Pricing American Interest Rate Options Under the Jump-Extended CIR and CEV Short Rate Models
73 Pages Posted: 16 May 2007
Date Written: May 2007
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 Classification: G11, G12, G13, G21, G22, G23
Suggested Citation: Suggested Citation
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