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Lévy-Vasicek Models and the Long-Bond Return Process

Brody, Dorje C.; Hughston, Lane P. and Meier, David M. 2018. Lévy-Vasicek Models and the Long-Bond Return Process. International Journal of Theoretical and Applied Finance, 21(3), p. 1850026. ISSN 0219-0249 [Article]

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Abstract or Description

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 Lévy-Vasicek case, avoiding issues of market incompleteness. In the Lévy-Vasicek model the short rate is taken in the real-world measure to be a mean-reverting process with a general one-dimensional Lévy driver admitting exponential moments. Expressions are obtained for the Lévy-Vasicek bond prices and interest rates, along with a formula for the return on a unit investment in the long bond, defined by L_t=lim_{T→∞} P_{tT}/P_{0T}, where P_{tT} is the price at time t of a T-maturity discount bond. We show that the pricing kernel of a Lévy-Vasicek model is uniformly integrable if and only if the long rate of interest is strictly positive.

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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.


Vasicek model, Lévy models, interest-rate models, pricing kernels, long bond, long-term investment, long rate of interest, Ross recovery

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3 May 2018Accepted
28 May 2018Published

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Date Deposited:

23 Oct 2019 12:15

Last Modified:

22 Jan 2020 21:51

Peer Reviewed:

Yes, this version has been peer-reviewed.


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