Question

Suppose you have the following spot exchange rates in FX markets:

                         £1 = $1.29,      €1 = $1.17,    and     £1 = €1.13.

i) Please check if the cross rate between the euro (€) and the UK pound (£) is consistent or not.

           

2. How much profit (in $ terms) can you make from trading $1,000? Describe your trading process to get your profit, if there is any.

3. How much will you have profit or loss when you follow a reversed order of transaction between UK pound and euro from that in Q2. ii) above?

iv) How do you expect the current cross rate of £1 = €1.13 change after numerous arbitrage transactions in global FX markets take place– go up or down in the value of UK pound with respect to euro? Explain why and how.

3. You purchased a European foreign exchange option contract to buy 5000 UK pound at the price of $1.30/£ which expires today. You have paid $140 for the contract. Suppose the spot rate on the expiration date, today, is $1.32/£, what will be your optimal decision for the contract (exercise or not exercise)? Discuss why or why not.

Answer 1

cross rate between the euro (€) and the UK pound (£) is consistent or not.

£1 = $1.29

$1.29= €(1 /1.17)*1.29=€1.1026

Cross Rate should be

$1.29= €1.1026

£1=€1.1026

Cross rate is not consistent

How much profit (in $ terms) can you make from trading $1,000

Buy POUND with $1000 at rate £1 = $1.29

Pounds received=(1/1.29)*1000£=775.19 £

Convert Pounds to Euro (Rate£1 = €1.13.)

Euros received=775.19*1.13=875.96 €

Convert Euros to Dollar(€1 = $1.17)

Dollars received=875.96*1.17 Dollar=$1024.87

PROFIT=1024.87-1000=$24.87

when you follow a reversed order of transaction between UK pound and euro

Convert Dollar to Euro (€1 = $1.17)

You get (1000/1.17)=854.70€

Convert Euro to Pound (Rate£1 = €1.13.)

Amount of Pound Received=854.70/1.13=756.37 Pound

Covert Pound to Dollar (Rate £1 = $1.29)

You will get 756.37*1.29 dollars=$975.72

There will be loss =(1000-975.72)=$24.28

iv)After numerous arbitrage the rate will tend to be :

£1=€1.1026

The fair value of rate

3. Strike Rate:$1.30/£

Rate at expiration :$1.32/£

Payoff per Pound =(1.32-1.30)=$0.02

Total Payoff=5000*0.02=$100

Initial Cost=$140

Net Loss=(100-140)=-$40

what will be your optimal decision for the contract The option should be exercised.

By exercising the contract loss will be reduced.

If not exercised loss will be $140