A Simple Unified Model for Pricing Derivative Securities With Equity, Interest-Rate, and Default Risk

28 Pages Posted: 4 Dec 2003

See all articles by Sanjiv Ranjan Das

Sanjiv Ranjan Das

Santa Clara University - Leavey School of Business

Rangarajan K. Sundaram

New York University (NYU) - Department of Finance

Suresh M. Sundaresan

Columbia Business School - Finance and Economics

Date Written: January 2003

Abstract

We develop a model for pricing derivative and hybrid securities whose value may depend on different sources of risk, namely, equity, interest-rate, and default risks. In addition to valuing such securities the framework is also useful for extracting probabilities of default (PD) functions from market data. Our model is not based on the stochastic process for the value of the firm [which is unobservable], but on the stochastic process for interest rates and the equity price, which are observable. The model comprises a risk-neutral setting in which the joint process of interest rates and equity are modeled together with the default conditions for security payoffs. The model is embedded on a recombining lattice which makes implementation of the pricing scheme feasible with polynomial complexity. We present a simple approach for calibration of the model to market observable data. The framework is shown to nest many familiar models as special cases. The model 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 CDOs. We present several numerical and calibration examples to demonstrate the applicability and implementation of our approach.

Keywords: Risk-neutral, PDs, reduced-form models

Suggested Citation

Das, Sanjiv Ranjan and Sundaram, Rangarajan K. and Sundaresan, Suresh M., A Simple Unified Model for Pricing Derivative Securities With Equity, Interest-Rate, and Default Risk (January 2003). AFA 2004 San Diego Meetings. Available at SSRN: https://ssrn.com/abstract=472680 or http://dx.doi.org/10.2139/ssrn.472680

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)

Suresh M. Sundaresan

Columbia Business School - Finance and Economics ( email )

3022 Broadway
New York, NY 10027
United States
212-854-4423 (Phone)
212-316-9180 (Fax)

HOME PAGE: http://www0.gsb.columbia.edu/faculty/ssundaresan/

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