the question is shown below in pictures

Let do , and d32 generate two Wiener processes for which J d31 = (1Vt and So d52 = 32Vt, where 1 and (2 are standard normally distributed, independent random variables. Suppose that Microsoft stock and Apple stock have prices S, (t) and S2 (t), respectively. Also suppose that S1(0) = $181.40 and S2 (0) = $318.25, the returns are M1 = 0.1744 and M20.0624, and the volatilities are 61 = 0.34 and 62 = 0.46 respectively. It turns out the coefficient of correlation between the daily returns of the two stocks is p = 0.412. (a) (4 points) Write the Ito processes for Microsoft and Apple stock prices in terms of the Wiener processes dZ, and dZ2 respectively. Also write the Ito processes for each stock's return. (b) (6 points) The processes, dZ, and dZ2 are clearly not uncorrelated, and unlikely to be independent since p = 0.412. Given that you know this, find a formula for dZ, in terms of d31 and dZ2 in terms of d(1 and d32 so that the processes for the returns that you found in part (a) have the observed correlation. (c) (2 points) Given the processes you found in part (b), find the correlation between the daily price change in two stock prices