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Hull Example 5.6

Forward/Futures contracts on currencies

"Home" currency

1.0

CHF

Spot rate (foreign/home)

0.65

USD

per one unit of

CHF

Spot rate (home/foreign)

1.54

CHF

per one unit of

USD

Risk-free rate ("home")

3.00%

CHF

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 CHF

Start:

End:

1.00

CHF

1.01

CHF

Scenario #2:

Round trip invest in USD

Start:

End:

0.65

USD

0.66

USD

0.655

Convert forward

1.01

CHF

Direct use of Cost of Carry:

0.6554

Two scenarios illustrate arbitrage if forward is mis-priced

What if forward is mis-priced @

0.660

USD

Borrow

1,000

USD

Convert

1,538

CHF

Invest

3.00%

CHF

Grows to:

1,546

CHF

Convert with forward

1,020

USD

Payoff Loan

1,013

USD

Riskless profit

USD

What if forward is mis-priced @

0.660

USD

Borrow

1,000

CHF

Covert

650

USD

Invest

8.00%

USD

Grows to:

659

USD

Loan Due

1,005

CHF

Loan Due (convert with forward)

663

USD

Riskless profit

(5)

USD

Hull_05_14

Hull_05_14_homeUSD

Hull_05_14_homeAUD