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
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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

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