Deck 21: Interest Rate Options

Question 1

A bond's yield is 5% and the forward yield volatility is quoted as 20%. The modified duration of the bond at the maturity of the option is 6 years. What would the market assume to be the bond forward price volatility? _ _ _ _ _ _

Answer 1

6%

Question 2

A 10-year interest rate cap has a cap rate of 4%, quarterly resets, and a notional principal of $1 million.
i) How many caplets are there underlying the cap? _ _ _ _ _ _
ii) Suppose the three-month interest rate at time 2.5 years is 5.2% per annum. What is the payoff on the interest rate cap resulting from this?
_ _ _ _ __
iii) At what time measured in years from today) would the payoff in ii) be made?
_ _ _ _ _ _

Answer 2

i): 39 ii): $3000 iii) 2.75

Question 3

Which of the following are true? choose two)

A) A callable bond allows the lender to ask for the principal to be repaid early.
B) A puttable bond allows the lender to ask for the principal to be repaid early.
C) A swaption that gives the holder the right to receive fixed is equivalent to a put option on a bond where the strike price is the bond's par value.
D) A swaption that gives the holder the right to pay fixed is equivalent to a put option on a bond where the strike price is the bond's par value.

Answer 3

A puttable bond allows the lender to ask for the principal to be repaid early.
A swaption that gives the holder the right to pay fixed is equivalent to a put option on a bond where the strike price is the bond's par value.

Question 4

A Eurodollar futures option contract has a strike price of 97 and the Eurodollar interest rate is 2.50%.
i) What is the intrinsic value of the contract if the option is a call? _ _ _ _ _ _
ii) What is the intrinsic value of the contract if the option is a put? _ _ _ _ _ _

Question 5

What is assumed to be lognormal in the standard market model for valuing the following?
i) A bond option _ _ _ _ _ _ _
ii) A caplet _ _ _ _ _ _
iii) A swaption _ _ _ _ _ _