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.

- (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)
- (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.

- (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)
- (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.

- (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.

- (a) Compute all risk-free zero rates from the given information.
- (b) Find the value of Jonathan’s portfolio.
- (c) Explain what duration is and calculate the duration of bonds I, II, III and IV.
- (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.

- (a) Compute the price of an ATM European put option that matures in 1 year by using a 3-step binomial model. (5 marks)
- (b) Compute the price of an ATM American call option that matures in 1 year by using a 3-step binomial model. (5 marks)
- (c) Compute the price of an ATM Asian put option that matures in 1 year by using a 3- step binomial model. (5 marks)
- (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.