Lecture 1 Erik Lindstrm FMS161/MASM18 Financial Statistics Erik - PowerPoint PPT Presentation

Intro Stylized facts Lecture 1 Erik Lindström FMS161/MASM18 Financial Statistics Erik Lindström Lecture 1

Intro Stylized facts People and homepage ◮ Erik Lindstrom: erikl@maths.lth.se, 222 45 78, MH:129 (Lecturer) ◮ Carl Åkerlindh: carl.akerlindh@matstat.lu.se, 222 04 85 , MH:125a (Computer exercises) ◮ Maria Lövgren: marial@maths.lth.se, 222 45 77, MH:225 (Course secretary) ◮ http: //www.maths.lth.se/matstat/kurser/fms161mas229/ Erik Lindström Lecture 1

Intro Stylized facts Purpose: » The course should provide tools for analyzing data, and use these tools in combination with economic theory. The main applications are valuation and risk management. » The course used to be the inference part in a package of courses consisting of ’TEK180 Financial Valuation and Risk Management’, ’FMS170 Valuation of Derivative Assets’ and this course. Erik Lindström Lecture 1

Intro Stylized facts Recommended courses: » Mathematical statistics: FMS045/MASC04 Stationary processes (G2), FMSF05/MASC01 Probability theory, intermediate course (G2), FMS051/MASM17 Time series analysis (A), FMS155/MASM15 Extreme Value Theory (A), FMS170/MASM19: Valuation of Derivative Assets (A) and FMS161/MAS18: Financial Statistics (A). » Economics: TEK135 Microeconomics (G2), TEK180 Financial Valuation and Risk Management (A), TEK103 Financial economics, advanced course (A), TEK110 Empirical Financial economics (A) » Other: Programming courses (G2), Optimization (G2), Advanced analysis and prob. theory courses... Erik Lindström Lecture 1

Intro Stylized facts Inference problems? ◮ Forecast future prices, interest rates, volatilities ( P and Q ) ◮ Filtering of data (e.g. estimating hidden states such as stochastic volatility) ◮ Distribution of prediction errors; can we improve the model? ◮ What about extreme events? ◮ How do we estimate parameters in general models? ◮ Cross covariance and auto covariance. ◮ Non-linear, Non-Gaussian, Non-stationary... Erik Lindström Lecture 1

Intro Stylized facts Example I – Daily interest data STIBOR and REPO Yields 1992 REPO STIBOR 1W 500 STIBOR 1M STIBOR 3M STIBOR 6M 100 10 Q1−92 Q2−92 Q3−92 Q4−92 Q1−93 ◮ Models and distributions. ◮ Forecasts - 0.5 % or 500 %? ◮ Events ◮ Covariation with of market factors? Erik Lindström Lecture 1

Intro Stylized facts Example II – Forward prices on Nordpool What can we expect?? ◮ Traders are interested in predicting price movements on the futures on Nordpool on yearly contracts. ◮ Or predicting the movements on short horizons (days or weeks). ◮ Expected movement and/or prob. of declining prizes. ◮ What about fundamental factors? Hydrological situation is the energy stored as snow, ground water or in reservoirs. Time to maturity. Perfect or imperfect markets. ◮ Other factors – suggestions? Erik Lindström Lecture 1

Intro Stylized facts Electricity spot price and Hydrological situation Erik Lindström Lecture 1

Intro Stylized facts Ex – Forwards on Nordpool, contd. There is a strong dependence between the hydrological situation and the price. ◮ How do we model this dependence, e.g. what model should we use? ◮ How do we estimate the chosen model? ◮ How do we know if the model is working (or is good enough)? ◮ One supermodel or several models? ◮ Adaptive models? Erik Lindström Lecture 1

Intro Stylized facts Contents The course treats estimation, identification and validation in non-linear dynamical stochastic models for financial applications based on data and prior knowledge. There are rarely any absolutely correct answers in this course, but there are often answers that are absolutely wrong or to put it differently All models are wrong– but some are useful! Think for yourself, and question the course material! Erik Lindström Lecture 1

Intro Stylized facts Contents, 2 ◮ Discrete and continuous time. ◮ Parameter estimation, model identification and model validation. ◮ Prediction. ◮ Modelling of variance, ARCH, GARCH, ..., and other approaches. ◮ Calibration ◮ Risk ◮ Stochastic calculus and SDEs. ◮ State space models, and filters (Kalman filters and versions thereof), particle filters Erik Lindström Lecture 1

Intro Stylized facts Course goals -Knowledge and Understanding For a passing grade the student must: ◮ handle variance models such as the GARCH family, stochastic volatility, and models use for high-frequency data, ◮ use basic tool from stochastic calculus: Ito’s formula, Girsanov transformation, martingales, Markov processes, filtering, ◮ use tools for filtering of latent processes, such as Kalman filters and particle filters, ◮ statistically validate models from some of the above model families. Erik Lindström Lecture 1

Intro Stylized facts Course goals -Skills and Abilities For a passing grade the student must: ◮ be able to find suitable stochastic models for financial data, ◮ work with stochastic calculus for pricing of financial contracts and for transforming models so that data becomes suitable for stochastic modelling, ◮ understand when and how filtering methods should be applied, ◮ validate a chosen model in relative and absolute terms, ◮ solve all parts of a modelling problem using economic and statistical theory (from this course and from other courses) where the solution includes model specification, inference, and model choice, ◮ present the solution in a written technical report, as well as orally, ◮ utilise scientific articles within the field and related fields. Erik Lindström Lecture 1

Intro Stylized facts Literature Literature: ◮ Lindström, E., Madsen, H., Nielsen, J. N. Statistics for Finance , Lund, 2014. ◮ Handouts Course program. Erik Lindström Lecture 1

Intro Stylized facts Properties of financial data ◮ No Autocorrelation in returns ◮ Unconditional heavy tails ◮ Gain/Loss asym. ◮ Aggregational Gaussianity ◮ Volatility clustering ◮ Conditional heavy tails ◮ Significant autocorrelation for abs. returns - long range dependence? ◮ Leverage effects ◮ Volume/Volatility correlation ◮ Asym. in time scales Evaluate claims on OMXS30 data. Erik Lindström Lecture 1

Intro Stylized facts Autocorrelation in returns 1.2 1 0.8 Autocorrelation, returns 0.6 0.4 0.2 0 −0.2 0 5 10 15 20 25 30 lag No or little autocorrelation. Erik Lindström Lecture 1

Intro Stylized facts Unconditional distribution Normal Probability Plot 0.999 0.997 0.99 0.98 0.95 0.90 0.75 Probability 0.50 0.25 0.10 0.05 0.02 0.01 0.003 0.001 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1 Data Normplot of the unconditional returns. Erik Lindström Lecture 1

Intro Stylized facts Gain/Loss asym. OMX S30 3 10 log(Index) 2 10 Jan95 Jan00 Jan05 Jan10 Jan15 Losses are larger than gains (data is log ( Index ) ). Erik Lindström Lecture 1

Intro Stylized facts Aggr. Gaussianity Normal Probability Plot Normal Probability Plot Normal Probability Plot 0.999 0.999 0.999 0.997 0.997 0.997 0.99 0.99 0.99 0.98 0.98 0.98 0.95 0.95 0.95 0.90 0.90 0.90 0.75 0.75 0.75 0.50 r2 0.50 r4 0.50 r 0.25 0.25 0.25 0.10 0.10 0.10 0.05 0.05 0.05 0.02 0.02 0.02 0.01 0.01 0.01 0.003 0.003 0.003 0.001 0.001 0.001 −0.05 0 0.05 0.1 −0.05 0 0.05 0.1 −0.1 0 0.1 Data Data Data Normal Probability Plot Normal Probability Plot Normal Probability Plot 0.999 0.997 0.999 0.997 0.997 0.99 0.99 0.98 0.99 0.98 0.98 0.95 0.95 0.95 0.90 0.90 0.90 0.75 0.75 0.75 r16 r32 r8 0.50 0.50 0.50 0.25 0.25 0.25 0.10 0.10 0.10 0.05 0.05 0.05 0.02 0.02 0.01 0.02 0.01 0.01 0.003 0.003 0.001 0.003 0.001 −0.1 0 0.1 0.2 −0.2 −0.1 0 0.1 0.2 −0.1 0 0.1 0.2 Data Data Data Returns are increasingly Gaussian. Interpretation? Erik Lindström Lecture 1

Intro Stylized facts Vol. Clustering 0.1 0.05 0 −0.05 −0.1 Nov91 Nov94 Nov97 Nov00 Nov03 Nov06 Volatility clusters. Average cluster size? Erik Lindström Lecture 1

Intro Stylized facts Conditional distribution Normal Probability Plot 6 0.999 0.997 0.99 4 0.98 0.95 0.90 2 0.75 Probability 0 0.50 0.25 −2 0.10 0.05 0.02 −4 0.01 0.003 0.001 −6 Nov91 Nov96 Nov01 Nov06 −6 −4 −2 0 2 4 Data Normplot of the conditional returns (GARCH(1,1) filter). Erik Lindström Lecture 1

Intro Stylized facts Dependence in returns 1.2 1 0.8 Autocorrelation, abs returns 0.6 0.4 0.2 0 −0.2 0 50 100 150 200 250 300 lag Significant autocorrelation. Long range dependence? Erik Lindström Lecture 1

Intro Stylized facts Leverage effects ◮ Most assets are negatively correlated with any measure of volatility. ◮ One popular explanation is corporate debt. ◮ Makes sense if you are risk averse. Erik Lindström Lecture 1

Intro Stylized facts Volume/Volatility correlation ◮ Trading volume is correlated with the volatility. ◮ Sometimes modelled with ’business time’ in option valuation community. Erik Lindström Lecture 1

Intro Stylized facts Asym. in time scales ◮ Coarse-grained measurements can predict fine scaled volatility ◮ While fine scaled volatility have difficulties predicting coarse scale volatility Erik Lindström Lecture 1