| This dissertation consists of three major parts that are closely interrelated. The first part of this dissertation creates a procedure for working with random, lognormally distributed process with autocorrelated increments that have predetermined volatility and autocorrelation. This is done by replacing the original discrete time process with a stochastic process having infinitesimally small time increments. Using this process an analytic option pricing model is derived, capable of providing a solution for a value of a derivatives on such an asset. Initially, a framework of random, normally distributed, process x is created, such that lnS = x, with autocorrelated increments that have volatility and autocorrelation. The results obtained from the model show that presence of return autocorrelation affects the volatility of an asset price, making it a function of correlation coefficient and time to expiration. In the final part of this dissertation a Monte Carlo procedure capable of pricing options in the presence of autocorrelation in asset returns is created and the analytical model is tested using both Monte Carlo procedure and Empirical testing against market data. |
