Finance-Assignment

Question 1

The term structure is a basic device that provides a snapshot of the interest rate environment in terms of lending/borrowing costs across the various terms.

  1. (a) Describe the nature of the term structure and how it is constructed in detail. Use Excel as an aid in your working. (15 marks)
  2. (b) Do the following exercises from Chapter 8 of the textbook: 81, 82. Be sure to express your answers clearly in your own words, based on your own understanding, with Python as an aid in your calculations and reasoning. (5 marks)

Question 2

The principle of no-arbitrage is a fundamental notion that is applied to relate prices or rates in the market on theoretical terms.

  1. (a) Apply the principle of no-arbitrage to find USDSGD if it is given that a broker quotes EURUSD as and EURSGD as . (10 marks)
  2. (b) Do the following exercises from Chapter 9 of the textbook: 85, 86. Be sure to express your answers clearly in your own words, based on your understanding, with Python as an aid in your calculations and reasoning. (10 marks)

Question 3

The equity option market is closely linked to the stock market but at the same time it is structurally different from the latter.

  1. (b) Do the following exercises from Chapter 11 of the textbook: 98, 100. Be sure to express your answers clearly in your own words, based on your own understanding, with Python as an aid in your calculations and reasoning. (5 marks)

Question 4

Jonathan’s portfolio of fixed income instruments comprises the following corporate bonds:

Jonathan collected the following data from government bonds:

Assume that all bonds listed pay semi-annual coupons (or none) and have $100 face value.

  1. (a) Compute all risk-free zero rates from the given information.
  2. (b) Find the value of Jonathan’s portfolio.
  3. (c) Explain what duration is and calculate the duration of bonds I, II, III and IV.
  4. (d) Explain what convexity is and estimate, using duration and convexity, the value of Jonathan’s portfolio if interest rate falls by 1.5%. (5 marks)

Show your workings clearly with calculations performed with Excel.

Corporate Bond

Coupon Rate

Maturity

Convexity

Number of Bonds

I

4.5%

12 months

0.33

600

II

5.5%

18 months

0.43

1200

III

6.5%

24 months

0.53

1800

IV

7.0%

6 months

0.63

2400

Maturity

Coupon Rate

Yield

6 months

0%

1.00%

12 months

0%

1.50%

18 months

1.5%

2.00%

24 months

2.0%

2.5%

(5 marks) (5 marks) (5 marks)

Question 5

Answer the following questions on option pricing.

Assume that the current price of a stock is $95, the risk-free rate is 3%, the up and down factors are 1.50 and 0.67 respectively.

  1. (a) Compute the price of an ATM European put option that matures in 1 year by using a 3-step binomial model. (5 marks)
  2. (b) Compute the price of an ATM American call option that matures in 1 year by using a 3-step binomial model. (5 marks)
  3. (c) Compute the price of an ATM Asian put option that matures in 1 year by using a 3- step binomial model. (5 marks)
  4. (d) Compare and contrast the price that is calculated in (a) with the price that is calculated with the Black-Scholes model.

Show your workings clearly with calculations performed with Python.