BUSFIN 7222-Forwards and Interest Rate Swaps
Question # 00463348
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Updated on: 01/15/2017 10:54 PM Due on: 01/16/2017
Business Finance 7222
Spring 2016
Assignment #2
Interest Rate Derivatives
Due Date: February 16, 2016
The focus of this assignment is to understand how to price di?erent interest rate derivatives
including forwards, futures, interest rate swaps, and interest rate options.
Please work in a group of 1 - 5 people. Each group should hand in one copy of their answers.
Please show your work and provide explanations where relevant. However, you do not need
to print out entire spreadsheets. Your answers should be summarized in a write-up with
relevant details of calculations, tables and charts (if applicable), and explanations.
The assignment can be turned in during class or via e-mail (shi.777@osu.edu). If you do
submit your assignment via e-mail, please submit it either as a Word document or as a PDF
?le. In particular, an Excel spreadsheet should not be your primary write-up – if you feel
that the Excel spreadsheet is relevant to providing details of your work, please copy and
paste the relevant portions into your Word document. You can e-mail an Excel spreadsheet
as a supplement to your write-up if you feel that it will be helpful in grading your assignment.
This particular assignment will require you to draw a number of trees. You should feel free
to use hand-drawn trees and submit handwritten solutions if you ?nd this to be easier.
Part 1: Forwards and Interest Rate Swaps
Suppose that you are given the following term structure of zero coupon yields (spot rates).
Maturity r
0.5
0.02
1
0.025
1.5
0.03
2
0.04
Semi-annually compounded interest rates
1. From the given spot rates, calculate the forward rates, f(0, 0.5, 1), f(0, 1, 1.5), and f(0,
1.5, 2).
2. Suppose that f(0, 1, 1.5) quoted by a FRA dealer is 4.5%. (This should be almost 0.5
percentage points higher than what you found above.) Using f(0, 1, 1.5) and the given
zero coupon yields, construct an arbitrage trading strategy to take advantage of this
mispricing.
3. What is the fair ?xed rate in a 2-year interest rate swap in which ?xed and ?oating
payments are exchanged every six months? Note that this is a little di?erent from the
lecture slides where payments were quarterly and the reference rate was the three-month
spot rate.
1 4. Suppose that half a year passes. The term structure of zero coupon yields is now
Maturity r
0.5
0.01
1
0.015
1.5
0.02
Semi-annually compounded interest rates
If you entered into a ?xed-for-?oating contract previously (with a notional of $100),
what is the value of your position now?
Part 2: Treasury Bond Futures
It is July 30, 2015. The cheapest-to-deliver bond in a September 2015 Treasury bond
futures contract is a 13% coupon bond with maturity at August 4, 2035. Delivery is expected
to be made on September 30, 2015. Coupon payments on the bond are made on February 4
and August 4 each year. The term structure is ?at, and the rate of interest with semiannual
compounding is 12% per annum.
1. Calculate the current (full) price of the cheapest-to-deliver bond.
2. Calculate the conversion factor for the bond.
3. Calculate the quoted futures price for the futures contract.
Part 3: Fixed Income Options
Suppose that you are given the following interest rate tree with semi-annually compounded
interest rates. Suppose that you are also told that ? = 0.015 and ? = 0.5.
2 1. Using the tree above, calculate the price of a 1.5-year cap with a strike of 3% and a
notional of $100.
2. Calculate the price of a 1.5-year bond with a coupon rate of 3% (coupons paid semiannually) and a face value of $100.
3. What is the price of a 1.5-year ?oor with a strike of 3% and a notional of $100?
Part 4: Callable Bonds
Now, let’s consider the pricing of callable bonds. We will compare this with non-callable
bonds.
1. Using the tree from Part 2, calculate the value of a 1.5-year bond with a coupon rate of
3% (coupons paid semi-annually) that is callable at $100 at each coupon date (starting
at t = 0.5) just after the coupon is paid. Recall that a callable bond price is equal to
an equivalent non-callable bond price minus the value of the call.
2. Add 0.001 to all of the interest rates in the tree from Part 2. Calculate the price of
the callable bond in (1) using this tree.
3. Subtract 0.001 from all of the interest rates in the tree from Part 2. Calculate the price
of the callable bond in (1) using this tree.
4. Using the callable bond prices in (1), (2), and (3), calculate the modi?ed duration of
the callable bond using
MD ? ? 1
B(y + ?y) ? B(y ? ?y)
×
2 × ?y
B(y) 5. Calculate the modi?ed duration of the non-callable version of the 1.5-year bond. You
should already have the prices you need for this in (1), (2), and (3). 3
Spring 2016
Assignment #2
Interest Rate Derivatives
Due Date: February 16, 2016
The focus of this assignment is to understand how to price di?erent interest rate derivatives
including forwards, futures, interest rate swaps, and interest rate options.
Please work in a group of 1 - 5 people. Each group should hand in one copy of their answers.
Please show your work and provide explanations where relevant. However, you do not need
to print out entire spreadsheets. Your answers should be summarized in a write-up with
relevant details of calculations, tables and charts (if applicable), and explanations.
The assignment can be turned in during class or via e-mail (shi.777@osu.edu). If you do
submit your assignment via e-mail, please submit it either as a Word document or as a PDF
?le. In particular, an Excel spreadsheet should not be your primary write-up – if you feel
that the Excel spreadsheet is relevant to providing details of your work, please copy and
paste the relevant portions into your Word document. You can e-mail an Excel spreadsheet
as a supplement to your write-up if you feel that it will be helpful in grading your assignment.
This particular assignment will require you to draw a number of trees. You should feel free
to use hand-drawn trees and submit handwritten solutions if you ?nd this to be easier.
Part 1: Forwards and Interest Rate Swaps
Suppose that you are given the following term structure of zero coupon yields (spot rates).
Maturity r
0.5
0.02
1
0.025
1.5
0.03
2
0.04
Semi-annually compounded interest rates
1. From the given spot rates, calculate the forward rates, f(0, 0.5, 1), f(0, 1, 1.5), and f(0,
1.5, 2).
2. Suppose that f(0, 1, 1.5) quoted by a FRA dealer is 4.5%. (This should be almost 0.5
percentage points higher than what you found above.) Using f(0, 1, 1.5) and the given
zero coupon yields, construct an arbitrage trading strategy to take advantage of this
mispricing.
3. What is the fair ?xed rate in a 2-year interest rate swap in which ?xed and ?oating
payments are exchanged every six months? Note that this is a little di?erent from the
lecture slides where payments were quarterly and the reference rate was the three-month
spot rate.
1 4. Suppose that half a year passes. The term structure of zero coupon yields is now
Maturity r
0.5
0.01
1
0.015
1.5
0.02
Semi-annually compounded interest rates
If you entered into a ?xed-for-?oating contract previously (with a notional of $100),
what is the value of your position now?
Part 2: Treasury Bond Futures
It is July 30, 2015. The cheapest-to-deliver bond in a September 2015 Treasury bond
futures contract is a 13% coupon bond with maturity at August 4, 2035. Delivery is expected
to be made on September 30, 2015. Coupon payments on the bond are made on February 4
and August 4 each year. The term structure is ?at, and the rate of interest with semiannual
compounding is 12% per annum.
1. Calculate the current (full) price of the cheapest-to-deliver bond.
2. Calculate the conversion factor for the bond.
3. Calculate the quoted futures price for the futures contract.
Part 3: Fixed Income Options
Suppose that you are given the following interest rate tree with semi-annually compounded
interest rates. Suppose that you are also told that ? = 0.015 and ? = 0.5.
2 1. Using the tree above, calculate the price of a 1.5-year cap with a strike of 3% and a
notional of $100.
2. Calculate the price of a 1.5-year bond with a coupon rate of 3% (coupons paid semiannually) and a face value of $100.
3. What is the price of a 1.5-year ?oor with a strike of 3% and a notional of $100?
Part 4: Callable Bonds
Now, let’s consider the pricing of callable bonds. We will compare this with non-callable
bonds.
1. Using the tree from Part 2, calculate the value of a 1.5-year bond with a coupon rate of
3% (coupons paid semi-annually) that is callable at $100 at each coupon date (starting
at t = 0.5) just after the coupon is paid. Recall that a callable bond price is equal to
an equivalent non-callable bond price minus the value of the call.
2. Add 0.001 to all of the interest rates in the tree from Part 2. Calculate the price of
the callable bond in (1) using this tree.
3. Subtract 0.001 from all of the interest rates in the tree from Part 2. Calculate the price
of the callable bond in (1) using this tree.
4. Using the callable bond prices in (1), (2), and (3), calculate the modi?ed duration of
the callable bond using
MD ? ? 1
B(y + ?y) ? B(y ? ?y)
×
2 × ?y
B(y) 5. Calculate the modi?ed duration of the non-callable version of the 1.5-year bond. You
should already have the prices you need for this in (1), (2), and (3). 3
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Solution: BUSFIN 7222-Forwards and Interest Rate Swaps