On the Pricing of Corporate Debt: The Risk Structure of Interest Rates
Source: Merton, R. C. (1974) · Journal of Finance 29(2), 449–470 · DOI: 10.1111/j.1540-6261.1974.tb03058.x
TL;DR
Founds the structural model of credit risk. Treating a firm's equity as a European call option on its assets (the debt's face value B as the strike), Merton prices risky corporate debt with Black–Scholes machinery: the firm defaults if asset value falls below what is owed at the debt's maturity. The credit spread — the "risk structure of interest rates" — follows from asset value, asset volatility, leverage, and maturity, and depends on default risk only (a flat, known term structure is assumed away).
What it prices
Risky corporate discount (zero-coupon) debt, and equivalently the yield spread of that debt over the riskless rate. The same no-arbitrage logic links a firm's capital structure to the value of equity and debt: equity holders hold a call on the firm's assets (limited liability), debt holders effectively hold riskless debt while being short a put on the firm's assets.
Setup & assumptions
Frictionless markets: no taxes/transaction costs, continuous trading, unrestricted short sales, borrow/lend at the same rate (A.1–A.5).
Modigliani–Miller holds (firm value invariant to capital structure); the term structure is flat and known, P(τ) = e^{−rτ} (A.6, A.7).
Firm value V follows a diffusion (A.8): dV = (αV − C)dt + σV dz, with C the total payout rate and σ the (constant) asset volatility.
Debt is a single zero-coupon obligation of face value B maturing at T; default occurs if V_T < B.
Key result
Equity is a European call on firm value, so (with no payouts, C=0) its value is the Black–Scholes formula:
Risky debt value = V − f(V,τ) = Be^{−rτ} − (a put on V). Its yield-to-maturity defines the risk structure: the credit spread rises with leverage (B·e^{−rτ}/V) and asset volatility σ, and falls with the firm's distance to default, and is a function only of those two quantities (plus maturity). Comparative statics yield the characteristic term structure of spreads.
Inputs & implementation
Inputs: firm asset value V, asset volatility σ, leverage/face value B, riskless rate r, maturity τ.
V and σ are not directly observable and must be backed out from equity value and equity volatility (the basis for the KMV/Moody's distance-to-default and expected-default-frequency implementations).
Limitations
Predicts counterfactually low short-maturity spreads (a solvent firm almost never defaults suddenly) — addressed by jump-diffusion and first-passage (barrier) extensions.
Assumes a single debt maturity, constant volatility, a flat/known term structure, and a default trigger only at T; ignores strategic default, coupons (handled separately in the paper), and stochastic interest rates.
Asset value/volatility are unobservable, so estimates inherit equity-based inference error.
Key references
Merton, R. C. (1974) — On the Pricing of Corporate Debt: The Risk Structure of Interest Rates — Journal of Finance
Black, F. & Scholes, M. (1973) — The Pricing of Options and Corporate Liabilities — Journal of Political Economy
Bharath, S. & Shumway, T. (2008) — Forecasting Default with the Merton Distance to Default Model — Review of Financial Studies
Provenance: verified/generated from the paper's full text.
