medium · Quantitative Finance

If the risk-free rate r = 3%, how is the risk-neutral probability of default calculated?

1. It is represented by Φ(-d_2), where d_2 is the same parameter used in the Black-Scholes formula for a call on the firm's assets.
2. It is calculated as 1 - Φ(d_1), representing the likelihood that the firm's underlying assets grow beyond their current value.
3. It equals the credit spread of the firm's bond divided by the loss given default, expressed as (1-R) in the denominator.
4. It is the ratio of the debt face value to the current asset value, D/A_0, further scaled by the annualized asset volatility.

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