Question

Consider a stock that provides an expected return of 15% per annum and has a volatility of 40% per annum.  Suppose that a time interval of .01 year is used for the binomial model, Calculate u, d, and p.  Show that they give correct values for the expected return and the variance of return during the time interval.  Suppose the stock price starts at $50.  What are the possible stock prices at the end of .03 year?  What is the probability of each one occurring?

Answer 1

      
Expected return -        0.15
Volatility (s)       0.40
time interval       0.01
S - Stock price today      
      
u:- The factor by which the price rises (assuming it rises).      
d:- The factor by which the price falls (assuming it falls).      

u= e ^ s sqrt t
u	e ^ 0.40sqrt .01
	e = 2.7182
	0.04
u =	0.108728
d = 1/u
d	9.197263
Probability of up move (pu)	e^rt - d	-9.17959	1.010019
			u-d	-9.08853
(here, assuming risk free rate (r )as - 10yr treasury bill rate - 0.65%
Probability of down move (pd)	1-pu	-0.01002