Problem 7.15 U.S. Dollar/British Pound- How much more would a call option on pounds be if the maturity was doubled from 90 to 180 days? What percentage increase is this for twice the length of maturity?

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%.