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# P2.T6.403. Stulz on Merton model: credit risk as an option

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
AIMs: [Stulz on credit risks as option.] Explain the relationship between credit spreads, time to maturity, and interest rates.

Questions:

403.1. A firm has an asset value (V) of $110.00 million with asset volatility of 30.0% per annum. Its only debt is a zero-coupon bond with face value of$80.0 million that matures in five years. The riskfree rate is 4.0%. In Stulz's notation, V=110, sigma(V)= 0.30, F=80.0, T=5.0 and r=0.04. The Black-Scholes Merton (BSM) price of a put option,p, on the firm's assets with strike price equal to the face value of the bond is $6.95 million; i.e., p(V=110, F=80, sigma=0.30, T=5, r=0.04) =$6.95 million. Which is nearest to the current value of the firm's debt?

a. $6.95 million b.$41.30 million
c. $58.55 million d.$65.50 million

403.2. Assume the Merton model for credit risk with a simple capital structure, where the debt is a single long-term zero-coupon bond. Each of the following is true under an implied ceteris paribus (all other parameters fixed), EXCEPT which is false?

a. Higher firm asset volatility implies higher equity value (given constant firm asset value and debt maturity)
b. Higher firm asset volatility implies lower debt value (given constant firm asset value and debt maturity)
c. As maturity of debt approaches, as T --> 0, the value of firm equity decreases (given constant firm asset value and asset volatility)
d. As maturity of debt approaches, as T --> 0, the value of firm's debt decreases (given constant firm asset value and asset volatility)

403.3. Debt with five years to maturity (T = 5.0 years) has a face value of $1,000 and a current price of$834.00. If the riskfree rate is 2.0% per annum, which is nearest to the credit spread (both with continuous compounding)?

a. 0.950%
b. 1.630%
c. 2.044%
d. 3.360%

#### cdbsmith

##### Member
Hi Guys,

Regarding 403.2, why is D not the correct answer? The explanation provided seems to imply D should be correct. Can you please clarify?

I correctly answered the other 2 questions (403.1 & 403.3).

Thanks,

Charles

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Yes, my mistake, you are absolutely correct! Thanks for, you know, being smart and such. I corrected (and awarded you a star) in the (source) full Q&A here.

#### cdbsmith

##### Member
Cool!

I got all three questions correct now!

Thanks!