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Article overview
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L'evy-Vasicek Models and the Long Rate of Interest | Dorje C. Brody
; Lane P. Hughston
; David M. Meier
; | Date: |
23 Aug 2016 | 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 L’evy-Vasicek case, avoiding issues of market incompleteness. In the
L’evy-Vasicek model the short rate is taken in the real-world measure to be a
mean-reverting process with a general one-dimensional L’evy driver admitting
exponential moments. Expressions are obtained for the L’evy-Vasicek bond
prices and interest rates, along with a formula for the corresponding long-bond
return process defined by $L_t = lim_{T o infty} P_{tT} / P_{0T}$, where
$P_{tT}$ is the price at time t of a T-maturity discount bond. We show that the
pricing kernel of a L’evy-Vasicek model is uniformly integrable if and only if
the long rate of interest is strictly positive. | Source: | arXiv, 1608.6376 | Services: | Forum | Review | PDF | Favorites |
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