Question

You are attempting to value a call option with an exercise price of $109 and one year to expiration. The underlying stock pays no dividends, its current price is $109, and you believe it has a 50% chance of increasing to $130 and a 50% chance of decreasing to $88. The risk-free rate of interest is 12%. Calculate the call option’s value using the two-state stock price model.

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	=	12.0000%
u=	up factor	=	1.1927
d=	Down factor	=	0.8073
∏=	Risk neutral probability	=
		=	0.5000
	1- ∏=	=	0.5000
S0 =	Stock price today	=	109
S1+ =	= 109*1.1927	=	130
S1- =	= 109*0.8073	=	88
X =	Exercise price	=	75
c1+ =	= Max(0, S1+ - X)
	= Max(0, 130 - 75)	=	55
c1- =	= Max(0, S1- - X)
	= Max(0, 88 - 75)	=	13
c0=	(0.5*55 + 0.5*13) /(1+0.12 )	=	30.36

Answer is:

30.36