Topics in statistical finance

This thesis is divided into three parts. The first part investigates the presence of long term dependence in stock price data via a permutation test based on the correlation structure of the underlying stock prices. These tests reveal the short term nature of stock price dependence structure. The second part extends Ramprasath and Singh(2007)'s 'statistical options' to define a group of American type options based on robust estimators of location. The payoff functions of these path dependent options are based on a new set of stochastic processes which are defined using various robust estimators of location. The asymptotic distributional behavior of these new processes is ascertained which in turn is used in pricing the options. Markov Chain Monte Carlo (MCMC) methods were used to compute the prices of the statistical options. The third part explores a stock price model parameter estimation problem and interprets a growth rate parameter.