Question

Current stock price is $50; volatility is 40%; risk-free rate is 5%. We have an American style put option expires in 6 months. Its strike price is the maximum price over the life of the option; this means: its payoff in 6 months is max(0, S_max – S_T). No dividend payments during the 6 months. Use a 2-step CRR binomial model to price this option.

Answer 1

T = 6 months; n = 2 steps;

t = T / n = 6 months / 2 = 3 months = 3/12 = 0.25 year

d = 1/u = 0.8187

p = risk neutral probability of an up move

Strock price tree

Path	S0	S1	S2	Smax	Payoff = max (0, Smax - S2)	Joint probability	Joint probability value	Probability x payoff
A - B - D	50.00	u x S0 = 61.07	u x S1 = 74.59	74.59	-	p x p	0.23	-
A - B - E	50.00	u x S0 = 61.07	d x S1 = 50.00	61.07	11.07	p x (1 - p)	0.25	2.76
A - C - E	50.00	d x S0 = 40.94	u x S1 = 50.00	50.00	-	(1 - p) x p	0.25	-
A - C - F	50.00	d x S0 = 40.94	d x S1 = 33.52	50.00	16.48	(1 - p) x (1 - p)	0.27	4.43
Total								7.20

Hence, price of the put option = PV of probability weighted payoff = Probability weighted payoff x e-rT

= 7.20 x e-0.05 x 6/12 = $  7.02