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An Integrated Model for Hybrid Securities

Management Science, Vol. 53, No. 9, pp. 1439-1451, 2007

Posted: 29 Aug 2010 Last revised: 14 Mar 2011

Sanjiv Ranjan Das

Santa Clara University - Leavey School of Business

Rangarajan K. Sundaram

New York University (NYU) - Department of Finance

Date Written: September 1, 2007

Abstract

We develop a model for pricing securities whose value may depend simultaneously on equity, interest rate, and default risks. The framework may also be used to extract probabilities of default (PD) functions from market data. Our approach is entirely based on observables such as equity prices and interest rates, rather than on unobservable processes such as firm value. The model stitches together in an arbitrage-free setting a constant elasticity of variance (CEV) equity model (to represent the behavior of equity prices prior to default), a default intensity process, and a Heath-Jarrow-Morton (HJM) model for the evolution of riskless interest rates. The model captures several stylized features such as a negative relation between equity prices and equity volatility, a negative relation between default intensity and equity prices, and a positive relationship between default intensity and equity volatility. We embed the model on a discrete-time, recombining lattice, making implementation feasible with polynomial complexity. We demonstrate the simplicity of calibrating the model to market data and of using it to extract default information. The framework is extensible to handling correlated default risk and may be used to value distressed convertible bonds, debt-equity swaps, and credit portfolio products such as collateralized debt obligations (CDOs). Applied to the CDX INDU (credit default index-industrials) Index, we find the S&P 500 index explains credit premia.

Keywords: securities, hybrid models, default, credit risk

JEL Classification: M41, G1, G12, C41, C52

Suggested Citation

Das, Sanjiv Ranjan and Sundaram, Rangarajan K., An Integrated Model for Hybrid Securities (September 1, 2007). Management Science, Vol. 53, No. 9, pp. 1439-1451, 2007. Available at SSRN: https://ssrn.com/abstract=1667082

Sanjiv Ranjan Das (Contact Author)

Santa Clara University - Leavey School of Business ( email )

Department of Finance
316M Lucas Hall
Santa Clara, CA 95053
United States

HOME PAGE: http://algo.scu.edu/~sanjivdas/

Rangarajan K. Sundaram

New York University (NYU) - Department of Finance ( email )

Stern School of Business
44 West 4th Street
New York, NY 10012-1126
United States
212-998-0308 (Phone)
212-995-4233 (Fax)

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