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

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.