Question

You buy a call on Pfizer (PFE) with a strike price of $35. Pfizer's current price is $37.82, has a u of 1.08, and a d of 0.92. The risk free rate is 1% per period. Use a one period binomial model. If Pfizer's price goes up, what is your holding period return? Note: Answer in decimal form, report four decimal places.

Answer 1

S	37.82
X	35
u	1.08
d	0.92
p	0.56
(1-p)	0.44
r	1.01

p = r-d / u-d

p = 1.01-0.92 / 1.08-0.92 = 0.56

	Period 0			Period 1
			uS	40.85
			C+	5.85
S	37.82
C	3.26
			dS	34.7944
			C-	0.00

C+ = MAX(40.85-35),0 = 5.85

C- = MAX(34.79-35),0 = 0

C= (p*C+) + (1-p)*C- / (1+r)

C = (0.56*5.85) + (0.44*0) / 1.01 = 3.26

Price of call option today = 3.26

we will buy this option at 3.26 and if the price goes up the value of the call option will be 5.85

Holding Period Return = (5.85-3.26) / 3.26 = 0.7955 or 79.5556%