medium · Quantitative Finance
A structural credit model (Merton-style) views a firm's equity as a call option on its assets.
If a firm has assets of 200 million, asset volatility of 30%, and 150 million in debt due in 2 years, how would you calculate the risk-neutral probability of default?
- Calculate 1 - Φ(d_2) where d_2 is the Black-Scholes term using asset values and debt
- Divide the observed credit spread by the assumed loss given default, or 1-R.
- Calculate Phi(d_1) using the firm's asset value and debt face value at maturity.
- Apply the reduced-form hazard rate formula e to the minus lambda T directly to the asset value.
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