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
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  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
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