Question

The current price of a non-dividend paying stock is $50. Use a two-step tree to value a American put option on the stock with a strike price of $50 that expires in 12 months. Each step is 6 months, the risk free rate is 5% per annum, and the volatility is 50%. What is the value of the option according to the two-step binomial model. Please enter your answer rounded to two decimal places (and no dollar sign).

Answer 1

S	50
X	50
u	1.4241
d	0.7021
p	0.45
(1-p)	0.55
r	1.0253

Period 0			Period 1			Period 2
					uuS	101.40
					P++	0.00
		uS	71.205
		P+	0.00
50					uds	49.99
7.36					P+-	0.00
		dS	35.105
		P-	13.66
					ddS	24.65
					P--	25.35

Value of put at "node dS" can be calculated using the formulae
P- = (p * P+-) + ((1-p) * +--))/(1+r)

P- = [(0.45*0) + (0.55*25.35)] / 1.0253 = 13.66

similarly P = 0.45*0 + 0.55*13.66 / 1.0253 = 7.36