Equity and Debt Valuation with default Risk: a Discrete Structural Model

Structural models’ main source of uncertainty is the stochastic evolution of the firm’s asset value. These models are commonly used to value corporate debt at the issue and hence to determine its yield given the amortization plan. This paper proposes two discrete models to value securities issued by a firm which can default before the maturity of its debt either for exogenous or endogenous causes. In either case the equity value is set as the price of a knock-out call option with a discrete monitoring barrier. The first model considers a debt refundable through the payment of known endowments and takes into account that the firm defaults as it fails to meet a promised payment. In the second model the firm’s debt is made of a single issue of zero coupon bonds and includes the possibility that the firm defaults prior to the maturity of the debt if its asset value falls below a time dependent barrier. The particular evolution of the asset value, which shows discontinuity in the drift and diffusion coefficient, prevents the use of closed form solutions for options with a discrete monitoring barrier. The evaluation of the option is performed through non-recombining binomial trees.