Question

Merv Corp stock is currently trading at $105. The stock price a year from now will be either $175 or $70 with equal probabilities. The interest rate at which investors invest in riskless assets is 6%. Using the binomial OPM, the value of a put option with an exercise price of $150 and an expiration date 1 year from now should be worth __________ today. (Round intermediate calculation to 2 decimal places)

• $44.24

• $43.00

• $45.67

• $45.06

Answer 1

p0=	Put price	=	[∏p1+ + (1-∏)p1- ]/ (1+r)
	Where
∏=	Risk neutral probability	=	(1+r-d)/(u-d)
r=	risk free interest rate	=	6%
u=	up factor	=	1.66667
d=	Down factor	=	0.66667
∏=	Risk neutral probability	=	(1+0.06-0.6667)/(1.6667-0.6667)
		=	0.3933
	1- ∏=	=	0.6067
S0 =	Stock price today	=	105
S1+ =	= 105 × 1.6667	=	175.00
S1- =	= 105 × 0.6667	=	70.00
X =	Exercise price	=	150.00
p1+ =	= Max(0, X - S1+)
	= Max(0, 150 - 175)	=	0
p1- =	= Max(0, X - S1-)
	= Max(0, 150 - 70)	=	80.0000
p0=	(0.3933 × 0 + 0.6067 × 80) /(1+0.06 )	=	45.79

Answer is:

45.67