A pure-jump mean-reverting short rate model
Volume 7, Issue 2 (2020), pp. 113–134
Pub. online: 20 April 2020
Type: Research Article
Open Access
Open Access
Received
23 April 2019
23 April 2019
Revised
27 March 2020
27 March 2020
Accepted
27 March 2020
27 March 2020
Published
20 April 2020
20 April 2020
Abstract
A new multi-factor short rate model is presented which is bounded from below by a real-valued function of time. The mean-reverting short rate process is modeled by a sum of pure-jump Ornstein–Uhlenbeck processes such that the related bond prices possess affine representations. Also the dynamics of the associated instantaneous forward rate is provided and a condition is derived under which the model can be market-consistently calibrated. The analytical tractability of this model is illustrated by the derivation of an explicit plain vanilla option price formula. With view on practical applications, suitable probability distributions are proposed for the driving jump processes. The paper is concluded by presenting a post-crisis extension of the proposed short and forward rate model.
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