2 Valuation of Risky Debt : a Multi - Period Bayesian Model

The paper describes model of a new type for valuation of risky bonds and loans that we call Bayesian Multi-Period (BMP) model. BMP is neither structural model nor reduced form and not a Merton-type model at all. BMP proceeds from concept of a risky bond (loan) value as Net Present Value (NPV) of a cash flow, generated by a bond. For a defaultable bond NPV is random value, and BMP identifies “fair” price of a risky bond as its mean NPV. Statistical properties of a (random) difference between NPV of a risky bond and NPV of risk-free bond with the same terms of issuance characterize riskness of a bond. 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 exact contractual cash flow schedule of each specific debt issue and combines it with probabilities of a borrower’s default at all stages of cash flow process. Default prognosis in turn accounts for joint influence of all outstanding debt of a firm. BMP uses multi-period default prognosis of Bayesian type based on indices of borrower’s current financial position with accounting for predictive abilities of repayment schedule of a firm’s long-term debt. This type prognosis can additionally incorporate other predictive variables like 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 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. That is much more, than usually explain Merton-type models The paper discusses relation between multi-period default probabilities and credit ratings.