Pricing Currency Options on the Euro A U.S.-based firm wishing to buy A British
ID: 2820847 • Letter: P
Question
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 $
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
%
Explanation / Answer
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%
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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