Find the swap rate of a 1.5-year plain vanilla swap 3 months after initiation with the following characteristics
Need help with this fixed income assignment with work shown. PLEASE SHOW WORK.
- If the bond face value is not given, assume that it is $100.
Question 1 10 pts
The forward projection method
Group of answer choices
a.cannot be applied to only the fixed rate leg.
b.All of these are correct.
c.is a technique to price the floating rate leg of an interest rate swap using forward rates as proxies for future short rates.
d.is equivalent to the zero coupon method for plain vanilla swaps.
e.requires the full term structure of spot rates to be observable.
Question 2 10 pts
|
t = |
0 |
0.5 |
|
4% |
||
|
2% |
||
|
1% |
Assume each period is 6 months. Using the short rate tree given above, what values can a one year zero coupon bond take at t = 0.5?
Group of answer choices
None of these.
a.$97.02 and $99.50.
b.$98.02 and $99.50.
c.$98.02 and $97.50.
d.$99.02 and $96.50.
Question 3 10 pts
|
t = |
0 |
0.5 |
|
4% |
||
|
2% |
||
|
1% |
Using the short rate tree given above, what is the replicating portfolio for a European option on interest rates with maturity t = 0.5, rK = 2.5% and payoff: 100*max(rt – rK,0). You use the two period to maturity zero coupon bond to replicate, which is trading at $97.7779. Find values of N1 (one-period) and N2 (two-period). Assume risk neutral probability is 50%.
Group of answer choices
a.N1 = 1.0126 and N2 = -1.0075.
b.N1 = -1.0126 and N2 = 1.0075.
c.N1 = -1.0075 and N2 = 1.0126.
d.None of these.
e.N1 = 1.0075 and N2 = -1.0126.
Question 4 10 pts
Find the swap rate of a 1.5-year plain vanilla swap 3 months after initiation with the following characteristics: N = $100, semi-annual payments, and price is $0.3188. The floating leg is referenced to the 6-month LIBOR, which was at 4% 3 months ago.
|
T |
Z(0,T) |
|
0.25 |
0.9840 |
|
0.5 |
0.9730 |
|
0.75 |
0.9650 |
|
1 |
0.9440 |
|
1.25 |
0.9390 |
|
1.5 |
0.9340 |
Group of answer choices
a.5.0%
b.4.8%
c.5.1%
d.4.7%
e.4.9%
Question 5 10 pts
Find the swap rate of a plain vanilla swap at initiation with 2 years to maturity, notional amount of $100 million, and semi-annual payments on both the fixed and floating legs. Assume the term structure is flat at 5% a year. Use semi-annual compounding.
Group of answer choices
a.5.2%.
b.5.1%.
c.5.3%.
d.4.9%.
e.5.0%.
Question 6 10 pts
|
t = |
0 |
0.5 |
|
5% |
||
|
3% |
||
|
2% |
Using the short rate tree given above, find the price of a European option on interest rates with maturity t = 0.5, rK = 3% and payoff: 100*max(rK – rt,0). Assume risk neutral probability (seeing higher rates) of 70%.
Group of answer choices
a.0.5074
b.0.4926
c.0.7045
d.None of these.
e.0.2955
Question 7 10 pts
|
t = |
0 |
0.5 |
|
5% |
||
|
3% |
||
|
2% |
Using the short rate tree given above, find the market price of interest risk. Assume risk neutral probability (seeing higher rates) of 70%. The physical probability is 50%.
Group of answer choices
a.0.197
b.0.253
c.None of these.
d.-0.197
e.-0.253
Question 8 10 pts
Which of the following is false about pricing via the replicating portfolio?
Group of answer choices
a.It depends on the law of one price.
b.The portfolio always contains two bonds.
c.These statements are all true.
d.No arbitrage has to be assumed.
e.It is based on relative pricing.
Question 9 10 pts
Build a short rate tree using the MONTHLY Ho_Lee model with the following parameters. The current short rate is 0.4%. The volatility of the short rate is 1%. Monthly drift is constant at 0.3%. Which interest rate below is NOT possible in month 2?
Group of answer choices
a.0.45%
b.-0.13%
c.-0.77%
d.1.03%
e.None of these.
Question 10 10 pts
Which of the following statement is false about the Ho-Lee model?
Group of answer choices
a.It can perfectly fit the term structure of interest rates.
b.It requires calibration to data.
c.It’s an additive model.
d.It can produce negative short rates.
e.None of these.
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