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1) A one-year zero-coupon bond X will pay either $1,000 (par value) or $450 (default value) at maturity

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1) A one-year zero-coupon bond X will pay either $1,000 (par value) or $450 (default value) at maturity. You observe that this bond currently trades at $890. Assuming risk-free rate of return to be zero, you have INSUFFICIENT information to calculate which of the following?

a.
The risk-neutral probability of default

b. 
The physical probability of default

c.
The percentage of par value recovered in default

d.

The bond's promised yield to maturity

 

2) A two-year zero-coupon bond has a par value 100 and is priced to yield 5% per year. The annual risk-free interest rate is 3%. Calculate the approximate premium of a put option on the firm's assets, assuming Merton's (1974) model.

 

3) A zero-coupon bond has par value $95 and one year to maturity, at which time it may default. From Merton's model, you estimate that the risk-neutral probability of default to be 20% and the present value of recovery to be $51. Find the expected value that will be recovered at maturity, given risk-free interest rate of 5%. Hint: in default, it's the recovery value at that point; if there is no default, it's the par value.

 

4) Which of the following is NOT the output of the Merton's (1974) credit risk model?

 

a. 
Recovery

b. 
Risk-neutral probability of default

c. 
Credit Spread

d. 
Volatility of the firm's assets