Problem 7.14 Euro/Japanese Yen. A French firm is expection to recieve JPY10.4 million in 90 days as a result of an export sale to Japanese semiconductor firm. What will it cost, in total to purchase an options to sell the YEN at EURO 0.0072/JPY?

Pricing Currency Options on the Euro/Yen Crossrate

A Japanese firm wishing to buy

A European firm wishing to buy

or sell euros (the foreign currency)

or sell yen (the foreign currency)

Variable

Value

Variable

Value

Spot rate (domestic/foreign)

S0

JPY 133.89

S0

0.01

Strike rate (domestic/foreign)

X

JPY 136.00

X

0.01

Domestic interest rate (% p.a.)

rd

0.09%

rd

2.19%

Foreign interest rate (% p.a.)

rf

2.19%

rf

0.09%

Time (years, 365 days)

T

0.247

T

0.247

Days equivalent

90

90

Volatility (% p.a.)

s

10.00%

s

10.00%

Call option premium (per unit fc)

c

JPY 1.50

c

0.00

Put option premium (per unit fc)

p

JPY 4.30

p

0.00

(European pricing)

Call option premium (%)

c

1.12%

c

1.30%

Put option premium (%)

p

3.21%

p

2.90%

A European-based firm like Legrand (France) would need to purchase a put option on the Japanese yen. The company wishes a strike rate of 0.0072 euro for each yen sold (the strike rate) and a 90-day maturity. Note that the "Time" must be entered as the fraction of a 365 day year, in this case, 90/365 = 0.247.

Put option premium (euro/JPY)

0.00

Notional principal (JPY)

JPY 10,400,000

Total cost (euro)

2,167.90

Problem 7.15 U.S. Dollar/British Pound

Pricing Currency Options on the British pound

A U.S.-based firm wishing to buy

A British firm wishing to buy

or sell pounds (the foreign currency)

or sell dollars (the foreign currency)

Variable

Value

Variable

Value

Spot rate (domestic/foreign)

S0

$1.87

S0

0.5355

Strike rate (domestic/foreign)

X

$1.80

X

0.5556

Domestic interest rate (% p.a.)

rd

1.45%

rd

4.53%

Foreign interest rate (% p.a.)

rf

4.53%

rf

1.45%

Time (years, 365 days)

T

0.493

T

0.493

Days equivalent

180

180

Volatility (% p.a.)

s

9.40%

s

9.40%

Call option premium (per unit fc)

c

$0.07

c

0.0091

Put option premium (per unit fc)

p

$0.03

p

0.0207

(European pricing)

Call option premium (%)

c

3.73%

c

1.70%

Put option premium (%)

p

1.64%

p

3.87%

Call option premiums for a U.S.-based firm buying call options on the British pound:

180-day maturity ($/pound)

$0.07

90-day maturity ($/pound)

$0.07

Difference ($/pound)

$0.00

The maturity doubled while the option premium rose only about 4%.

Problem 7.16 Euro/British Pound

Pricing Currency Options on the British pound/Euro Crossrate

A European firm wishing to buy

A British firm wishing to buy

or sell pounds (the foreign currency)

or sell euros (the foreign currency)

Variable

Value

Variable

Value

Spot rate (domestic/foreign)

S0

1.47

S0

0.6789

Strike rate (domestic/foreign)

X

1.50

X

0.6667

Domestic interest rate (% p.a.)

rd

4.00%

rd

4.16%

Foreign interest rate (% p.a.)

rf

4.16%

rf

4.00%

Time (years, 365 days)

T

0.247

T

0.247

Days equivalent

90

90

Volatility (% p.a.)

s

11.40%

s

11.40%

Call option premium (per unit fc)

c

0.02

c

0.0220

Put option premium (per unit fc)

p

0.05

p

0.0097

(European pricing)

Call option premium (%)

c

1.45%

c

3.24%

Put option premium (%)

p

3.30%

p

1.42%

When the euro's interest rate rises from 2.072% to 4.000%, the call option premium on British pounds rises:

Call option on pounds when euro interest is 4.000%

0.02

Call option on pounds when euro interest is 2.072%

0.02

Change, an increase in the premium

0.02