Conditions and assumptions
One period, two outcomes (states) S = current stock price u = 1 + return if stock goes up d = 1 + return if stock goes down r = risk-free rate
h
Cu Su
Cd Sd
,
hu
Cu2 Su 2
Cud Sud
,
hd
Cud Sud
Cd2 Sd2
THE TWO-PERIOD BINOMIAL MODEL (CONTINUED)
An Illustrative Example
Su2 = 100(1.25)2 = 156.25 Sud = 100(1.25)(.80) = 100 Sd2 = 100(.80)2 = 64 The call option prices are as follows
Value of investment: V = 556($100) 1,000($14.02) = $41,580. (This is how much money you must put up.)
Stock goes to $125
Value of investment = 556($125) - 1,000($25) = $44,500
V(1+r) = Vu (or Vd)
Substituting for V and Vu
(hS - C)(1+r) = hSu - Cu
THE ONE-PERIOD BINOMIAL MODEL (CONTINUED)