Question 4

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 second period (t = 2). You try to find a theoretically fair value of the call using a two-period binomial option pricing model. (Hint: See Ch 16 Teaching Notes and Excel Spreadsheet)

t = 0		t = 1		t = 2
				Suu = (c)
		Su = (a)
S = $80				Sud = (d)
		Sd = (b)
				Sdd = (e)
				Cuu = (f)
		Cu = (i)
C = (k)				Cud = (g)
		Cd = (j)
				Cdd = (h)

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

Compute three values at expiration (t = 2) of a European call option ((f), (g), (h)).

Compute two values at time t = 1 of European call options ((i), (j)).

Find the theoretical fair value of the call option today.

Compare the call price computed in #1 part (6). Which price is higher? Why is that price higher?