Consider the geometric SDE:
dSt = μStdt + σStdWt,
where St is assumed to represent an equity index. The current value of the index is
S0 = 940
It is known that the annual percentage volatility is 0.15. The risk-free interest rate is constant at 5%. Also, as is the case in practice, the effect of dividends is eliminated in calculating this index. Your interest is confined to an 8-day period. You do not see any harm in dividing this horizon into four consecutive 2-day intervals denoted by ?.
(a) Use coin tossing to generate random errors that will approximate the term dWt, with
H = + 1,
T = - l,
(b) How can you make sure that the limiting mean and variance of the random process generated by coin tossing matches that of dWt, εs ? → 0?
(c) Generate three approximate random paths for St over this 8-day period.