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

Preview	Text Brody Hughston Meier 2018.pdf - Submitted Version Available under License Creative Commons Attribution Non-commercial. Download (243kB) | Preview
Preview	Text Brody Hughston Meier 3 May 2018.pdf - Accepted Version Available under License Creative Commons Attribution Non-commercial. Download (221kB) | Preview

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.

Item Type:	Article
Identification Number (DOI):	https://doi.org/10.1142/S0219024918500267
Additional Information:	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
Keywords:	Vasicek model, Lévy models, interest-rate models, pricing kernels, long bond, long-term investment, long rate of interest, Ross recovery
Departments, Centres and Research Units:	Computing
Dates:	Date Event 3 May 2018 Accepted 28 May 2018 Published
Item ID:	27272
Date Deposited:	23 Oct 2019 12:15
Last Modified:	09 Feb 2022 13:57
Peer Reviewed:	Yes, this version has been peer-reviewed.
URI:	https://research.gold.ac.uk/id/eprint/27272

View statistics for this item...

Edit Record (login required)