Advanced Finance

s Consider the following simple model for stock prices: P = P1+12 1 IID +1 With probability (buyer initiated) { -1 With probability 7 (seller initiated) Here, P is the fundamental value of the security, and s is the bid-ask spread. a) Assume that P = P* is fixed through time. Derive expressions for the variance, autocovariance, and autocorrelation of successive stock price changes. b) Now assume Pit is serially uncorrelated, and independent of It, and has increments with variance expressed as o (AP*). Derive a new set of expressions for the variance, autocovariance, and auto- correlation of successive stock price changes. c) What is this effect known as? Explain whether (and why) this might lead you to erroneous conclusions when estimating whether stock prices are weak-form efficient. s Consider the following simple model for stock prices: P = P1+12 1 IID +1 With probability (buyer initiated) { -1 With probability 7 (seller initiated) Here, P is the fundamental value of the security, and s is the bid-ask spread. a) Assume that P = P* is fixed through time. Derive expressions for the variance, autocovariance, and autocorrelation of successive stock price changes. b) Now assume Pit is serially uncorrelated, and independent of It, and has increments with variance expressed as o (AP*). Derive a new set of expressions for the variance, autocovariance, and auto- correlation of successive stock price changes. c) What is this effect known as? Explain whether (and why) this might lead you to erroneous conclusions when estimating whether stock prices are weak-form efficient