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In Search of Hybrid Models for Credit Risk: from Leland-Toft to Carr-Linetsky

by Chuang Yi of McMaster University, and
Tom Hurd of McMaster University

April 2008

Abstract: In this paper, we derive several forms of the equity volatility as a function of the equity value, from the structural credit risk literature. We then propose a new jump to default model by taking the equity volatility to be of the form implied by the models of Leland (1994) and Leland & Toft (1996). This model involves a process we call the Dual-Jacobi process and which has explicit formulae for its moments. Gram-Charlier expansions are then applied to approximate bond and call prices. Our model generalizes Linetsky (2006) by incorporating a local volatility which is bounded below by a positive constant. This local volatility will decrease to a positive constant for increasing stock prices, making the stock process asymptotic to Geometric Brownian Motion (GBM). In this sense, our model is more realistic than the Constant Elasticity of Variance (CEV) models..

Keywords: Hybrid Models, Constant Elasticity of Variance, Endogenous Bankruptcy.

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