Question

Rockford stock is trading at $20/share and can either increase to $26 or decrease to $18 over the course of one year. In a one-period binomial option model, given an interest rate of 5%, what is the price of an at-the money call on Rockford stock expiring in one year? (Use annual compounding.) Multiple Choice

$2.14

$2.88

$3.00

$2.50

Answer 1

c0=	Call price	=	[∏c1+ + (1-∏)c1- ]/ (1+r)
p0=	Put price	=	[∏p1+ + (1-∏)p1- ]/ (1+r)
	Where
∏=	Risk neutral probability	=	(1+r-d)/(u-d)
r=	risk free interest rate	=	5.0000%
u=	up factor	=	1.3000
d=	Down factor	=	0.9000
∏=	Risk neutral probability	=	(1+0.05-0.9)/(1.3-0.9)
		=	0.3750
	1- ∏=	=	0.6250
S0 =	Stock price today	=	20
S1+ =	= 20*1.3	=	26
S1- =	= 20*0.9	=	18
X =	Exercise price	=	20
c1+ =	= Max(0, S1+ - X)
	= Max(0, 26 - 20)	=	6
c1- =	= Max(0, S1- - X)
	= Max(0, 18 - 20)	=	0
c0=	(0.375*6 + 0.625*0) /(1+0.05 )	=	2.14

Answer is:

2.14

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