Question

What is the price of a six-month European call option on a stock expected to pay a dividend of $1.50 in two months when the stock price is $50, the strike price is $50, the risk-free interest rate is 5% per annum and the volatility is 30% p.a.? Show all working.

Answer 1

	Option price=	SN(d1) - Xe-r t N(d2)
	d1 =	[ ln(S/X) + ( r+ v2 /2) t ]/ v t0.5
	d2 =	d1 - v t0.5
	Where
	Current stock price=	50
	Less: present value of dividend
	Dividend	1.5
	Paid in (months)	2
	Present value of dividend	-1.51
S=	Stock price adjusted	48.49	48.49
X=	Exercise price=		50
r=	Risk free interest rate=		5.00%
v=	Standard devriation=		30%
t=	time to expiration (in years) =		0.5000
d1 =	[ ln(48.4874477716888/50) + ( 0.05 + (0.3^2)/2 ) *0.5] / [0.3*0.5^ 0.5 ]
d1 =	[ -0.030718 + 0.0475 ] /0.212132
d1 =	0.079111
d2 =	0.079111 - 0.3 * 0.5^0.5
	-0.133021
N(d1) =	N( 0.079111 ) =	0.53153
N(d2) =	N( -0.133021 ) =	0.44709
Option price=	48.4874477716888*0.531527781937932-50*(e^-0.05*0.5) *0.44708832198879
	3.97

Answer is 3.97

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