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 $

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	Â£	0.5355
Forward rate (domestic/foreign)	F0	$	1.8533			F0	Â£	0.5396
Strike rate (domestic/foreign)	X	$	1.8			X	Â£	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	Â£	0.0041
Put option premium (per unit fc)	p	$	0.0138			p	Â£	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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