medium · FRM Part 2 Credit Risk
A bank calculates the capital requirement for a corporate loan using the Merton model framework. The firm has assets V_0 = 140 m, debt face valueF = 100 m due in 1 year, and asset volatility σ_V = 25%. The risk-free rate is r = 4.0% (continuous).
If the bank mistakenly uses the firm's equity volatility σ_E in the d_2 formula instead of σ_V, what is the likely impact on the calculated Probability of Default (PD)?
- The PD will be unchanged because the Merton model is homogeneous of degree one in volatility.
- The PD will be understated because the debt face value F acts as a buffer.
- The PD will be overstated because σ_E includes the default risk premium while σ_V does not.
- The PD will be significantly overstated because σ_E > σ_V for a levered firm.
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