Pricing American Interest Rate Options Under the Jump-Extended CIR and CEV Short Rate Models

Abstract:     
This paper presents jump extensions to the Cox, Ingersoll, and Ross (CIR) and the constant-elasticity-of-variance (CEV) models of the short rate, with analytical solutions for the case of exponential jumps, and efficient lattice-based solutions for both exponential jumps and lognormal jumps. We demonstrate how to superimpose a recombining multinomial jump tree on the diffusion tree, creating the mixed jump-diffusion trees for CIR and CEV models extended with jumps. Finally we also present the preference-free versions of these models that allow these models to be fully calibrated to an initially observed forward rate curve, making them consistent with the HJM [1992] paradigm. Our simulations show fast convergence of the trees to the respective analytical solutions.

Keywords: Interest rate models, Term structure models, Jumps, CIR, CEV, Trees

JEL Classifications: G11, G12, G13, G21, G22, G23

Working Paper Series