×

zbMATH — the first resource for mathematics

Markovian term structure models in discrete time. (English) Zbl 1020.60060
Markovian term structure models in discrete time and with continuous state space are studied. More precisely, there are discussed the structural properties of such models if one has the Markov property for a part of the forward curve. The authors investigate two cases where these parts are either a true subset of the forward curve, including the short rate, or the entire forward curve. A version of the Heath, Jarrow and Morton drift condition is obtained. Under a Gaussian assumption a Heath-Jarrow-Morton-Musiela type equation is derived.

MSC:
60J05 Discrete-time Markov processes on general state spaces
91B28 Finance etc. (MSC2000)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] BJÖRK, T. (1998). Arbitrage Theory in Continuous Time. Oxford Univ. Press.
[2] DA PRATO, G. and ZABCZy K, J. (1992). Stochastic Equations in Infinite Dimensions. Cambridge Univ. Press. · Zbl 0761.60052
[3] DUFFIE, D. and KAN, R. (1996). A yield-factor model of interest rates. Math. Finance 6 379- 406. · Zbl 0915.90014
[4] FELLER, W. (1971). An Introduction to Probability Theory and Its Applications 2, 2nd ed. Wiley, New York. · Zbl 0219.60003
[5] FILIPOVI Ć, D. (2001). A general characterization of one-factor affine term structure models. Finance and Stochastics 5 389-412. · Zbl 0978.91033
[6] HEATH, D., JARROW, R. and MORTON, A. (1989). Bond pricing and the term structure of interest rates: a discrete time approximation. J. Financial Qualitative Anal. 25 419-440.
[7] HEATH, D., JARROW, R. and MORTON, A. (1992). Bond pricing and the term structure of interest rates: A new methodology. Econometrica 60 77-101. · Zbl 0751.90009
[8] HUBALEK, F. (2001). A counterexample involving exponential-affine Laplace transforms. Working paper, TU Vienna.
[9] JARROW, R. (1996). Modelling Fixed Income Securities and Interest Rate Options. McGrawHill, New York. · Zbl 1079.91532
[10] MUSIELA, M. (1993). Stochastic PDEs and term structure models. Journées Internationales de Finance, IGR-AFFi, La Boule.
[11] SHIRy AEV, A. N. (1999). Essentials of Stochastic Finance. World Scientific, Singapore. · Zbl 0926.62100
[12] ZABCZy K, J. (1996). Chance and Decision. Quaderni, Scuola Normale Superiore di Pisa.
[13] ZABCZy K, J. (2002). Selected Topics in Stochastic Processes. Appunti dei Corsi, Scuola Normale Superiore di Pisa, 1997-1999.
[14] PRINCETON, NEW JERSEY 08544 E-MAIL: dfilipov@princeton.edu POLISH ACADEMY OF SCIENCE P-00-950 WARSAW POLAND E-MAIL: zabczy k@panim.impan.gov.pl
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.