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Practice Questions from the Textbook (Hull, 2017)

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Practice Questions from the Textbook (Hull, 2017).

Problem 4.1.

A bank quotes you an interest rate of 14% per annum with quarterly compounding. What is the equivalent rate with (a) continuous compounding and (b) annual compounding?

Problem 4.4.

An investor receives $1,100 in one year in return for an investment of $1,000 now. Calculate the percentage return per annum with

a) annual compounding;

b) semiannual compounding;

c) monthly compounding and;

d) continuous compounding.

Problem 4.5.

Suppose that zero interest rates with continuous compounding are as follows:

Maturity (months) Rate (% per annum)

3                                     8.0

6                                    8.2

9                                   8.4

12                                   8.5

15                                   8.6

18                                 8.7

Calculate forward interest rates for the second, third, fourth, fifth, and sixth quarters.

Qtr

R_F = R₂ + (R₂ – R₁) T₁/T₂-T₁

Qtr 2 R(F) = 8.2 + (8.2-8.0) x (0.25/(0.5-0.25) = … = 8.4%

Problem 4.9.

What rate of interest with continuous compounding is equivalent to 15% per annum with monthly compounding?

Problem 4.11.

Suppose that 6-month, 12-month, 18-month, 24-month, and 30-month zero rates are, respectively, 4%, 4.2%, 4.4%, 4.6%, and 4.8% per annum with continuous compounding. Estimate the cash price of a bond with a face value of 100 that will mature in 30 months and pay a coupon of 4% per annum semiannually.

Problem 4.14.

Suppose that risk-free zero interest rates with continuous compounding are as follows:

Maturity( years) Rate (% per annum)

1                            2.0

2                           3.0

3                           3.7

4                             4.2

5                          4.5

Calculate forward interest rates for the second, third, fourth, and fifth years.

Problem 4.31.

An interest rate is quoted as 5% per annum with semiannual compounding. What is the equivalent rate with (a) annual compounding, (b) monthly compounding, and (c) continuous compounding?

Problem 4.32.

The 6-month, 12-month. 18-month, and 24-month zero rates are 4%, 4.5%, 4.75%, and 5% with semiannual compounding.

a) What are the rates with continuous compounding?

b) What is the forward rate for the six-month period beginning in 18 months?

c) What is the value of an FRA where the holder pays LIBOR and receives 7% (semiannually compounded) for a six-month period beginning in 18 months? The current forward rate for this period is 6% (semiannually compounded). The principal is $1 million.

Extra question

d) What is the two-year par yield?

Problem 4.34.

The following table gives the prices of bonds

Bond Principal ($)	Time to Maturity (yrs)	Annual Coupon ($)*	Bond Price ($)
100	0.5	0.0	98
100	1.0	0.0	95
100	1.5	6.2	101
100	2.0	8.0	104

 

 *Half the stated coupon is paid every six months

a) Calculate zero rates for maturities of 6 months, 12 months, 18 months, and 24 months.

b) What are the forward rates for the periods: 6 months to 12 months, 12 months to 18 months, 18 months to 24 months?

c) What are the 6-month, 12-month, 18-month, and 24-month par yields for bonds that provide semiannual coupon payments?

d) Estimate the price and yield of a two-year bond providing a semiannual coupon of 7% per annum.