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Levy-Vasicek Models and the Long-Bond Return Process

Brody, Dorje, Hughston, L and Meier, D (2018) Levy-Vasicek Models and the Long-Bond Return Process International Journal of Theoretical and Applied Finance, 21 (3).

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Abstract

The classical derivation of the well-known Vasicek model for interest rates is reformulated in terms of the associated pricing kernel. An advantage of the pricing kernel method is that it allows one to generalize the construction to the Levy-Vasicek case, avoiding issues of market incompleteness. In the Levy-Vasicek model the short rate is taken in the real-world measure to be a mean-reverting process with a general one-dimensional Levy driver admitting exponential moments. Expressions are obtained for the Levy-Vasicek bond prices and interest rates, along with a formula for the return on a unit investment in the long bond, defined by Lt = limT1 PtT =P0T , where PtT is the price at time t of a T-maturity discount bond. We show that the pricing kernel of a Levy-Vasicek model is uniformly integrable if and only if the long rate of interest is strictly positive.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
NameEmailORCID
Brody, Dorjed.brody@surrey.ac.uk
Hughston, L
Meier, D
Date : 28 May 2018
DOI : 10.1142/S0219024918500267
Copyright Disclaimer : Electronic version of an article published as International Journal of Theoretical and Applied Finance, 21, 3, 2018, DOI:10.1142/S0219024918500267 © copyright World Scientific Publishing Company. https://www.worldscientific.com/worldscinet/ijtaf
Uncontrolled Keywords : Vasicek model Lévy models interest-rate models pricing kernels long bond long-term investment long rate of interest Ross recovery
Depositing User : Melanie Hughes
Date Deposited : 04 May 2018 15:19
Last Modified : 28 May 2019 02:08
URI: http://epubs.surrey.ac.uk/id/eprint/846361

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