Question

10. 2 marks Suppose that S, is the price of a nondividend paying stock at time t. Sy follows a lognormal model. You are given So = $40, the stock's volatility o = 0.3 and the stock's continuously compounded expected growth rate a = 0.15 (a) (1 marks) What is the average price of the stock after 6 years? (b) 1 marks What is the expected value of the log-returns on the stock in a time interval of 4 years? 2 months?

Answer 1

Solution-

Formula of lognormal distribution is given as below-

1off_")+"su je 's u (11048-)]e="su-isu JO

(A) In first part, we have T = 6, u = 0.15, sigma = 0.3 and S0 = 40

So, Expected value of log(stock price) = Ln(40) + (0.15-0.3*0.3/2)*6

= 4.319

Thus, average stock price is = e^()

= 75.10

(B) After 4 years-

the average lognormal stock price is- Ln(40) + (0.15-0.3*0.3/2)*4

=4.109

After 4 years-

the average lognormal stock price is- Ln(40) + (0.15-0.3*0.3/2)*2/12

= 3.706