    4. Brenner, Robin J. & Harjes, Richard H. & Kroner, Kenneth F., 1996. "Another Look at Models of the Short-Term Interest Rate," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(01), pages 85-107, March.
    5. Philippe Jorion, 1988. "On Jump Processes in the Foreign Exchange and Stock Markets," Review of Financial Studies, Society for Financial Studies, vol. 1(4), pages 427-445.
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    Cited by:

    1. Hjalmarsson, Erik, 2003. "Does the Black-Scholes formula work for electricity markets? A nonparametric approach," Working Papers in Economics 101, University of Gothenburg, Department of Economics.
    2. Duffie, Darrell, 2005. "Credit risk modeling with affine processes," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2751-2802, November.
    3. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    4. Hao Zhou, 2001. "Jump-diffusion term structure and Ito conditional moment generator," Finance and Economics Discussion Series 2001-28, Board of Governors of the Federal Reserve System (U.S.).
    5. Fernando Antonio Lucena Aiube & Edison Americo Huarsaya Tito, 2009. "Evaluating cash benefits as real options for a commodity producer in an emerging market," Brazilian Review of Finance, Brazilian Society of Finance, vol. 7(3), pages 361-375.
    6. repec:wsi:ijtafx:v:08:y:2005:i:06:n:s0219024905003268 is not listed on IDEAS
    7. Marco Antônio Guimarães Dias & Katia Maria Carlos Rocha, 2015. "Petroleum Concessions with Extendible Options: Investment Timing and Value Using Mean Reversion and Jump Processes for Oil Prices," Discussion Papers 0082, Instituto de Pesquisa Econômica Aplicada - IPEA.
    8. Lundgren, Jens & Hellström, Jörgen & Rudholm, Niklas, 2008. "Multinational Electricity Market Integration and Electricity Price Dynamics," HUI Working Papers 16, HUI Research.
    9. Steven Kou, 2000. "A Jump Diffusion Model for Option Pricing with Three Properties: Leptokurtic Feature, Volatility Smile, and Analytical Tractability," Econometric Society World Congress 2000 Contributed Papers 0062, Econometric Society.
    10. Cossin, Didier & González, Fernando & Huang, Zhijiang & Backé, Peter, 2003. "A framework for collateral risk control determination," Working Paper Series 209, European Central Bank.
    11. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance,in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742 Elsevier.
    12. J. Benson Durham, 2005. "Jump-diffusion processes and affine term structure models: additional closed-form approximate solutions, distributional assumptions for jumps, and parameter estimates," Finance and Economics Discussion Series 2005-53, Board of Governors of the Federal Reserve System (U.S.).

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