Advanced Financial Economics Assignment

ECON – 477

Problem Set 4

Spring 2021

Due by 2:30pm CST on April 20th 2021 (submission via Canvas)

Problem 1. (6 points)

The process for the prices of a 5-year maturity zero-coupon bond and of a derivative on

the interest rate that matures in three years are decribed by the following trees. The

probablities that an analyst associates with going up and down are 60% and 40% at each

node of the tree, respectively. (NOTE: These are NOT the risk neutral probabilities.)

5-year zero coupon bond price

period =⇒ i = 0 i = 1 i = 2 i = 3 i = 4 i = 5 time (in years) =⇒ t = 0 t = 1 t = 2 t = 3 t = 4 t = 5

Z50 Z 5 1 Z

5 2 Z

5 3 Z

5 4

100

84.33

70.91 100

61.81 87.02

55.55 75.49 100

52.03 67.07 89.12

63.08 79.05 100

74.84 91.31

86.57 100

95.86

100

1

Derivative

period =⇒ i = 0 i = 1 i = 2 i = 3 time (in years) =⇒ t = 0 t = 1 t = 2 t = 3

154.5

108.72

68.04 103

40.33 49.17

23.92 10.3

4.64

0

1. Suppose that you hold a portfolio of 10 five-years zeros and 20 derivatives. How does

the portfolio payoff evolve over three years? Construct the tree.

2. How can you change your position in the derivative in order to make the portfolio

riskless between date t = 0 and t = 1?

3. What is the implied interest-rate tree up to t = 2?

4. What is the price of a zero-coupon bond that matures at time t = 2?

5. Suppose that at time t = 1 the interest rate is 12.48%. How many the 3-year

zero-coupon bonds do you need to hold for each unit of the derivative to obtain

a Sharpe ratio of 0.75? (Hint: Recall that the variance of a security X is σ2X =

E [ (X −E (X))2

] Problem 2. (2 points)

The following table shows some annualized, continuously compounded zero-coupon yields

and forward rates:

y(0,T) f(0,T −1,T) f(0,T −2,T) f(0,T −3,T) T = 1 4.00% ? — — T = 2 ? 6.00% ? — T = 3 6.00% ? ? ?

1. What are the missing six values, y(0,2), f(0,0,1), f(0,2,3), f(0,0,2), f(0,1,3) and

f(0,0,3)? (denoted by “?”in the table). Select values that ensure that there are no

arbitrage opportunities.

2. Suppose the six missing numbers are as you calculated in Part 1, but now f(0,1,2)

is equal to 7% rather than 6%. Are there arbitrage opportunities? If so, explain how

2

you would exploit such an opportunity? Specify which bonds you would buy and

sell, the quantities, and which forward contracts you would enter and their notional

values. If not, explain briefly why the alternative forward rate is consistent with the

absence of arbitrage.

Problem 3. (2 points)

Today you observe the following term structure of swap rates.

Maturity (years) Period i ci0 0.5 1 2.6542%

1 2 2.9055%

1.5 3 3.1546%

2 4 3.3623%

2.5 5 3.6570%

3 6 3.8865%

Determine the price of a 10-year Treasury note issued 8 years ago that pays a semi-

annual coupon at 2.75% annual rate, and has face value $10,000.

3

The price is based on these factors:

Academic level

Number of pages

Urgency

Basic features

- Free title page and bibliography
- Unlimited revisions
- Plagiarism-free guarantee
- Money-back guarantee
- 24/7 support

On-demand options

- Writer’s samples
- Part-by-part delivery
- Overnight delivery
- Copies of used sources
- Expert Proofreading

Paper format

- 275 words per page
- 12 pt Arial/Times New Roman
- Double line spacing
- Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Delivering a high-quality product at a reasonable price is not enough anymore.

That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read moreEach paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read moreThanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read moreYour email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read moreBy sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more