This calculator assumes you know the firm's asset value (V) and asset volatility. In practice, these must be inferred from observable equity prices using numerical calibration. This tool helps you understand how the Merton model works, not estimate real-world default probabilities.
Model Inputs
Capital Structure
Default Probability
Formula Breakdown
Model Assumptions
- Asset value (V) and asset volatility are known (in practice, must be calibrated)
- Single zero-coupon debt maturing at time T
- No dividends or intermediate payouts
- Assets follow geometric Brownian motion with constant volatility
- Default occurs only at maturity if V < D
- Continuous trading with no transaction costs
- Flat term structure (constant risk-free rate)
For educational purposes. Not financial advice. Physical PD is highly sensitive to the expected return assumption.
Understanding the Merton Credit Model
What is the Merton Model?
The Merton structural credit model (1974) is the foundation of modern credit risk analysis. It treats a firm's equity as a call option on the firm's assets, with the debt face value as the strike price. This elegant insight allows us to apply Black-Scholes option pricing to credit risk.
Strike = Debt face value (D)
Underlying = Firm asset value (V)
At maturity: Equity = max(V - D, 0)
Risk-Neutral vs Physical Default Probability
The Merton model produces two different default probabilities that serve different purposes:
Risk-Neutral PD
Uses risk-free rate (r)
For pricing debt and credit derivatives. Higher than physical PD due to risk premia embedded in market prices.
Physical PD
Uses expected return (μ)
For forecasting actual defaults. Represents real-world default frequency under physical probability measure.
Distance to Default (DD)
Distance to Default measures how many standard deviations the firm's asset value is above the default point. It's the primary credit metric used by KMV/Moody's:
- DD > 3: Very safe - default is more than 3 standard deviations away
- DD 1.5-3: Watch list - elevated but manageable credit risk
- DD < 1.5: Distressed - high probability of default
Merton vs Reduced-Form Models
Credit risk models fall into two paradigms:
- Structural (Merton): Default is endogenous - it occurs when assets fall below debt. You can see it coming as asset value declines. Provides economic intuition.
- Reduced-Form: Default is exogenous - modeled as a surprise Poisson event with intensity lambda. Easier to calibrate to CDS spreads but less economically intuitive.
Frequently Asked Questions
Disclaimer
This calculator is for educational purposes only. The Merton model makes simplifying assumptions that may not hold in practice. Asset value and volatility are unobservable inputs that must be calibrated in real applications. Physical default probability is highly sensitive to the expected return assumption. This tool should not be used for investment or credit decisions without professional consultation.
