Question

Consider a stock currently worth $80 (S = 80) that can go up or down by 25 percent per period. The exercise price is $80 (X = $80) and the risk-free rate is 5 percent (r = .05). The option will expire at the end of the third period (t = 3). You try to find a theoretically fair value of the put option using a three-period binomial option pricing model. Answer the following questions.

t = 0		t = 1		t = 2
				Suu = (c)
		Su = (a)
S = $80				Sud = (d)
		Sd = (b)
				Sdd = (e)
				Puu = (f)
		Pu = (i)
P = (k)				Pud = (g)
		Pd = (j)
				Pdd = (h)

a) What are three possible stock prices at time t = 2 (c, d, and e)?

b) Compute three values at time t = 2 of European put options. (P_uu, P_ud, and P_dd)

c) Compute two values at time t = 1 of a European put options (P_u and P_d).

d) Find the theoretical fair value of the put option today (P).

e) Compute the riskless hedge ratio (h).

f) Construct a riskless hedge position with stocks and 1,000 put options at the theoretically fair value using the riskless hedge ratio (h).