From Physics to Finance. Dr. Oliver Hein XXV Heidelberg Physics Graduate Days, October 5, 2010

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1 From Physics to Finance Dr. Oliver Hein XXV Heidelberg Physics Graduate Days, October 5, 010

2 Agenda The banks role in the economy Time series in finance non linearity and the prediction of the future The mechanics of the balance sheet an engineers approach

3 Time series in finance The Banks 3

4 The banks role in the economy The Banking banks landscape role in the in economy Germany three pillars Universalbanken 68 Kreditbanken 5 Großbanken 163 Regionalbanken und sonstige Kreditbanken 100 Zweigstellen ausländischer Banken 1.34 Genossenschaftliche 1.3 Kreditgenossenschaften Kreditinstitute Genossenschaftliche Zentralbanken 453 Öffentlich-rechtliche Kreditinstitute 44 Sparkassen 11 Landesbanken Spezialbanken 5 Bausparkassen Realkreditinstitute 17 Kreditinstitute mit Sonderaufgaben data source: Deutsche Bundesbank, april 008 4

5 The banks role in the economy The role of banks Bank Mediator Capital demand: big, long term demanded capital amounts Transformation: Quantity Term Risk Capital supply: many small, rather short term supplied capital amounts 5

6 The banks role in the economy Traditional tasks of a bank Liquidity transformation Risk taking Information offset term transformation volume transformation Both forms of transformation hold specific risks for the bank which need to be quantified and controlled: Term transformation Liquidity Risk and Interest Rate Risk Volume transformation Credit Risk (Currency transformation FX Rate Risk) 6

7 The banks role in the economy Germans still invest the largest part of their capital in Saving- / Sight- / Term-Deposits and Cash, as well as Insurances Sparverhalten der Deutschen Sparvermögen der Deutschen in Mrd. Euro Spar-, Sicht-, Termineinlagen und Bargeld Investmentfonds Festverzinsliche Wertpapiere Geldanlagen bei Versicherungen Aktien Sonstiges Quelle: Bundesbank/Bankenverband 7

8 The banks role in the economy Distribution of savings in the German 3-pillar-model Rest; 16,60% Genossenschaftsbanken; 30,00% Sparkassen und Landesbanken; 53,40% Savings deposits of non-banks, source Bankenverband, 006 8

9 The banks role in the economy Historical analogy Northern Rock, On Sep 14th NR depositors lined up in front of NR branches to withdraw their money in fear that NR would go bankrupt for lack of liquidity. An estimated amount of GBP bn. was withdrawn. New York, Wall Street Crash: New York's American Union Bank incurred a bank run early in the Great Depression. The Bank opened in 1917 and went out of business on June 30,

10 Agenda The banks role in the economy Time series in finance non linearity and the prediction of the future The mechanics of the balance sheet an engineers approach 10

11 Time series in finance The yield curve interest rates (i) yield curve Y Y 3Y 5Y 7Y 10Y term (t) Term Transformation is at the heart of banking business! 11

12 Time series in finance Interest rates and their dynamics term term structure changes over time 1

13 Time series in finance How to explain the curves different approaches Reference: B. B. Mandelbrot, Börsenturbulenzen neu erklärt, Spektrum der Wissenschaft, Mai 1999, Content: The article shows different approaches to adapt real price curves by theoretical models. The theoretical models considered are of Bachelier (random walk assumption), improved versions of it and those from Mandelbrot (Lévy stable random process or factional Brownian motion and multi fractional models). They are compared with real prices from IBM shares and the exchange rate DM vs. US$. The conclusion is, that although the first attempts by Bachelier and Mandelbrot showed significant deficiencies in explaining actual price movements refined multi fractional models imitate the real price curves pretty well. 13

14 Time series in finance How to explain the curves the stochastic approach 6M Libor The basic model X t = σ t Z t with {Z t } is IID with mean 0, variance 1, e.g. N(0,1) very simple: fixed σ, more advanced: {σ t } is a volatility process 14

15 Time series in finance The GARCH model X t = σ t Z t GARCH(p,q) process (General AutoRegressive Conditional Heteroscedastic) σ t = c + c X + L+ X + β σ + L+ β σ 0 1 t-1 c p t-p 1 t-1 q t-q. special case ARCH(1) X t = ( c 1 0 = c Z t t = A X + c X X 1 t-1 t-1 t-1 + c + B t )Z 0 t Z t 15

16 Time series in finance Stochastic volatility models X t = σ t Z t σ t is a second process, independent of Z t model for the volatility (Taylor 1986) logσ t = α 0 + α 1 logσ t 1 + α ε t, { ε t}~ IIDN(0,1) Stochastic recurrence model X t = X t 1 t t t t ε +η mit { ε, η }~ IID 16

17 Time series in finance Extensions to the basic model general formula: bilinear (Granger / Andersen 1978): ARCH(1, 1) (Engle 198): GARCH(1, 1) (Bollerslev 1986): EGARCH (Nelson 1990): log( σ ) = c t 0 + c 1 log( σ t 1 rt =σtεt σ t r σ σ = t 1 t = c0 + c1r t 1 t = c0 + c1r t 1 + cσ t 1 π further: ARCH-M, AARCH, NARCH, PARCH, PNP_ARCH, STARCH, SWARCH, Component-ARCH, IARCH, multiplicative ARCH for weather derivatives e.g. the ARFIMA-FIGARCH approach is used ) + c ε σ t 1 t 1 + c 3 ε t 1 σ t 1 17

18 Time series in finance The patient financial markets 18

Time series in finance Physical models applied to financial markets The application of stochastic methods to questions from the world of finance is nowadays an

$Time will tell which of them will also have practical relevance. Ising models, chaos theory, fractals, etc.$

19 Time series in finance Physical models applied to financial markets The application of stochastic methods to questions from the world of finance is nowadays an established standard. Many well understood paradigms from physics can be applied to problems arising in a financial context. Time will tell which of them will also have practical relevance. Ising models, chaos theory, fractals, etc. The main problem is: Our models have in fact become extremely complex but are still too simple to be able to incorporate the whole spectrum of variables that drive the global economy. A model is necessarily an abstraction without all details of the real world. 19

20 Time series in finance Trends in Statistical Physics Econophysics selected books Fractals and Scaling in Finance Discontinuity, Concentration, Risk by B. B. Mandelbrot: Springer-Verlag, 1997 An Introduction to Econophysics Correlations and Complexity in Finance by R. N. Mantegna and H.E. Stanley Cambridge, England: Cambridge University Press, 000 New Directions in Statistical Physics Econophysics, Bioinformatics, and Pattern Recognition by L. T. Wille Springer-Verlag, 004 0

21 Agenda The banks role in the economy Time series in finance non linearity and the prediction of the future The mechanics of the balance sheet an engineers approach 1

22 The mechanics of the balance sheet Consolidation: The ball model Purpose: Simultaneous consideration of interest rate risk and liquidity risk Liquidity Gaps 4 credits 0 - time -4 Interest Rate Gaps bonds capital commitment, no interest rate commitment capital and interest rate commitment

23 The mechanics of the balance sheet Consolidation: The ball model 3

24 The mechanics of the balance sheet Thoughts about the optimal form How can we achieve an optimal match between business structure, liquidity structure, and interest rate structure while taking into account their dynamics? 4

25 The mechanics of the balance sheet The four business dimensions B u s i n e s s A c u m e n Global bank management Liquidity risk Greed Fear Modelling Interest rate risk Risk duty of due care 5

26 Your Contact Dr. Oliver Hein Senior Manager d-fine Frankfurt München London Hong Kong Zürich Zentrale d-fine GmbH Opernplatz Frankfurt am Main Deutschland T F:

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