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November, 1994 An Arbitrage Theory of the Term Structure of Interest Rates
Kristian R. Miltersen
Ann. Appl. Probab. 4(4): 953-967 (November, 1994). DOI: 10.1214/aoap/1177004898


In the setting of the Heath-Jarrow-Morton model, this paper presents sufficient conditions to assure that the stochastic forward rates are strictly positive while maintaining the martingale property of the discounted bond price processes in the case where the stochastic forward rates are described as stochastic differential equations with explicitly state dependent stochastic volatility. Moreover, the stochastic development of the term structure of interest rates is generalized to be described by a class of continuous local martingales instead of Wiener processes. An example showing that this is a true extension of the Heath-Jarrow-Morton model is provided.


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Kristian R. Miltersen. "An Arbitrage Theory of the Term Structure of Interest Rates." Ann. Appl. Probab. 4 (4) 953 - 967, November, 1994.


Published: November, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0818.90008
MathSciNet: MR1304768
Digital Object Identifier: 10.1214/aoap/1177004898

Primary: 90A09
Secondary: 60G44 , 60H05 , 60H10 , 60H30

Keywords: continuous local martingale , financial bond market , forward rate process , pure default-free bond , spot rate process , stochastic differential equation (SDE) , Term structure of interest rates , time changed wiener process

Rights: Copyright © 1994 Institute of Mathematical Statistics


Vol.4 • No. 4 • November, 1994
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