Testing Merton's Model for Credit Spreads on Zero-Coupon Bonds

Abstract

Structural models for valuing corporate bonds (beginning with Merton (1974)) have been criticised for giving spreads which are (a) too small and (b) have a term structure in which spreads diminish with extra time to maturity. Empirical tests of models are hampered by the complexity of real-world bonds, which have coupons, calls and sinking funds, and also by the complicated and changing capital structures adopted by companies. This paper exploits a new database of zero-coupon bonds issued by closed-end funds in the UK. These companies have very simple capital structures and transparent values for both assets and liabilities. Between 20 and 78 bonds are observable monthly over the period February 1992 to April 2001. Counter to previous research, we find that model and market spreads are on average of similar magnitude. Similar to previous research, market spreads are high (relative to model spreads) for bonds which have low risk and for bonds which are near to maturity. While the observed term-structure of credit spreads is upward-sloping, this may be explained by a predictable drift in leverage over time. On the whole, the results are surprisingly supportive of Merton's model and suggest that it is important to allow for expected changes in leverage when computing credit spreads.

Estimating Structural Models of Corporate Bond Prices

“…Only in very few special cases is the estimation of structural models straightforward. Gemmill (2002), for instance, picks data on British closed-end funds that issue zero coupon bonds. For this data set, asset values of the funds are readily available (indeed, they are published daily), and the entire debt of the entity consists of one zero coupon bond.…”

Risk Assessment Techniques for Split Capital Investment Trusts

“…3.2 Contemporary U.K. Splits A ZDP may be considered equal in value to the present value of a riskfree bond less the value of a put option on the trust's gross assets (Gemmill, 2002). The exercise price of the put equals the sum of the payments due at maturity on prior charges and the bond.…”

Macroeconomic Dynamics and Credit Risk: A Global Perspective

“…The APT model architecture allows us to achieve this in a parsimonious manner, while at the same time taking proper account of return heterogeneities across firms. 11 10 For a discussion of the power of Merton default prediction models see Falkenstein and Boral (2001) and Gemmill (2002) who find that the Merton model generally does well in predicting default (Falkenstein and Boral) and credit spreads (Gemmill). Duffee (1999) points out that due to the continuous time diffusion processes underlying the Black Scholes formula, short-term default probabilities may be underestimated.…”

“…As we shall see below, for the purpose of simulating the loss distribution of a given portfolio, the conditional probability distribution of ∆y T +n is needed. 31 Using (17) and after some algebra we obtain…”

“…where B i`i s defined by (31). But if the shock is unanticipated (which we consider to be more relevant for credit risk analysis) we have…”