A pure-jump mean-reverting short rate model
Open Access
- 20 April 2020
- journal article
- research article
- Published by VTeX in Modern Stochastics: Theory and Applications
- Vol. 7 (2), 113-134
- https://doi.org/10.15559/20-vmsta152
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 jumpOrnstein-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.Keywords
Other Versions
This publication has 30 references indexed in Scilit:
- A Lévy HJM multiple-curve model with application to CVA computationQuantitative Finance, 2014
- A multiple-curve HJM model of interbank riskMathematics and Financial Economics, 2012
- STochastic Modeling of Electricity and Related MarketsAdvanced Series on Statistical Science and Applied Probability, 2008
- A Non‐Gaussian Ornstein–Uhlenbeck Process for Electricity Spot Price Modeling and Derivatives PricingApplied Mathematical Finance, 2007
- A deterministic–shift extension of analytically–tractable and time–homogeneous short–rate modelsFinance and Stochastics, 2001
- Interest Rate Models Theory and PracticePublished by Springer Science and Business Media LLC ,2001
- Option valuation using the fast Fourier transformJournal of Computational Finance, 1999
- The Market Model of Interest Rate DynamicsMathematical Finance, 1997
- Bond Market Structure in the Presence of Marked Point ProcessesMathematical Finance, 1997
- A Theory of the Term Structure of Interest RatesEconometrica, 1985