# Interest rates Assigmnent – Trading session . In a recent trading session, the benchmark 30-year Treasury bonds market price went up 8.62 dollars per $10

Interest rates Assigmnent – Trading session . In a recent trading session, the benchmark 30-year Treasury bonds market price went up

8.62 dollars per $1000 face value to 1032.38 dollars, while its yield fell from .07 to .068. The

bonds market price then went up another 7.62 dollars per $1000 face value as the yield

fell further to .0665 from .068. Report answers for the following (using average of latest

two bond prices for duration and average of latest three bond prices for convexity):

1. Convexity, using the average of all three market prices of the bond in the denominator

of the formula.

2. First modified duration, using average of first two market prices of the bond in the

denominator of the formula.

3. Second modified duration, using average of second and third prices of the bond.

4. The expected rise in bond price if the interest rate were to fall another 20 basis points

(.002) from .0665, using the average of two modified durations and convexity.

B. Estimate term structure of discount factors, spot rates and forward rates by using data

on five semi-annual coupon paying bonds with $100 face value each: The bonds,

respectively, have 1.25, 5.35, 10.4, 15.15 and 20.2 years to maturity; pay coupon at

annual rates of 4.62, 5.62, 6.62, 7.62, and 8.62 percent of face value; and are trading at quoted

spot market prices in dollars of 98.62, 99.62, 100.62, 101.62 and 102.62. Specify the discount factor

function d(t) by a third degree polynomial with unknown parameters a, b, and c, as

done in class. Using estimated d(t) function, determine spot rate and forward rate

functions by assuming half-year compounding. Then write the values of the following

based on your estimation.

5. Coefficient of parameter a in first bond price equation.

6. Coefficient of parameter b in first bond price equation.

7. Coefficient of parameter c in first bond price equation.

8. Coefficient of parameter a in second bond price equation.

9. Coefficient of parameter b in second bond price equation.

10.Coefficient of parameter c in second bond price equation.

11.Coefficient of parameter a in third bond price equation.

12.Coefficient of parameter b in third bond price equation.

13.Coefficient of parameter c in third bond price equation.

14.Coefficient of parameter a in fourth bond price equation.

15.Coefficient of parameter b in fourth bond price equation.

16.Coefficient of parameter c in fourth bond price equation.

17.Coefficient of parameter a in fifth bond price equation.

18.Coefficient of parameter b in fifth bond price equation.

19.Coefficient of parameter c in fifth bond price equation.

20.Parameter a.

21.Parameter b.

22.Parameter c.

23.Current price of a dollar at 5th year.

24.Current price of a dollar at 7th year.

25.Current price of a dollar at 10th year.

26.Current price of a dollar at 15th year.

27.Spot rate for term 2 year.

28.Spot rate for term 5 year.

29.Spot rate for term 10 year.

30.Spot rate for term 17 year.

31.Forward rate for half year period 2.5 to 3.0 years.

32.Forward rate for half year period 5.5 to 6.0 years.

33.Forward rate for half year period 10.5 to 11.0 years.

34.Forward rate for half year period 15.5 to 16.0 years.

C. Estimate the 2-year, 5-year, and 10-year key rate durations of a 20-year bond carrying a

coupon of 8.6 percent on face value $100 paid semi-annually. The given term structure

starts with 3.1 percent spot rate of interest at time zero and rises at a rate of 0.002 (.2%)

per half year thereafter. Take a 20 basis point (.002) move in each key interest rate to

calculate the key rate durations by the method done in class and given in textbook.

Report answers for the following:

35. Current fair price of the bond with the given term structure.

36. Price change needed to calculate 2-year key rate duration.

37. Price change needed to calculate 5-year key rate duration.

38. Price change needed to calculate 10-year key rate duration.

39. 2-year key rate duration.

40. 5-year key rate duration.

41. 10-year key rate duration.

D. Using the following data on the price of a bond and the corresponding interest rate

(assuming a flat term structure) and regression method, estimate convexity and duration of

the bond:

Price Interest Rate

99 .06

100 .057

101.5 .052

102 .049

105 .044

106.5 .038

108 .033

108.5 .031

110.1 .028

42. What is the estimated value of Duration?

43. What is the estimated value of Convexity? Interest rates are expressed as annualized rates for the term specified. Report your

interest rate answers as fractional numbers like 0.11 for 11% per year.

A. In a recent trading session, the benchmark 30-year Treasury bonds market price went up

8.62 dollars per $1000 face value to 1032.38 dollars, while its yield fell from .07 to .068. The

bonds market price then went up another 7.62 dollars per $1000 face value as the yield

fell further to .0665 from .068. Report answers for the following (using average of latest

two bond prices for duration and average of latest three bond prices for convexity):

1. Convexity, using the average of all three market prices of the bond in the denominator

of the formula.

2. First modified duration, using average of first two market prices of the bond in the

denominator of the formula.

3. Second modified duration, using average of second and third prices of the bond.

4. The expected rise in bond price if the interest rate were to fall another 20 basis points

(.002) from .0665, using the average of two modified durations and convexity.

B. Estimate term structure of discount factors, spot rates and forward rates by using data

on five semi-annual coupon paying bonds with $100 face value each: The bonds,

respectively, have 1.25, 5.35, 10.4, 15.15 and 20.2 years to maturity; pay coupon at

annual rates of 4.62, 5.62, 6.62, 7.62, and 8.62 percent of face value; and are trading at quoted

spot market prices in dollars of 98.62, 99.62, 100.62, 101.62 and 102.62. Specify the discount factor

function d(t) by a third degree polynomial with unknown parameters a, b, and c, as

done in class. Using estimated d(t) function, determine spot rate and forward rate

functions by assuming half-year compounding. Then write the values of the following

based on your estimation.

5. Coefficient of parameter a in first bond price equation.

6. Coefficient of parameter b in first bond price equation.

7. Coefficient of parameter c in first bond price equation.

8. Coefficient of parameter a in second bond price equation.

9. Coefficient of parameter b in second bond price equation.

10.Coefficient of parameter c in second bond price equation.

11.Coefficient of parameter a in third bond price equation.

12.Coefficient of parameter b in third bond price equation.

13.Coefficient of parameter c in third bond price equation.

14.Coefficient of parameter a in fourth bond price equation.

15.Coefficient of parameter b in fourth bond price equation.

16.Coefficient of parameter c in fourth bond price equation.

17.Coefficient of parameter a in fifth bond price equation.

18.Coefficient of parameter b in fifth bond price equation.

19.Coefficient of parameter c in fifth bond price equation.

20.Parameter a.

21.Parameter b.

22.Parameter c.

23.Current price of a dollar at 5th year.

24.Current price of a dollar at 7th year.

25.Current price of a dollar at 10th year.

26.Current price of a dollar at 15th year.

27.Spot rate for term 2 year.

28.Spot rate for term 5 year.

29.Spot rate for term 10 year.

30.Spot rate for term 17 year.

31.Forward rate for half year period 2.5 to 3.0 years.

32.Forward rate for half year period 5.5 to 6.0 years.

33.Forward rate for half year period 10.5 to 11.0 years.

34.Forward rate for half year period 15.5 to 16.0 years.

C. Estimate the 2-year, 5-year, and 10-year key rate durations of a 20-year bond carrying a

coupon of 8.6 percent on face value $100 paid semi-annually. The given term structure

starts with 3.1 percent spot rate of interest at time zero and rises at a rate of 0.002 (.2%)

per half year thereafter. Take a 20 basis point (.002) move in each key interest rate to

calculate the key rate durations by the method done in class and given in textbook.

Report answers for the following:

35. Current fair price of the bond with the given term structure.

36. Price change needed to calculate 2-year key rate duration.

37. Price change needed to calculate 5-year key rate duration.

38. Price change needed to calculate 10-year key rate duration.

39. 2-year key rate duration.

40. 5-year key rate duration.

41. 10-year key rate duration.

D. Using the following data on the price of a bond and the corresponding interest rate

(assuming a flat term structure) and regression method, estimate convexity and duration of

the bond:

Price Interest Rate

99 .06

100 .057

101.5 .052

102 .049

105 .044

106.5 .038

108 .033

108.5 .031

110.1 .028

42. What is the estimated value of Duration?

43. What is the estimated value of Convexity?

Purchase answer to see full

attachment

## We've got everything to become your favourite writing service

### Money back guarantee

Your money is safe. Even if we fail to satisfy your expectations, you can always request a refund and get your money back.

### Confidentiality

We don’t share your private information with anyone. What happens on our website stays on our website.

### Our service is legit

We provide you with a sample paper on the topic you need, and this kind of academic assistance is perfectly legitimate.

### Get a plagiarism-free paper

We check every paper with our plagiarism-detection software, so you get a unique paper written for your particular purposes.

### We can help with urgent tasks

Need a paper tomorrow? We can write it even while you’re sleeping. Place an order now and get your paper in 8 hours.

### Pay a fair price

Our prices depend on urgency. If you want a cheap essay, place your order in advance. Our prices start from $11 per page.