International Finance
Dr. Luong Thi Thu Hang
Type 1: Cross Exchange Rate
Case 1:
Given the available rates:
USD/CHF = 1,1807/1,1874
USD/HKD = 7,7515/7,7585
Calculate cross rate: CHF/HKD



-
Exporter from Swiszerland
Importer from Hongkong
Exporter receives HKD 100,000. He wants to
convert HKD into CHF. Which rate is used?
Convert HKD into USD
Convert USD into CHF



-
Importer from Swiszerland
Exporter from Hongkong
Importer has a payable HKD 100,000. He
wants to buy HKD by CHF (convert CHF into
HKD). Which rate is used?
Convert CHF into USD
Convert USD into HKD
Case 1:
Formula:
Bid CHF/HKD = Min (USD/HKD : USD/CHF)
= Bid USD/HKD : Ask USD/CHF
= 7,7515 : 1,1874 = 6,5218
Case 1:
Formula:
Ask CHF/HKD=Max (USD/HKD : USD/CHF)
= Ask USD/HKD : Bid USD/CHF
= 7,7585 : 1,1807 = 6,5711
Case 2:
Given the available rates:
GBP/USD = 2,0345/2,0415
EUR/USD= 1,4052/1,4152
Calculate cross rate: GBP/EUR
GBP/EUR = GBP/USD : EUR/USD
Case 2:
Formula:
Bid GBP/EUR = Min (GBP/USD : EUR/USD)
= Bid GBP/USD : Ask EUR/USD
= 2,0345 : 1,4152 = 1,4376
Case 2:
Formula:
Ask GBP/EUR=Max (GBP/USD : EUR/USD)
= Ask GBP/USD : Bid EUR/USD
= 2,0415 : 1,4052 = 1,4528
Case 3:
Given the available rates:
EUR/USD = 1,4052/1,4140
USD/HKD = 7,7515/7,7585
Calculate cross rate: EUR/HKD
EUR/HKD = EUR/USD * USD/HKD
Case 3:
Formula:
Bid EUR/HKD = Min (EUR/USD x USD/HKD)
= Bid EUR/USD x Bid USD/HKD
= 1,4052 x 7,7515 =
Case 3:
Formula:
Ask EUR/HKD=Max (EUR/USD x USD/HKD)
= Ask EUR/USD x Ask USD/HKD
= 1,4140 x 7,7585 =
Homework

Given the available rates :
GBP/USD = 2,0345/2,0415
USD/SEK = 6,4205/6,5678
USD/NOK = 5,3833/5,4889
USD/DKK = 5,2367/5,2410
EUR/USD = 1,4052/1,4140
USD/CHF = 1,1807/1,1874
USD/HKD = 7,7515/7,7585

Calculate the cross rate:
GBP/NOK; GBP/EUR; EUR/HKD; HKD/SEK; HKD/CHF; CHF/EUR
Type 2: ARBITRAGES
2.1 Locational Arbitrage
2.2 Triangle Arbitrage
Locational Arbitrage
(1) The process of buying a currency at the location where it is
priced cheap and immediately selling it at another location
where it is priced higher.
(2) Condition for the locational Arbitrage
The ask price in one location is < the bid price in the other
location.
(3) Realignment due to locational arbitrage drives prices to
adjust in different locations so as to eliminate discrepancies.
Local Arbitrage
17
Locational Arbitrage
18
Locational Arbitrage

Bank A:
GBP/USD = 2.0315/2.0355
GBP/EUR = 1.4388/1.4428

Bank B:
USD/GBP = 0.4870/0.4910
USD/EUR = 0.7072/0.7116
Given this information, is locational arbitrage possible for
GBP/USD, USD/EUR. Compute the profit from this strategy
if you had $1 million to use.
Locational Arbitrage
Solution: GBP/USD
Locational Arbitrage

Solution: USD/EUR
Bank A: Calculate the cross exchange rate USD/EUR

Bid USD/EUR = Bid GBP/EUR : Ask GBP/USD
= 1.4388 : 2.0355 = 0.7068

Ask USD/EUR = Ask GBP/EUR : Bid GBP/USD
= 1.4428 : 2.0315 = 0.7102
Local Arbitrage

Solution: USD/EUR
Bank A: USD/EUR = 0.7068/0.7102
Bank B: USD/EUR = 0.7072/0.7116
=> Conclusion: No arbitrage
Triangle Arbitrage
(1) Currency transactions in the spot market to capitalize on
discrepancies in the cross exchange rates between two
currencies.
(2) Realignment due to triangle arbitrage forces exchange
rates back into equilibrium.
Triangle Arbitrage
Example 1:

Bank A: EUR/USD = 1.4052/40

Bank B: USD/CHF = 1.1807/74

Bank C: EUR/CHF = 1.6375/49
Given this information, is triangle arbitrage possible?
Compute the profit from this strategy if you had $1 million to
use.
Triangle Arbitrage
Solution:

From Bank B & Bank C: Calculate cross exchange rate
EUR/USD.
Bid EUR/USD = Bid EUR/CHF : Ask USD/CHF
= 1.6375 : 1.1874 = 1.3790
Ask EUR/USD = Ask EUR/CHF : Bid USD/CHF
= 1.6449 : 1.1807 = 1.3931
Triangle Arbitrage
Solution:

Bank B&C: EUR/USD = 1.3790/1.3931

Bank A:
EUR/USD = 1.4052/1.4140
SaskEUR/USD (Bank B&C) < Sbid EUR/USD (Bank A)
=> Conclusion: Buy EUR/USD from Bank B and C and Sell
EUR/USD from Bank A
Triangle Arbitrage
Solution:
1/ Buy EUR/USD from Bank B and C
a/ Convert USD to CHF through Bank B at Sbid USD/CHF = 1.1807

The amount of CHF: 1,000,000 * 1.1807 = CHF1,180,700
b/ Convert CHF to EUR through Bank C at Sbid CHF/EUR = 1/1.6449 = 0.6079

The amount of EUR: 1,180,700 * 0.6079 = EUR717,747.53
2/ Sell EUR/USD from Bank A
Convert EUR to USD through Bank A at Sbid EUR/USD = 1.4052

The amount of USD: 717,747.53 * 1.4052 = USD1,008,578.83

Profit: USD8,578.83
Triangle Arbitrage
Example 2:

Bank A: EUR/USD = 1.4052/40

Bank B: USD/CHF = 1.1807/74

Bank C: EUR/CHF = 1.6375/49
Given this information, is triangle arbitrage possible?
Compute the profit from this strategy if you had EUR
150,000 to use.
Result: EUR 1,296.7025
Triangle Arbitrage
Example 3:
Bank A: EUR/USD=1,1255/75
Bank B: USD/CHF=1,5642/42
Bank C: EUR/CHF=1,7890/10
Given this information, is triangle arbitrage possible? Compute
the profit from this strategy if you had CHF 500,000 to use.
Result: CHF 3,924.5181
Type 3: Hedging Exposure

Hedging Exposure to Payables

Hedging Exposure to ReceivablesCHF 3,924.5181
Hedging Exposure Payables
[1] Forward Hedge on Payables
Long in a currency forward contract to purchase the amount of foreign
currency needed to cover the payables at a specific exchange rate.
Ex: Long position in a forward contract on EUR 100,000. The 1-year
forward rate is EUR/USD = 1.2.
The USD cost in 1 year: 100,000 * 1.2 = USD120,000
Hedging Exposure Payables
[2] Call option Hedge on Payables
Long in a currency call option to buy the foreign currency to pay the
payables.
Call option contract as following:
- The size of contract: EUR 100,000
- Premium: EUR/USD = 0.03
- Exercise price: EUR/USD = 1.2
Hedging Exposure Payables
[2] Call option Hedge on Payables
Cost of call options based on currency forecast.
Exercise price: USD1.2/EUR
Pro Spot rate at T Premium
Exercise
Cost/EUR
0.2
EUR/USD=1.16 USD0.03 per
EUR
No
EUR/USD=1.19 USD119,000
0.7
EUR/USD=1.22 USD0.03 per
EUR
Yes
EUR/USD=1.23 USD123,000
0.1
EUR/USD=1.24 USD0.03 per
EUR
Yes
EUR/USD=1.23 USD123,000
Expected total payment at time=T:
Total
Payment
Hedging Exposure Payables
[3] No Hedge
Pro
Spot rate at T
Total Payment
0.2
EUR/USD=1.16
USD116,000
0.7
EUR/USD=1.22
USD122,000
0.1
EUR/USD=1.24
USD124,000
Expected total payment at time=T:
0.2*116,000 + 0.7*122,000 + 0,1*124,000 = USD121,000
Hedging Exposure Payables
[4] Comparison of Techniques to Hedge Payables
The cost of the forward hedge can be determined with certainty
The currency call option hedge has different outcomes depending on
the future spot rate at the time payables are due
(1) Select optimal hedging technique
(2) Choose optimal hedge versus no hedge for payables
Hedging Exposure Payables
Example 1:
Assume that Loras Corp (CHF) imported goods from UK and needs
GBP500,000 30 days from now. It considers 3 hedging techniques:
(1) Long position in a forward contract on GBP500,000.
(2) Long position in call option on GBP500,000.
(3) No Hedge
Given information:
Forward rate: GBP/CHF =2.4276
Call options are available for a premium of CHF0.002 per GBP
Exercise price: GBP/CHF = 2,4416
The forecasted spot rate GBP/CHF in 30 days follows:
Future spot rate
Probability
GBP/CHF = 2.4400
20%
GBP/CHF = 2.4416
50%
GBP/CHF = 2.4476
30%
Hedging Exposure Payables
[1] Long position in a forward contract on GBP 500,000.
The 30 days forward rate is GBP/CHF = 2.4276

The CHF cost in 30 days: 500,000 * 2.4276 = CHF
1,213,800
Hedging Exposure Payables
[2] Call option Hedge on Payables
Exercise price: CHF2.4416/GBP
Pro Spot rate at T
Premium
Exe
rcis
e
Cost/EUR
Total Payment
0.2
GBP/CHF=2.4400 CHF0.002 per
GBP
No
GBP/CHF=2.4420 CHF1.221.000
0.5
GBP/CHF=2.4416 CHF0.002 per
GBP
No
GBP/CHF=2.4436 CHF1.221.800
0.3
GBP/CHF=2.4476 CHF0.002 per
GBP
Yes
GBP/CHF=2.4436 CHF1.221.800
Expected total payment at time=T:
Hedging Exposure Payables
[3] No Hedge
Pro
Spot rate at T
Total Payment
0.2
GBP/CHF=2.4400
CHF1.220.000
0.5
GBP/CHF=2.4416
CHF1.220.800
0.3
GBP/CHF=2.4476
CHF1.223.800
Expected total payment at time=T:
0.2*1.220.000 + 0.5*1.220.800 + 0,3*1.223.800 = CHF1.221.540
Conclusion: Long in position in a forward contract
Hedging Exposure Payables
Example 2:
Assume that Earns Corp (SEK) imported goods from Swizerland and needs
CHF500,000 90 days from now. It considers 3 hedging techniques:
(1) Long position in a forward contract on CHF500,000.
(2) Long position in call option on CHF500,000.
(3) No Hedge
Given information:
Forward rate: CHF/SEK =5.0194
Call options are available for a premium of SEK0.001 per CHF
Exercise price: CHF/SEK = 5.0260
The forecasted spot rate GBP/CHF in 90 days follows:
Future spot rate
Probability
CHF/SEK = 4,9860
30%
GBP/CHF = 5.0260
40%
GBP/CHF = 5.1976
30%
Hedging Exposure Receivables
[1] Forward Hedge on Receivables
Short a currency forward contract to sell the amount of receivables
foreign currency at a specific exchange rate.
Ex: Short position in a forward contract on CHF200,000. The 6-month
forward rate is CHF/USD=0.71
The USD receipt in 6 months: 200,000 * 0.71 = USD142,000
Hedging Exposure Receivables
[2] Put option hedge on receivables
Long in a currency put option to sell the amount of receivables in
foreign currency.
Put option contract as following:
- The size of contract: CHF200,000
- Premium: USD0.02 per CHF
- Exercise price: CHF/USD=0.72
Hedging Exposure Receivables
[2] Put option Hedge on Receivables
Receipt from put options based on currency forecast:
Pro Spot rate at T Premium
Exercise
Cost/EUR
0.3
CHF/USD=0.71 USD0.02 per
CHF
Yes
CHF/USD=0.70 USD140,000
0.4
CHF/USD=0.74 USD0.02 per
CHF
No
CHF/USD=0.72 USD144,000
0.3
CHF/USD=0.76 USD0.02 per
CHF
No
CHF/USD=0.74 USD148,000
Expected total payment at time=T:
0.3*140,000 + 0.4*144,000 + 0,3*148,000 = USD144,000
Total Receipt
Hedging Exposure Receivables
[3] No Hedge
Pro
Spot rate at T
Total Payment
0.3
CHF/USD=0.71
USD142,000
0.4
CHF/USD=0.74
USD148,000
0.3
CHF/USD=0.76
USD152,000
Expected total payment at time=T:
0.3*142,000 + 0.4*148,000 + 0.3*152,000 = USD147,400
Conclusion: No Hedge
Hedging Exposure Receivables
[4] Comparison of Techniques to Hedge Receivables
The receipt from the forward hedge can be determined with certainty
The currency put option hedge has different outcomes depending on
the future spot rate at the time receivables are due
(1) Select optimal hedging technique
(2) Choose optimal hedge versus no hedge for receivables
Hedging Exposure Receivables
Example 1:
Assume that Lamas Corp (CHF) exported goods to UK and receives
GBP500,000 30 days from now. It considers 3 hedging techniques:
(1) Short position in a forward contract on GBP500,000.
(2) Long position in put option on GBP500,000.
(3) No Hedge
Given information:
Forward rate: GBP/CHF =2.4276
Put options are available for a premium of CHF0.002 per GBP
Exercise price: GBP/CHF = 2,4416
The forecasted spot rate GBP/CHF in 30 days follows:
Future spot rate
Probability
GBP/CHF = 2.4400
20%
GBP/CHF = 2.4416
50%
GBP/CHF = 2.4476
30%
Hedging Exposure Receivables
[1] Short position in a forward contract on GBP 500,000.
The 30 days forward rate is GBP/CHF = 2.4276

The CHF receipt in 30 days: 500,000 * 2.4276 = CHF
1,213,800
Hedging Exposure Receivables
[2] Put option Hedge on Receivables
Exercise price: CHF2.4416/GBP
Pro Spot rate at T
Premium
Exe
rcis
e
Cost/EUR
Total Payment
0.2
GBP/CHF=2.4400 CHF0.002 per
GBP
Yes
GBP/CHF=2.4396 CHF1.219.800
0.5
GBP/CHF=2.4416 CHF0.002 per
GBP
No
GBP/CHF=2.4396 CHF1.219.800
0.3
GBP/CHF=2.4476 CHF0.002 per
GBP
No
GBP/CHF=2.4456 CHF1.222.800
Expected total payment at time=T:
Hedging Exposure Receivables
[3] No Hedge
Pro
Spot rate at T
Total Payment
0.2
GBP/CHF=2.4400
CHF1.220.000
0.5
GBP/CHF=2.4416
CHF1.220.800
0.3
GBP/CHF=2.4476
CHF1.223.800
Expected total payment at time=T:
0.2*1.220.000 + 0.5*1.220.800 + 0,3*1.223.800 = CHF1.221.540
Conclusion: No Hedge
Hedging Exposure Receivables
Example 2:
Assume that Tucson Corp (USD) exported goods to New Zealand and receives
NZD250,000 90 days from now. It considers 3 hedging techniques:
(1) Short position in a forward contract on NZD250,000.
(2) Long position in put option on NZD250,000.
(3) No Hedge
Given information:
Forward rate: NZD/USD =0.4
Put options are available for a premium of USD0.03 per NZD
Exercise price: NZD/USD =0.49
The forecasted spot rate NZD/USD in 90 days follows:
Future spot rate
Probability
NZD/USD =0.44
30%
NZD/USD =0.4
50%
NZD/USD =0.38
20%