Clustering financial time series for volatility modeling

One of the oldest pieces of wisdom is "don't put all your eggs in one basket". That is essentially what we would be doing if we invest all our fortune in stocks that are highly correlated with each other. Thus, modeling the correlation dynamics of financial time series, such as stock prices, has many important applications in portfolio construction and risk management.

However, in many cases correlations have been shown to change over time, hence various models have been proposed in the literature to describe the correlation dynamics. Unfortunately, many of these models require too many parameters, especially when considering a large number of stocks. The flexible dynamic conditional correlation (FDCC) model attempts to solve this issue by essentially grouping the stocks into different baskets and giving each basket its own set of parameters. However, the problem is the model assumes you know which stocks belong in which baskets. In this thesis we develop a systematic method to determine the number of baskets to use as well as how to allocate the stocks to baskets. We show through simulation that the method does well in identifying the baskets, and apply the method to real data, showing its performance. We also develop and apply a Bayesian approach to this same problem.

Furthermore, we propose an instantaneous measure of correlation that can be used in many volatility models, and in fact show that it outperforms the popular sample Pearson's correlation coefficient for small sample sizes, thus opening the door to applications in fields other than finance.