Question

In: Finance

Pricing Currency Options on the Euro A U.S.-based firm wishing to buy A British firm wishing...

Pricing Currency Options on the Euro

A U.S.-based firm wishing to buy

A British firm wishing to buy

or sell euros (the foreign currency)

or sell dollars (the foreign currency)

Variable

Value

Variable

Value

Spot rate (domestic/foreign)

S0

$

1.8674

S0

£

0.5355

Forward rate (domestic/foreign)

F0

$

1.8533

F0

£

0.5396

Strike rate (domestic/foreign)

X

$

1.8000

X

£

0.5556

Domestic interest rate (% p.a.)

rd

1.453

%

rd

4.525

%

Foreign interest rate (% p.a.)

rf

4.525

%

rf

1.453

%

Time (years, 365 days)

T

0.247

T

0.247

Days equivalent

90.00

90.00

Volatility (% p.a.)

s

9.400

%

s

9.400

%

d1

0.64800

d1

-0.60212

d2

0.60128

d2

-0.64884

N(d1)

0.74151

N(d1)

0.27355

N(d2)

0.72617

N(d2)

0.25822

Call option premium (per unit fc)

c

$

0.0669

c

£

0.0041

Put option premium (per unit fc)

p

$

0.0138

p

£

0.0199

(European pricing)

Call option premium (%)

c

3.58

%

c

0.77

%

Put option premium (%)

p

0.74

%

p

3.72

%

PrintDone

U.S. Dollar/British Pound. Assuming the same initial values for the dollar/pound cross rate in this table

how much more would a call option on pounds be if the maturity increases from 90 to 180

days? What percentage increase is this for the length of maturity?

If the maturity increases from 90 to 180 days, a call option on pounds would be $

Solutions

Expert Solution

Pricing Currency Options on the Euro

A U.S.-based firm wishing to buy

A British firm wishing to buy

or sell pounds

or sell dollars

Variable

Value

Variable

Value

Spot rate (domestic/foreign)

S0

$1.8674

S0

£0.5355

Forward Rate (Domestic/Foreign)

F0

$1.8393

F0

£0.5437

Strike rate (domestic/foreign)

X

$1.8000

X

£0.5556

Domestic interest rate (% p.a.)

rd

1.453%

rd

4.525%

Foreign interest rate (% p.a.)

rf

4.525%

rf

1.453%

Time (years, 365 days)

T

0.493

T

0.493

Days equivalent

180.00

180.00

Volatility (% p.a.)

s

9.400%

s

9.400%

d1

0.3604

-0.36

d1

-0.29

0.29

d2

0.2944

-0.29

d2

-0.36

0.36

N(d1)

0.6407

0.36

N(d1)

0.38

0.62

N(d2)

0.6158

0.38

N(d2)

0.36

0.64

Call option premium (per unit fc)

c

$0.0696

c

£0.0091

Put option premium (per unit fc)

p

$0.0306

p

£0.0207

(European pricing)

Call option premium (%)

c

3.73%

c

1.70%

Put option premium (%)

p

1.64%

p

3.87%

Pricing Currency Options on the Euro

A U.S.-based firm wishing to buy

A British firm wishing to buy

or sell euros

or sell dollars

Variable

Value

Variable

Value

Spot rate (domestic/foreign)

S0

$

1.8674

S0

£

0.5355

Forward rate (domestic/foreign)

F0

$

1.8533

F0

£

0.5396

Strike rate (domestic/foreign)

X

$

1.8

X

£

0.5556

Domestic interest rate (% p.a.)

rd

1.453

%

rd

4.525

%

Foreign interest rate (% p.a.)

rf

4.525

%

rf

1.453

%

Time (years, 365 days)

T

0.247

T

0.247

Days equivalent

90

90

Volatility (% p.a.)

s

9.4

%

s

9.4

%

d1

0.648

d1

-0.60212

d2

0.60128

d2

-0.64884

N(d1)

0.74151

N(d1)

0.27355

N(d2)

0.72617

N(d2)

0.25822

Call option premium (per unit fc)

c

$

0.0669

c

£

0.0041

Put option premium (per unit fc)

p

$

0.0138

p

£

0.0199

(European pricing)

Call option premium (%)

c

3.58

%

c

0.77

%

Put option premium (%)

p

0.74

%

p

3.72

%

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

180-day maturity ($/pound)

0.06962

90-day maturity ($/pound)

0.06690

Difference

0.00272

The maturity doubled while the option premium rose by:00272/0.06962

3.90%


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