Study Guide 2 CH 5 & 7
7. Suppose that the following weekly interest rate volatility estimates are computed as:
absolute rate change = 3.85 basis points and percentage rate change = 2.14%.
Answer the below questions.
(a) What is the annualized volatility for the absolute rate change?
(b) What is the annualized volatility for the percentage rate change?
8. Explain the mean reversion property found in an interest-rate model. Write down the
mean reversion process and explain each variable and parameter.
9. Explain the treatment of the dynamics of the volatility term for the Cox-Ingersoll-Ross
interest rate model. 10. The current on-the-run yields for the Ramsey Corporation are as follows:
Maturity
(years)
1
2
3 Yield to Maturity (%) Market Value 7.5
7.6
7.7 100
100
100 Assume that each bond is an annual-pay bond. Each bond is trading at par, so its coupon
rate is equal to its yield to maturity.
Answer the below questions.
(a) Using the bootstrapping methodology, complete the following table:
Year Spot Rate
(%) One-Year Forward Rate (%) 1
2
3
(b) Using the spot rates, what would be the value of an 8.5% option-free bond of this
issuer? (c) Using the one-year forward rates, what would be the value of an 8.5% coupon option-free
bond of this issuer?
(d) Using the binomial model (which assumes that one-year rates undergo a lognormal
random walk with volatility ), show that if is assumed to be 10%, the lower one-year
forward rate one year from now cannot be 7%.
(e) Demonstrate that if ? is assumed to be 10%, the lower one-year forward rate one year
from now is 6.944%.
(f) Demonstrate that if ? is assumed to be 10%, the lower one-year forward rate two years
from now is approximately 6.437%.
(g) Show the binomial interest-rate tree that should be used to value any bond of this issuer.
(h) Determine the value of an 8.5% coupon option-free bond for this issuer using the binomial
interest-rate tree given in part g.
(i) Determine the value of an 8.5% coupon bond that is callable at par (100) assuming that
the issue will be called if the price exceeds par.
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