Advanced Finance

Structural Credit Models and Distance to Default

Read a company's default risk out of its share price, by treating equity as a call option on the firm's assets — and learn exactly which of the model's assumptions is doing the work when the answer looks wrong.

  • Expert
  • 15 min total
  • 14 chapters

What decision this helps you make: Whether an issuer's credit has deteriorated before the rating, the spread, or the accounts say so — and how much weight to put on a number produced by a model that assumes one zero-coupon liability and lognormal assets.

What this topic is

A structural credit model derives the probability of default from the capital structure itself. The firm owns assets whose value moves randomly; the debt has a face value; default happens when the assets are worth less than what is owed. Merton's 1974 formulation makes this exact: equity is a European call option on the firm's assets, struck at the face value of the debt and expiring when the debt matures. Because the option pricing formula links asset value, asset volatility, leverage and equity value, you can invert it — take the observable equity market capitalization and equity volatility, and solve back for the unobservable asset value and asset volatility. Distance to default is then the number of standard deviations of asset value that sit between where the firm is now and the point where it defaults.

Why it matters

Ratings move in discrete steps, months late, through a committee. Accounting statements arrive quarterly and describe a period that has ended. Equity trades every second. A structural model is the only mainstream credit tool whose input updates continuously, which is why it repeatedly flags deterioration before the agencies do — and why every bank credit function, every counterparty risk desk, and every equity-credit relative value trader runs some version of it. It is also the only framework that puts equity and debt on the same state variable, so it can tell you what a share price move should have done to a spread.

Who should learn it

Credit analysts and portfolio managers, counterparty and enterprise risk teams, capital-structure and equity-credit traders, and anyone who has to defend a default probability estimate to a committee that will ask where the number came from.

What you will understand

  • How equity becomes a call option on assets, and how to invert that to recover asset value and asset volatility
  • How to compute distance to default two different ways and why the two answers differ
  • Why the risk-neutral default probability the model produces is not the real-world one, and roughly how far apart they sit
  • Where the model breaks — short maturities, financials, jumps, and the credit spread puzzle — and what the literature has done about it

Prerequisites

Common misconception

"The model gives you the probability of default." It gives you a probability of default under a specific and very restrictive set of assumptions: a single zero-coupon liability maturing at a known date, asset value following geometric Brownian motion with constant volatility and no jumps, frictionless bankruptcy at maturity, and an asset value you can infer cleanly from equity. Change any one of them and the number moves materially. Worse, the raw output N(−d2) is a risk-neutral probability — it embeds a risk premium and typically exceeds the real-world probability by a factor of roughly one and a half to several times. Moody's KMV does not report N(−d2) at all; it maps distance to default onto an empirical database of observed defaults, precisely because the normal tail is too thin to be believed at the investment-grade end.