FRM Part I · FRM Exam Part I · Measuring Credit Risk
A firm has zero-coupon debt with face value 100 maturing in one year. The risk-free rate is 5% continuously compounded. In the Merton model the put option on the firm's assets (strike 100) is worth 4.00. What is the credit spread, in continuously compounded terms, on the debt?
The credit spread is about 4.30%. Risky debt equals the risk-free present value of 95.12 less the 4.00 put, or 91.12. Its continuous yield is about 9.30%, and subtracting the 5% risk-free rate leaves the spread of roughly 4.30%.
- A4.30%Correct
- B9.30%
- C4.00%
- D5.00%
Explanation
Risk-free debt value = 100e^-0.05 = 95.123. Risky debt = 95.123 - 4.00 = 91.123. Yield = ln(100/91.123) = 9.295%. Spread = 9.295% - 5% = about 4.30%. The 9.30% option is the yield, not the spread; 4.00% confuses the put price with a rate.
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