Hull_05_14 |
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Hull Example 5.6 |
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Forward/Futures contracts on currencies |
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"Home" currency |
1.0 |
CHF |
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Spot rate (foreign/home) |
0.65 |
USD |
per one unit of |
CHF |
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Spot rate (home/foreign) |
1.54 |
CHF |
per one unit of |
USD |
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Risk-free rate ("home") |
3.00% |
CHF |
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Risk-free rate ("foreign") |
8.00% |
USD |
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Time (T) |
0.167 |
years |
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No-arbitrate |
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Scenario 1: |
Invest at Home |
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Scenario 2: |
Invest in Foreign & "take a round trip" |
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i.e., Convert at spot (home to foreign), invest @ foreign rate, convert back at forward rate (FF to GBP) |
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Scenario #1 |
Invest in CHF |
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Start: |
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End: |
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1.00 |
CHF |
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1.01 |
CHF |
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Scenario #2: |
Round trip invest in USD |
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Start: |
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End: |
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0.65 |
USD |
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0.66 |
USD |
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0.655 |
Convert forward |
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1.01 |
CHF |
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Direct use of Cost of Carry: |
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0.6554 |
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Two scenarios illustrate arbitrage if forward is mis-priced |
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What if forward is mis-priced @ |
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0.660 |
USD |
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Borrow |
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1,000 |
USD |
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Convert |
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1,538 |
CHF |
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Invest |
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3.00% |
CHF |
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Grows to: |
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1,546 |
CHF |
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Convert with forward |
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1,020 |
USD |
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Payoff Loan |
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1,013 |
USD |
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Riskless profit |
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7 |
USD |
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What if forward is mis-priced @ |
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0.660 |
USD |
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Borrow |
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1,000 |
CHF |
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Covert |
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650 |
USD |
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Invest |
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8.00% |
USD |
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Grows to: |
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659 |
USD |
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Loan Due |
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1,005 |
CHF |
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Loan Due (convert with forward) |
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663 |
USD |
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Riskless profit |
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(5) |
USD |
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Hull_05_14_homeUSD |
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Hull Example 5.6 |
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Forward/Futures contracts on currencies |
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| |
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"Home" currency |
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1.0 |
USD |
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Spot rate (foreign/home) |
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0.8426 |
AUD |
per one unit of |
USD |
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Spot rate (home/foreign) |
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1.1868 |
USD |
per one unit of |
AUD |
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Risk-free rate ("home") |
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8.00% |
USD |
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Risk-free rate ("foreign") |
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3.00% |
AUD |
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Time (T) |
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0.167 |
years |
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No-arbitrate |
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Scenario 1: |
Invest at Home |
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|
|
|
|
|
| |
Scenario 2: |
Invest in Foreign & "take a round trip" |
|
|
|
|
|
|
| |
i.e., Convert at spot (home to foreign), invest @ foreign rate, convert back at forward rate (FF to GBP) |
|
|
|
|
|
|
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| |
|
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Scenario #1 |
Invest in USD |
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Start: |
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End: |
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1.00 |
USD |
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1.01 |
USD |
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Scenario #2: |
Round trip invest in AUD |
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Start: |
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End: |
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0.84 |
AUD |
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0.85 |
AUD |
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0.836 |
Convert forward |
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1.01 |
USD |
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Direct use of Cost of Carry: |
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0.8356 |
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Two scenarios illustrate arbitrage if forward is mis-priced |
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|
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What if forward is mis-priced @ |
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0.660 |
AUD |
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Borrow |
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1,000 |
AUD |
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Convert |
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1,187 |
USD |
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Invest |
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8.00% |
USD |
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Grows to: |
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1,203 |
USD |
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Convert with forward |
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794 |
AUD |
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Payoff Loan |
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1,005 |
AUD |
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Riskless profit |
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(211) |
AUD |
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What if forward is mis-priced @ |
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0.660 |
AUD |
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Borrow |
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1,000 |
USD |
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Covert |
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843 |
AUD |
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Invest |
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3.00% |
AUD |
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Grows to: |
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847 |
USD |
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Loan Due |
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1,013 |
USD |
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Loan Due (convert with forward) |
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669 |
AUD |
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Riskless profit |
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178 |
AUD |
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Hull_05_14_homeAUD |
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Hull Example 5.6 |
|
|
|
|
|
|
|
| |
Forward/Futures contracts on currencies |
|
|
|
|
|
|
|
| |
|
|
|
|
|
|
|
|
| |
"Home" currency |
|
|
1.0 |
AUD |
|
|
|
| |
Spot rate (foreign/home) |
|
|
1.187 |
USD |
per one unit of |
AUD |
|
| |
Spot rate (home/foreign) |
|
|
0.8426 |
AUD |
per one unit of |
USD |
|
| |
Risk-free rate ("home") |
|
|
3.00% |
AUD |
|
|
|
| |
Risk-free rate ("foreign") |
|
|
8.00% |
USD |
|
|
|
| |
Time (T) |
|
|
0.167 |
years |
|
|
|
| |
|
|
|
|
|
|
|
|
| |
No-arbitrate |
|
|
|
|
|
|
|
| |
Scenario 1: |
Invest at Home |
|
|
|
|
|
|
| |
Scenario 2: |
Invest in Foreign & "take a round trip" |
|
|
|
|
|
|
| |
i.e., Convert at spot (home to foreign), invest @ foreign rate, convert back at forward rate (FF to GBP) |
|
|
|
|
|
|
|
| |
|
|
|
|
|
|
|
|
| |
Scenario #1 |
Invest in AUD |
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Start: |
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End: |
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1.00 |
AUD |
|
1.01 |
AUD |
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|
| |
|
|
|
|
|
|
|
|
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Scenario #2: |
Round trip invest in USD |
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Start: |
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End: |
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1.19 |
USD |
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1.20 |
USD |
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1.197 |
Convert forward |
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1.01 |
AUD |
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Direct use of Cost of Carry: |
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1.1967 |
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|
|
| |
|
|
|
|
|
|
|
|
| |
Two scenarios illustrate arbitrage if forward is mis-priced |
|
|
|
|
|
|
|
| |
|
|
|
|
|
|
|
|
| |
What if forward is mis-priced @ |
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|
0.660 |
USD |
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|
| |
Borrow |
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1,000 |
USD |
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Convert |
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843 |
AUD |
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Invest |
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3.00% |
AUD |
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Grows to: |
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847 |
AUD |
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Convert with forward |
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559 |
USD |
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Payoff Loan |
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|
1,013 |
USD |
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Riskless profit |
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(455) |
USD |
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What if forward is mis-priced @ |
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0.660 |
USD |
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Borrow |
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|
1,000 |
AUD |
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Covert |
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|
1,187 |
USD |
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Invest |
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8.00% |
USD |
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Grows to: |
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1,203 |
USD |
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Loan Due |
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|
1,005 |
AUD |
|
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|
| |
Loan Due (convert with forward) |
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|
663 |
USD |
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Riskless profit |
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539 |
USD |
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