This thesis work is concerned with identifying and trading sparse mean reverting portfolios based on observing random, multidimensional asset price time series. Mean reverting portfolios play a central role in convergence type of trading, as taking a position when being away from the mean and closing the position when returning the mean, one can obtain a considerable amount of profit (e.g. buying below the mean and selling when returning to the mean).
Since mean reverting stochastic processes can be modeled by the so-called Ornstein-Uhlenbeck stochastic differential equations, developing fast algorithms to identify OU processes as a linear combination of the asset prices has become one of the central research area of algorithmic trading. The complexity of the problem is greatly increased by the need for identifying sparse portfolios with a given cardinality constraint (i.e. only a subset of the assets are used in a portfolio), which casts the problem as a ,,subset selection problem'' proven to be NP hard. Sparse portfolios are important, when one wants to minimize the transaction costs of trading with the assets.
In the thesis, I review some basic approaches of describing and identifying mean reverting processes. My contribution lies in developing stochastic models for trading with mean reverting portfolios in the presence of bid-ask spread, or trading on the book.
I have developed these random models and included them into a comprehensive software package for detailed performance analysis. The method has been tried out on historical data of S&P 500 and swap rates.
The numerical results have clearly proven that mean reverting trading as a new form of low and high frequency algotrading is viable in the presence of secondary effects on daily as well as on intraday price series.