In the Roll model, we define efficient price by mt , and we assume mt = mt1+ut , where ut are i.i.d. zero-mean random variables (ut N(0, 2 u )). The bid-ask spread is at bt = 2c, a constant. At time t, there is a trade at transaction price pt , which may be expressed as: pt = mt + qtc where qt is a trade direction indicator set to +1 if the customer is buying and -1 if the customer is selling. We also assume that buys and sells are equally likely, serially independent (a buy this period does not change the probability of a buy next period), and that agents buy or sell independently of ut (a customer buy or sell is unrelated to the evolution of mt). By definition we have pt = (qtqt1)c+ut , and we can write the variance and autocovariance as: 0 V ar(pt) = 2c 2 + 2 u . 1 Cov(pt1, pt) = c 2 . For this assignment, you need to do the following (please DO NOT use logarithmic return): (a) Please derive the value ` , ` 2? (b) Use the Roll model to estimate the bid-ask spread and fundamental volatility of GE stock during the period from September 26, 2007 to September 26, 2017. Please use the same dataset for the last two problems (GE 20072017.csv).