Assignment

Question 1

(a) Mary expects to borrow in 4 months' time and is afraid that interest rates will rise at the time of borrowing. She buys a 4x6 FRA priced at 10.19%/10.25% from a bank. 4 months later, the actual 2-month (61-day) LIBOR is 11.2%.

Calculate the effective interest settlement if payment is made in advance and compare this to the situation if payment is made in arrears, assuming the principal amount is GBP 1,000. Who pays and what is the amount that changes hands? Use Python in your calculations.

(b) Describe one difference and one similarity between Non-Deliverable Forwards (NDFs) and conventional forwards. Illustrate the mechanics of an NDF transaction involving MYR and USD on a notional amount of MYR1 million stating any other assumptions you make.

Question 2

Using Excel, calculate the following using the bond information in the table below:

(a) 1-year, 2-year, 3-year and 4-year zero coupon yields

(b) 1-year, 2-year, 3-year and 4-year par yields

(c) 1-year v 2-year, 2-year v 3-year and 3-year v 4-year forward-forward yields

Question 3

Use Excel in your calculations.

Mary, a fund manager with ABC Bank, holds the following corporate bonds in her bond portfolio.

Corporate Bond Coupon Rate Maturity Number of Bonds
A 2% 6 months 2,000
B 3% 12 months 3,500
C 4% 18 months 8,000
D 5% 24 months 5,000

All the bonds have a face value of $1,000 and pay coupons on a semi-annual basis.

The yield curve for government bonds for the next 24 months is given as follows.

Maturity Coupon Rate Yield
6 months 0.0% 1%
12 months 0.0% 1.5%
18 months 2.5% 2%
24 months 4% 2.3%

All the government bonds have a face value of $1,000 and also pay coupons on a semi-annual basis.

(a) What is the price of the 18 month and the 24-month government bond?

(b) Calculate all the zero coupon discount factors from the data given.

(c) Calculate the value of each bond in the corporate bond portfolio.

(d) Calculate the current value of the corporate bond portfolio.

Question 4

Use Python in your calculations.

(a) You have USD1 million to invest for 3 months (92 days). You have 2 alternatives. Alternative 1 is to deposit your USD for 3 months at USD LIBOR. Alternative 2 is to convert your USD to GBP and invest in a GBP commercial paper yielding LIBOR + 5bp, at the same time entering into a forward contract to sell the GBP for USD at the end of 3 months.

Compute the difference in absolute returns between the two investment choices.

Spot GBPUSD: 1.2477 - 83
3-month swap: 60/70
3 month GBP interest rates: 0.39% - 0.42%
3 month USD interest rates:0.90% - 0.92%

(b) You observe the following quotes at a bank:

Spot GBPSGD: 1.7668 - 77
Spot SGDJPY: 77.09 - 12

(i) Your Japanese friend wishes to travel to the United Kingdom and wishes to buy GBP1,000. How much JPY must he pay?

(ii) What is the 3-month (92 day) GBPSGD forward outright given the following:

92 day SGD interest rate: 0.5%
92 day GBP interest rate:1.2%

Which currency is trading at a forward premium?

Question 5

(a) SBO stock is currently selling in the market for $55.00. You are looking at its 3-month call and put options which have a strike price of $57. The stock price is expected to either rise or fall by 2% each month and the risk-free interest rate is 5% per annum. Using Excel, compute the price of both the call and put options using a three-step binomial tree.

(b) Suppose that the stock price of a company X is currently USD110, has a volatility of 35% and the prevailing risk-free rate is 2%. Find, by applying the Black-Scholes formula, the price of a call and a put option, both with the same strike price of USD120, that matures in 3 months. Use Python in your calculations.