Question 2 a) Suppose the following exchange rate quotations are available: Citi

Question

Question 2
a) Suppose the following exchange rate quotations are available:
Citibank quotes U.S. dollars per Euro: $1.2223/€
Barclays Bank quotes U.S. dollars per pound sterling: $1.8410/£
Dresdner Bank quotes Euros per pound sterling: €1.5100/£
You are a market trader with $1,000,000. Will you be able to make an arbitrage profit using these
quotes? If yes, what will be the profit? Show your calculations.
(5 marks)
b) Forward contracts are not as liquid as Futures contracts. Why is this so?
(5 marks)
c) ABC enjoys a different credit rating than XYZ in the debt market. It can either borrow at a fixed
interest rate of 9% or at a floating rate which equals LIBOR + 2%. XYZ can borrow at 10.5%
fixed rate or at a floating rate of LIBOR + 1.5%.
ABC wishes to borrow on a floating rate basis and XYZ wishes to borrow on a fixed rate basis.
The quality spread differential is 2%.
Because ABC is more better in borrowing at a fixed rate basis than XYZ is at borrowing on a
floating rate basis, it is agreed that 1.5% of the potential gain is to go to ABC and the remaining
0.5% belongs to XYZ.
Fortunately, they come in contact with each other, doing away with the need of a swap dealer.
Construct an interest rate swap between ABC and XYZ which will be mutually beneficial.
(5 marks)
d) A Put option with a maturity of 5 months sells for $8.10. A call with the same expiration sells for
$6.12. If the exercise price is $70 and the stock is currently priced at $66.81, what is the annual
continuously compounded interest rate?
(5 marks)
e) Let us say that a put and a call have the same maturity and strike price. If they have the same
price, what will be the value of the stock?
(5 marks)

Explanation / Answer

a) Let us first find cross raet between citibank and Barclays bank

Citi bank : 1 euro = 1.2223$

1$ = 0.818 euro

Barclays Bank : 1 Pound = 1.8410$

Cross rate : 1 pound = 1.8410(0.818)

1 pound = 1.5062 euro

The cross rate is not same as of Dresdner bank hence opportunity of arbitrage exists.

Steps :

1) Sell $1000,000 to barclay's bank for $1000000/1.8410 = Pound 543,183

2) Sell this pound to Dresdner Bank to citi bank = 543183*1.51 = euro 820,206

3) sell this euro to citibank for dollors = 820206*1.2223 = $ 1002538

Profit = 2538$

B) Forwand contract unlike future contract are not standardise and are not traded on exchange. In forward contract there is always risk of counter party default where as in futures contract such risk does not exist as exchange guarantees transaction. Most importantly futures are quoted on exchange and are traded hence it is highly liquid. Thus forward contracts are highly liquid

C) Let first prepare summary of the situation

ABC wants floating rate and XYZ wants fixed rate.

Table showing swap

Thus effective rate of interest for ABC = Libor +2% - 1.5% = Libor+0.5%

Thus effective rate of interest for XYZ = 10.5% - 0.5% = 10%

D) Put- call parity = C+Xe^-rt = p +s

C = price of call option

r= rate of interest

t = time to expiry

p= price of put option

s= current market price

X = strike price

6.12 + 70e^-r*5/12 = 8.1 + 66.81

6.12 + 70e^-0.417r = 74.91

70e^-0.471r = 68.79

70/(1+(-0.471r) =68.79

70 = 68.79(1-0.471r)

70 = 68.79 - 32.4r

32.4r = 1.21

r = 3.73%

Particulars ABC XYZ Fixed rate 9% 10.50% Floating rate LIBOR + 2% LIBOR + 1.5%

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