Course Catalog Description
The course will apply certain concepts from statistical physics to the description of real-life financial time series. It will introduce the notion of Random Walk from the physicist stand-point and propose various statistical tests as comparisons of real-life financial time series properties with those of a Random Walk. The course will introduce statistical description of financial data with emphasis on long-memory correlation functions. The course will introduce Levy stochastic processes and their analytical properties and use them to parameterize the real-life financial time series probability density functions. Through homework's and final project, the course will stress phenomenological hands-on work with financial data. The course will culminate with the final project in which students will learn to extract the learned price anomalies through development of basic trading strategies. The dangers of over fitting of financial data will be studied through walk-forward out-of-sample trading simulations, which will teach student to become more prudent practical quantitative analysis.
Financial engineers or quantitative analysts of today are facing many challenges related to being self-critical and going outside of common-core quantitative finance subjects such as portfolio theory, rational option pricing. Issues related to limits of classical finance, which normally surface at short-term price changes (less than a day), specifically in the most liquidly traded financial instruments, and are normally scarcely covered in financial engineering programs.
Risk-management quantitative analysts, trading strategies quantitative analysts, targeted by either banks or hedge funds, will benefit from this course. They will expand their classical finance knowledge with the understanding of the short-term price anomalies related to: fat-tailed distribution functions, short- and long-range correlations present in high-frequency financial data. The hands-on work related to over-fitting effects in modeling of financial data has been the subject of the most recent criticism of quantitative analyst work. They will learn to be more conscious of the effects of over-fitting, and they will be able to estimate the scope of potential over-fitting present in their models.
The practical problems from the homework's and the final project can be used by students during the job interviews and will help them in their job search.
For an arbitrary real-life financial price series, students will be able to:
1) Develop and apply certain statistical tests that will rationally compare the properties against those of a Random Walk.
2) Students will know the basic analytical and statistical tools that can be used for statistical price description.
3) Determine possible price anomalies that may be present in it, such as: fat tails of price-change distribution function; presence of short- and/or long-correlations in price changes or their functions, such as short-term volatility.
4) Based on those price anomalies develop basic trading strategies exploiting them.
5) Develop a set of robust (with minimized over-fitting) techniques to parameterize the trading strategies.
Introduction to Econophysics: Correlations and Complexity in Finance. By R.N. Mantegna, H.E.
Stanley. ISBN-10: 0521039878.
||Card counting. Position sizing. Fixed-fraction betting. Kelly optimal betting. The combined strategy. St. Petersburg Paradox. Can markets be beaten?
||Ch. 1 and 2
| Week 2
||Working with financial data. Futures markets: exchanges, expirations (maturities). Conventions. Back-adjustment techniques.
| Week 3
||Elementary notions of statistics, or particularly, of "statistical fluid mechanics" or of "statistical turbulence" theory. Probability Density Function. Mean. Stationary process.
| Week 4
||Langevin equation. Continuous random walk. Log-Brownian motion. Mean-reversion model (Ornstein-Uhlenbeck process). Computer simulations of both for various values of parameters.
| Week 5
||Long memory Effects. Second deviation from Random Walk: Counting "c"ontinuations and "r"eversals: evidence of mean-reversion. Physical meaning of auto-correlation. Memory in stochastic processes: short-range memory vs. long-range memory.
| Week 6
| Week 7
||Levy distribution. Definitions of Symmetric and Asymmetric Levy distribution functions.
| Week 8
||Analogies between the high-frequency finance and the physics of fluid turbulence
| Week 9
||Limit order book (LOB)
| Week 10
||Sector-by-sector analysis of stock push-response diagrams and variance ratio tests.
| Week 11
||Buying Winners and Selling Losers: Investigation of Momentum.
| Week 12
||Elements of trading system design
| Week 13
||The notion of drawdown
| Week 14