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IntermediateOptions, Derivatives & FinancePython

Run this module

cd "Finance - Credit Risk"
python "merton_model.py"

View source on GitHub

Merton Credit Risk Model

The Merton (1974) structural credit model treats a firm's equity as a call option on its assets. Default occurs when asset value falls below debt face value at maturity.

Functions

Function Description
merton_equity(V, F, r, sigma_V, T) Equity value via Black-Scholes formula
merton_model(V, F, r, sigma_V, T) Full analytics: DD, PD, credit spread
implied_asset_value(E, F, r, sigma_E, T) Back out asset value from observable equity

Key Outputs

  • Distance to Default (DD): How many standard deviations the firm is from the default threshold. DD > 3 is considered safe; DD < 1 is distressed.
  • Probability of Default (PD): PD = N(-DD). Risk-neutral default probability.
  • Credit Spread: yield_on_debt - risk_free_rate. Excess yield investors demand for bearing default risk.

The Intuition

Equity  = Call(Assets, Strike=Debt, T=Maturity)
Debt    = Assets - Equity  (bondholders own residual if equity worthless)
Default = Assets < Debt at maturity

Example

from merton_model import merton_model

result = merton_model(V=100e6, F=80e6, r=0.05, sigma_V=0.20, T=1.0)
print(f"PD: {result['probability_of_default']:.2%}")
print(f"Credit Spread: {result['credit_spread_bps']:.1f} bps")

Limitations

  • Assumes simple capital structure (one class of debt with fixed maturity)
  • Asset value and volatility are unobservable — must be inferred from equity
  • Better suited for investment-grade firms; CDS-based models preferred for distressed credits

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