Question

A stock is currently trading for $100 each month the stock when I the increase in price by a factor of U equals 1.05 or fall by a factor of D equals 0.90 the risk free rate of interest per month is 0.1668% in simple terms and investment of a dollar at the risk free rate returned 1.01668 after 1 month what is the price of a 100 strike to month European put option?

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	=	0.1668%
u=	up factor	=	1.0500
d=	Down factor	=	0.9000
∏=	Risk neutral probability	=	(1+0.00167-0.9)/(1.05-0.9)
		=	0.6778
	1- ∏=	=	0.3222
S0 =	Stock price today	=	100
S1+ =	= 100*1.05	=	105
S1- =	= 100*0.9	=	90
X =	Exercise price	=	100
c1+ =	= Max(0, S1+ - X)
	= Max(0, 105 - 100)	=	5
c1- =	= Max(0, S1- - X)
	= Max(0, 90 - 100)	=	0
c0=	(0.6778*5 + 0.3222*0) /(1+0.00167 )	=	3.38
p1+ =	= Max(0, X - S1+)
	= Max(0, 100 - 105)	=	0
p1- =	= Max(0, X - S1-)
	= Max(0, 100 - 90)	=	10
p0=	(0.6778*0 + 0.3222*10) /(1+0.001668 )	=	3.22

Put option price is $3.22

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