Machine Learning in Finance ISB presentation Claudio Moni 25/03/2010 Main applications Forecasting financial time series to identify trading opportunities. Estimating assets distributions, for trading and risk-management.

Derivatives pricing (small) Forecasting Difficult! High level of noise in financial time series. Suppose we want to estimate the equity market (annualised) return, which is of the order of 5%, with a +-5% confidence interval. How many years of daily data do we need, assuming historical volatility is 20%? 64 years!

Situation improves at high frequencies, as more data are available. Forecasting Difficult! High level of noise in financial time series. Suppose we want to estimate the equity market (annualised) return, which is of the order of 5%, with a +-5% confidence interval. How many years of daily data do we need, assuming historical

volatility is 20%? 64 years! Situation improves at high frequencies, as more data are available. Forecasting Difficult! High level of noise in financial time series. Suppose we want to estimate the equity market (annualised) return, which is of the order of 5%, with a +-5% confidence interval. How many years

of daily data do we need, assuming historical volatility is 20%? 64 years! Situation improves at high frequencies, as more data are available. Forecasting 2 Financial time series are non-stationary. Business cycles. Small disjuncts alternative. We can try to forecast an asset in isolation or a

set of interrelated assets all. Regression vs. Classification Financial forecasting is (usually) a regression problem. It is not enough to know that the expected return from a financial bet is positive to decide to make it and to decide how much to bet. It makes financial sense to invest more in the most profitable opportunities (see Kelly criterion)

This applies to a single strategy across time, or when the strategy is part of a portfolio. Technical Analysis Set of standard trading rules, mainly based on graphical patterns. No theoretical justification. Usually not thoroughly back-tested. Can become self-fulfilling prophecies. TA rules are often used as building blocks for

Machine Learning systems. TA Example: 2 crossing moving averages signalling the beginning of a trend. Empirical approach Instead of estimating the dynamics of the underlying processes and then construct strategies exploiting these dynamics, estimate the trading strategies directly.

Metric: trading performance, usually measured by the Sharpe ratio = mean/stdev. Robust with respect to process misspecification. Quantization Often useful to turn a continuous process into a discrete one. Subdivide R into a set of intervals, user defined or obtained by clustering. Limit case for returns: {Ret<0, Ret>=0}.

Reduces noise but throws away information. Allows Markov chains models to be used. Markov Chain Models Markov chain of order L: Pt 1 ( X (t ) xi ) P( X (t ) xi |{ X (t j ) xi ( j ) } j 1:L ). Probabilities can be estimated from historical frequencies: P X (t ) xi |{ X (t j ) xi ( j ) } j 1:L

P ( xi ( L ) , xi ( L 1) ,..., xi (1) , xi ) P ( xi ( L ) , xi ( L 1) ,..., xi (1) ) If L is large, the historical probabilities could be smoothed by K-NN or other methods. . Evolutionary approaches

The empirical strategy selection can be very naturally generated through evolution. Fitness: trading performance. Mutation: small parameter changes. Crossover: combination of parts of different strategies. For example (S1,S2) = [A*and(B,C), D*and(E,F)] -> (S3,S4) = [A*and(B,F), D*and(E,C)]. Neural Networks

Non-linear regression. The independent variables can be given by the underlying process (e.g. daily returns), or more commonly by a set of trading signals generated by user defined trading rules. Has been found to generate positive trading results, although not necessarily better than those obtained by using simpler models. News mining

News are part of the information available to human traders. Machines need to be able to use this source of information too. Natural Language Processing. News classification, Bag of words, SVM. Useful to human traders too, to filter incoming news by relevance. Reinforcement Learning

Can be used for game-theoretic problems. Optimal trade execution, to minimize market impact. Often large numbers of shares need to be bought (or sold), and the trade has to be split in a number of smaller trades since not enough shares are for sale at a given moment in time, or not a good price. Need to hide our intentions to prevent price from rising.

Estimating assets distributions Standard statistical techniques. Filtering. Dimensionality reduction. Filtering Hidden variable models. Example 1: Stochastic volatility models. Example 2: Factor models. Some factors may not be observable or observable only at

discrete times. E.g. Interest rates, inflation, GDP, ... Kalman Filter. Extended KF, Unscented KF. Particle Filtering. Dimensionality reduction Example: Interest rate curve. PCA: 3 factors typically explain 90%-95% of the variance. Derivatives pricing

Small area of application for ML since here we work with risk-neutral probabilities instead of historical ones. One main application: approximation of American style option by parametric functions of the state variables, through regression. Monte Carlo simulation, Local Least Squares. Questions?

References [AD09] Adamu, K. (2009) Modelling Financial Time Series using Grammatical Evolution. Talk given at the AMLCF 2009 conference, London. http://videolectures.net/amlcf09_london/ [AL10] Aldridge, I. (2010) High Frequency Trading. John Wiley and Sons. [AE01] Alexander, C. (2001) Market Models. John Wiley and Sons. [BB03] Boguslavsky, M. Boguslavskaya, E. (2003) Optimal Arbitrage Trading. Working paper. [BI06] Bishop, C. (2006) Pattern Recognition and Machine Learning. Springer. [CH09] Chang, E.P. (2009) Quantitative Trading. John Wiley and Sons.

[DH09a] Dhar, V. (2009) Prediction in Financial Markets: The Case for Small Disjuncts. Working paper. [DH09b] Dhar, V. (2009) Machine Learning Predictions in Financial Markets. Talk given at the AMLCF 2009 conference, London. http://videolectures.net/amlcf09_london/ [ES03] Eiben, A.E. Smith, J.E. (2003) Introduction to Evolutionary Computing. Springer [FV00] Franses, P.H. Van Dijk, D. (2000) Non-linear time series models in empirical finance. Cambridge.

[GI07] Gifford, B. (2007) No News is Bad News. The Trade, Issue 13, July-Sept. [HTF08] Hastie, T. Tibshirani, R. Friedman, J. (2008) The Elements of Statistical Learning. Second Edition.Springer. [IV09] Ibanez, A. Velasco, C. (2009) The Optimal Method to Price Bermudan Options by Simulation. Working paper. [JLG03] Javaheri, A. Laurent, D. Galli, A. (2003) Filtering in Finance. Willmot Magazine (Vol 5). [KA98] Kaufman, P. (1998) Trading Systems and Methods. John Wiley and Sons. [LS01] Longstaff, F.A. Schwartz E.S. (2001) Valuing American Options by

Simulation: a Simple Least Squares Approach. Review of Financial Studies. [LU09] Luss, R. (2009) Predicting Abnormal Returns from News using Text Classification. Talk given at the AMLCF 2009 conference, London. http://videolectures.net/amlcf09_london/ [MA09] Mahler, N. (2009) Modelling S&P 500 Index using the Kalman Filter and the LagLasso. Talk given at the AMLCF 2009 conference, London. http://videolectures.net/amlcf09_london/

[NFK06] Nevmyvaka, Y. Feng, Y. Kearns, M. (2006) Reinforcement Learning for Optimized Trade Execution. ICML. [RA09] Ramamoorthy, S. (2009) Multi-Strategy Trading Utilizing Market Regimes. Talk given at the AMLCF 2009 conference, London. http://videolectures.net/amlcf09_london/

[TSD01a] Tino, P. Schittenkopf, C., Dorffner, G. (2001) Volatility trading via Temporal Pattern Recognition in Quantized Financial Time Series. Pattern Analysis and Applications, 4(4). [TSD01b] Tino, P. Schittenkopf, C., Dorffner, G. (2001) Financial Volatility trading using Recurrent Neural Networks. IEEE Transactions on Neural Networks.