Download This PaperA Lower-Bounded Short Rate Model
Modern Stochastics: Theory and Applications, 2020, Vol. 7, No. 2, 113-134
27 Pages Posted: 27 Dec 2017 Last revised: 29 Jun 2020
Date Written: September 7, 2019
Abstract
We present a new multi-factor short rate model 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 price possesses an affine representation. We also provide the dynamics of the associated LIBOR and instantaneous forward rate and derive a condition under which the model can be market-consistently calibrated. We further establish customized probability measure changes to the respective forward measures. The analytical tractability of our model is illustrated by the derivation of explicit option price formulas. With view on practical applications, we propose suitable probability distributions for jump noise modeling. We conclude the paper by presenting multi-curve extensions of our short, forward and LIBOR rate models.
Keywords: short rate, zero-coupon bond, forward rate, LIBOR rate, spot rate, option pricing, market-consistent calibration, multi-curve model, Lévy process, multi-factor model, Ornstein-Uhlenbeck process, stochastic differential equation, Poisson random measure, Doléans-Dade exponential
JEL Classification: G12, G22, C02, D52
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