A Simple Model for Pricing Derivative Securities with Equity, Interest-Rate, Default and Liquidity Risk

22 Pages Posted: 23 Jul 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: June 2002

Abstract

This paper develops a model for pricing securities that may be a function of several different sources of risk, namely, equity, interest-rate, default and liquidity risks. The model is also useful for extracting probabilities of default (PDs) in a model with equity, interest rate and credit risk. The model is not based on the stochastic process for the value of the firm, but on the stochastic process for interest rates and the equity price, which are observable. The model comprises two components. First, a risk-neutral setting in which the joint process of interest rates and equity are modelled together with the boundary conditions for security payoffs. Second, the model is embedded on a recombining lattice generated using an approximation technique. This makes implementation of the pricing scheme feasible with polynomial complexity. We present a simple approach to calibration of the model to market observable data. 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.

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

Suggested Citation

Das, Sanjiv Ranjan and Sundaram, Rangarajan K. and Sundaresan, Suresh M., A Simple Model for Pricing Derivative Securities with Equity, Interest-Rate, Default and Liquidity Risk (June 2002). EFA 2003 Annual Conference Paper No. 852. Available at SSRN: https://ssrn.com/abstract=424025 or http://dx.doi.org/10.2139/ssrn.424025

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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