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Long-term factorization in Heath–Jarrow–Morton models

Likuan Qin () and Vadim Linetsky ()
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Likuan Qin: Northwestern University
Vadim Linetsky: Northwestern University

Finance and Stochastics, 2018, vol. 22, issue 3, 621-641

Abstract: Abstract The long-term factorization decomposes the stochastic discount factor (SDF) into discounting at the rate of return on the long bond and a martingale that defines a long-term forward measure. We establish sufficient conditions for existence of the long-term factorization in HJM models. A condition on the forward rate volatility ensures existence of the long bond volatility. This yields existence of the long bond and convergence of T $T$ -forward measures to the long forward measure. It contrasts with the familiar risk-neutral factorization that decomposes the SDF into discounting at the short rate and a martingale defining the risk-neutral measure.

Keywords: Stochastic discount factor; Long-term factorization; Long bond; Long forward measure; HJM models; 60H15 (search for similar items in EconPapers)
JEL-codes: E43 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s00780-018-0365-7

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