| The field of financial risk management has evolved significantly in recent decades, as quantitative analysts have attempted to devise models that accurately characterize the uncertainty of future financial portfolio returns. To quantify these uncertainties, we make use of a sequential Bayesian filtering method, which is naturally suited to the task of tracking and predicting probability distributions of financial portfolio values on a daily basis. Specifically, we implement a particle filtering technique, called the bootstrap filter, which utilizes the clever notion of sequential importance resampling (SIR).; We focus specifically on a simple non-linear portfolio that solely contains a single European-style call option. Two state space models are devised to track and predict the dynamics of this simple portfolio, utilizing the famous Black-Scholes option pricing model (BSOPM) and the GARCH family of deterministic volatility models. We pass these two models through the bootstrap filter and test their predictive performance relative to two "control" models, namely, the persistence scenario and the standard BSOPM with constant volatility. Upon analyzing data for four authentic call options, it is discovered that the bootstrap filter yields predictive value distributions that exhibit much greater accuracy and precision than our two control models. These predictive value distributions tell the "full story" of an option holder's financial risk, and they facilitate the estimation of benchmark risk measures such as value-at-risk (VaR). (Abstract shortened by UMI.)... |
