Valuation of Risky Debt: A Multi-Period Bayesian Model

Abstract

The paper describes a model of a new type for valuation of risky bonds and loans that we call a Bayesian Multi-Period (BMP) model. BMP is neither a structural model nor a reduced form and not a Merton-type model at all. BMP proceeds from the concept of a risky bond (loan) value as the Net Present Value (NPV) of a cash flow generated by a bond. For a defaultable bond NPV is random value, and BMP identifies the “fair” price of a risky bond as its mean NPV. BMP supposes that a borrower (e.g. a firm) generally has several debt issues (bonds, loans) simultaneously - with different terms of issuance (interest rates, maturity horizons, payment schedules etc.) and calculates risk characteristics for each debt issue separately. It considers the exact contractual cash flow schedule of each specific debt issue and combines it with probabilities of a borrower’s default at all stages of the cash flow process. Default prognosis in turn accounts for the joint influence of all outstanding debts of a firm. BMP uses multi-period default prognosis of Bayesian type based on indices of a borrower’s current financial position accounting for the predictive abilities of the repayment schedule of a firm’s long-term debt. This type of prognosis can additionally incorporate other predictive variables like the familiar market factor - “distance to default”. BMP calculates “fair” interest rates for newly issued risky corporate bonds, “fair” prices and “fair” yield to maturity for risky bonds at intermediate moments of a bond’s life. We compare them with observed market prices, rates and spreads. The model explains on average about 70% of observed interest rates, credit spreads and market prices of a bond. This is much more than is usually explained by Merton-type models. The paper discusses the relation between multi-period default probabilities and credit ratings.