From Physics to Finance
XXXVII Heidelberg Physics Graduate Days
Heidelberg, October 10th, 2016
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© d- fine© d- —fine All — rights All rights reserved reserved | 1 Agenda
» The banks’ role in the economy 3 » Time series in finance – non-linearity and prediction of the future 12 » The mechanics of the balance sheet – an engineers approach 68 » The costs of the crisis 76 » Is the financial complexity manageable? 88
2016-10-10 | From Physics to Finance © d- fine© d- —fine All — rights All rights reserved reserved | 2 The banks’ role in the economy
2016-10-10 | From Physics to Finance | The banks’ role in the economy © d- fine© d- —fine All — rights All rights reserved reserved | 3 The “Banks”
Photo source: © NH1977 / PIXELIO
2016-10-10 | From Physics to Finance | The banks’ role in the economy (1/8) © d- fine© d- —fine All — rights All rights reserved reserved | 4 New players – Fintecs try to disrupt the banking industry
New opportunities arise from disrupting old and 250 Investitionen von Risikokapitalgebern inefficient processes in the banking business: in Deutschland in Finanz-Startups (in » Use of Blockchain technologies contemplated in: Millionen Euro) 200 › Money (Bitcoin etc.) › Stock exchange › Account management 150 › Interbanking transactions
› Title register… 100 » Brokerage of fix rate invest in foreign countries
» Assistance in changing the bank-account 50 » Support of collection services
» Credit rating with the help of user profiles/social 0 network data (currently not legal in Germany) 2015 I 2015 II 2015 III 2015 IV 2016 I 2016 II » First Fintechs in Germany are in possession of a bank licence » Established banks take notice Cooperation with or acquisition of Fintechs
Digitalization of the banking business is a trend for years to come
Source; Barkow-Consulting
2016-10-10 | From Physics to Finance | The banks’ role in the economy (2/8) © d- fine© d- —fine All — rights All rights reserved reserved | 5 Banking landscape in Germany
Universalbanken (1.637) 288 Kreditbanken 4 Großbanken 172 Regionalbanken und sonstige Kreditbanken 112 Zweigstellen ausländischer Banken three pillars 1.027 Genossenschaftliche 1.025 Kreditgenossenschaften Kreditinstitute 2 Genossenschaftliche Zentralbanken 422 Öffentlich-rechtliche 413 Sparkassen Kreditinstitute 9 Landesbanken
Spezialbanken (56) 21 Bausparkassen 16 Realkreditinstitute 19 Banken mit Sonderaufgaben
Stand: Jahresende 2015
Source: Bankenstatistik, Statistisches Beiheft 1 zum Monatsbericht, Deutsche Bundesbank, September 2016, S. 104
2016-10-10 | From Physics to Finance | The banks’ role in the economy (3/8) © d- fine© d- —fine All — rights All rights reserved reserved | 6 The banks’ role – Transforming money
Bank
Mediator
Transformation: Capital demand: » Quantity Capital supply: big, long term demanded capital » Term many small, rather short term amounts » Risk supplied capital amounts
Transformation is at the heart of banking business
Photo source: © segavax, Andreas Hermsdorf / PIXELIO
2016-10-10 | From Physics to Finance | The banks’ role in the economy (4/8) © d- fine© d- —fine All — rights All rights reserved reserved | 7 The banks’ role – Transforming money
BankSmall / fast
Mediator Big / slow Small / fast
Transformation: Capital demand: » Quantity Capital supply: big, long term demanded capital » Term many small, rather short term amounts » Risk supplied capital amounts
Transformation is at the heart of banking business
Photo source: © segavax, Andreas Hermsdorf / PIXELIO
2016-10-10 | From Physics to Finance | The banks’ role in the economy (5/8) © d- fine© d- —fine All — rights All rights reserved reserved | 8 Traditional tasks of a bank
Capital / Liquidity Information Risk taking transformation offset
Both forms of transformation hold specific risks for the bank which need to be quantified and controlled:
Volume » Volume transformation ↔ Credit Risk transformation
Term » Term transformation ↔ Liquidity Risk and transformation Interest Rate Risk
» Currency transformation ↔ FX Rate Risk
» Equity Prices, Stock Exchange Rates, …
Transformation is at the heart of banking business
2016-10-10 | From Physics to Finance | The banks’ role in the economy (6/8) © d- fine© d- —fine All — rights All rights reserved reserved | 9 German saving behaviour
» Germans still invest the largest part of their capital in savings- / sight- / term- deposits and cash, as well as insurances 6.000,00 Geldvermögen privater Haushalten in Deutschland in Mrd. Euro
5.000,00 198,70 193,40 299,50 185,20 259,10 4.000,00 228,00 201,10 201,10 221,50 215,10 201,70 201,70 370,60 181,90 1.468,90 1.551,70 1.400,20 1.284,80 1.284,80 3.000,00 1.190,70 1.215,00 216,00 247,10 238,20 265,50 265,50 449,50 297,00 267,10 394,90 420,10 2.000,00 416,20 416,20 467,40 379,80
1.000,00 1.860,80 1.927,50 2.014,90 2.082,20 1.602,80 1.737,50 1.788,10
0,00 2007 2008 2009 2010 2011 2012 2013
Spar-, Sicht-, Termineinlagen und Bargeld Investmentzertifikate Festverzinsliche Wertpapiere Geldanlagen bei Versicherungen Aktien Sonstiges
We have savings of about 5 trillion EUR
Source: Deutsche Bundesbank, September 2014
2016-10-10 | From Physics to Finance | The banks’ role in the economy (7/8) © d-fine © d —-fine All —rights All rightsreserved reserved | 10 The ten biggest banks in Europe
Total Assets of European Banks in trillion € (30.06.2016) 2.500
2.000
1.500
1.000
500
0 HSBC BNP Paribas Deutsche Credit Barclays PLC Societe Banco Groupe Royal Bank Lloyds Holdings Bank Agricole Generale Santander BPCE of Scotland Banking Group Group Group
Source: http://www.relbanks.com/, http://www.xe.com
2016-10-10 | From Physics to Finance | The banks’ role in the economy (8/8) © d-fine © d —-fine All —rights All rightsreserved reserved | 11 Time series in finance – non-linearity and prediction of the future
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future © d-fine © d —-fine All —rights All rightsreserved reserved | 12 The yield curve
interest rates (i)
yield curve
1Y 2Y 3Y 5Y 7Y 10Y 11Y 12Y 13Y 14Y 15Y term (t)
Term transformation, i.e., transformation in time, is a major transformation
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (1/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 13 The yield curve
6 3 3 interest rates (i)
yield curve
1Y 2Y 3Y 5Y 7Y 10Y 11Y 12Y 13Y 14Y 15Y term (t)
Term transformation, i.e., transformation in time, is a major transformation
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (2/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 14 Interest rates and their dynamics
15 Y
The change in interest rates follows no simple statistics
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (3/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 15 Interest rates and their dynamics
10 Y
The change in interest rates follows no simple statistics
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (4/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 16 Interest rates and their dynamics
9 Y
The change in interest rates follows no simple statistics
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (5/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 17 Interest rates and their dynamics
8 Y
The change in interest rates follows no simple statistics
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (6/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 18 Interest rates and their dynamics
7 Y
The change in interest rates follows no simple statistics
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (7/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 19 Interest rates and their dynamics
6 Y
The change in interest rates follows no simple statistics
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (8/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 20 Interest rates and their dynamics
5 Y
The change in interest rates follows no simple statistics
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (9/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 21 Interest rates and their dynamics
4 Y
The change in interest rates follows no simple statistics
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (10/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 22 Interest rates and their dynamics
3 Y
The change in interest rates follows no simple statistics
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (11/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 23 Interest rates and their dynamics
2 Y
The change in interest rates follows no simple statistics
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (12/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 24 Interest rates and their dynamics
1 Y
The change in interest rates follows no simple statistics
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (13/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 25 Interest rates and their dynamics
6 M
The change in interest rates follows no simple statistics
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (14/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 26 Interest rates and their dynamics
3 M
The change in interest rates follows no simple statistics
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (15/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 27 Interest rates and their dynamics
1 M
The change in interest rates follows no simple statistics
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (16/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 28 Interest rates and their dynamics
15 Y
1 M
The change in interest rates follows no simple statistics
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (17/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 29 Phenomenology of financial time series
Data are heteroscedastic, i.e., there are alterations of volatile and tranquil periods
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (18/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 30 Phenomenology of financial time series
Data are leptocurtic, i.e., the empirical distribution is more pronounced / steeper in the middle of the distribution as the normal distribution and it has more mass in the tails as a normal distribution (fat tails).
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (19/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 31 How to “explain” the curves – Different approaches
Can we see patterns?
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (20/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 32 How to “explain” the curves – Different approaches
The “Euclidean geometry” approach
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (21/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 33 How to “explain” the curves – Different approaches
The fractal geometry approach
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (22/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 34 How to “explain” the curves – Different approaches
The fractal geometry approach
Source: B. B. Mandelbrot, Börsenturbulenzen neu erklärt, Spektrum der Wissenschaft, Mai 1999, 74-77
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (23/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 35 How to “explain” the curves – Different approaches
The stochastic approach
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (24/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 36 How to “explain” the curves – Different approaches
P. Malliavin, A. Thalmaier, Stochastic Calculus of Variations in Mathematical Finance, Springer
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (25/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 37 How to “explain” the curves – Different approaches
P. Malliavin, A. Thalmaier,
Stochastic Calculus of Variations in Mathematical Finance,
Springer
P. Malliavin, A. Thalmaier, Stochastic Calculus of Variations in Mathematical Finance, Springer
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (26/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 38 How to “explain” the curves – Different approaches
Modelling the logarithmical price change
S(t dt) S(t) dt0d ln(S) S(t)
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (27/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 39 Interest rate models
» Basic model: Xt = σt Zt with
{Zt} is IID with mean 0, variance 1, e.g. N(0,1)
very simple: fixed σ, more advanced: {σt } is a volatility process
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (28/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 40 Interest rate models
» GARCH model
Xt = σt Zt GARCH(p,q) process (General AutoRegressive Conditional Heteroscedastic)
2 2 2 2 2 t c0 c1Xt-1 cpXt-p 1 t-1 q t-q .
Special case ARCH(1)
2 2 2 Xt (c0 c1Xt-1)Zt 2 2 2 c1Zt Xt-1 c0Zt 2 AtXt-1 Bt
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (29/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 41 Interest rate models
» Stochastic volatility models
Xt = σt Zt
σt is a second process, independent of Zt Model for the volatility (Taylor 1986)
2 2 logt 0 1 logt1 2t , {t }~ IID N(0, 1)
Stochastic recurrence model
Xt Xt1t t mit {t ,t }~ IID
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (30/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 42 Interest rate models
» Extensions to the basic GARCH model
General formula: rt tt 2 2 Bilinear (Granger / Andersen 1978): t rt1 ARCH(1, 1) (Engle 1982): 2 2 t c0 c1rt1 GARCH(1, 1) (Bollerslev 1986): 2 c c r 2 c 2 EGARCH (Nelson 1990): t 0 1 t1 2 t1
c 2 log( ) c c log( ) 2 t1 c t1 t 0 1 t1 3 t1 t1
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
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (31/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 43 Options in finance
Suppose we have a stock that is worth 100$ today. Tomorrow we have two scenarios: the stock can go up to 130$ with empirical probability of 60% or it can go down to 70$ with empirical probability of 40% .
t = 0 t = 1
p = 60% 130$
100$
p = 40% 70$
What is the fair price of such a contract today?
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (32/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 44 Options in finance
Suppose we have a stock that is worth 100$ today. Tomorrow we have two scenarios: the stock can go up to 130$ with empirical probability of 60% or it can go down to 70$ with empirical probability of 40% . Now define the following contract: The holder of the contract has the right to buy the stock tomorrow for 100$. If the price tomorrow is 130$, the holder can buy the stock for 100$ and immediately sell it for 130$, thus making a profit of 30$. If the price tomorrow is 70$ the holder will not use his right to buy the stock for 100$ since he can buy it in the market for 70$.
t = 0 t = 1 Payoff at t = 1
p = 60% 130$ 30$
100$ 100$ 0$
p = 40% 70$ 0$
What is the fair price of such a contract today?
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (33/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 45 Options in finance
Suppose we have a stock that is worth 100$ today. Tomorrow we have two scenarios: the stock can go up to 130$ with empirical probability of 60% or it can go down to 70$ with empirical probability of 40% . Now define the following contract: The holder of the contract has the right to buy the stock tomorrow for 100$. If the price tomorrow is 130$, the holder can buy the stock for 100$ and immediately sell it for 130$, thus making a profit of 30$. If the price tomorrow is 70$ the holder will notSuppose use their right to webuy the find stock forsomebody 100$ since they can who buy it in thepays market usfor 70$. thet = 0 expected profitt = 1of (60%*30$)Payoff at t = 18$1 for
p = 60% such 130$a contract. 30$
100$
p = 40% 70$ 0$
What is the fair price of such a contract today?
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (34/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 46 Options in finance
We could then accept the 18$ and do the following: we buy ½ of the stock today for 50$ and wait until tomorrow. If the stock goes up we have to deliver one stock for the price of 100$, so we have to buy another ½ for 65$. Having spent a total of 115$ and received a total of 118$ we make a profit of 3$. If the stock goes down we don’t have to deliver the stock and can sell our ½ stock for 35$, adding the 18$ we got for the contract and subtracting the 50$ we paid for the ½ stock at t = 0 again gives us a profit of 3$.
Money spent Money received Profit
130$ » Buy ½ stock at t = 0: -50$ » Initial contract: 18$ » Buy ½ stock at t = 1: -65$ » Delivery of 1 stock: 100$ » Total -115$ » Total 118$ 3$
100$
» Buy ½ stock at t = 0: -50$ » Initial contract: 18$ » Sell ½ stock at t = 1: 35$
70$ » Total -50$ » Total 53$ 3$
We make a profit of 3$, no matter what happens tomorrow!
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (35/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 47 Options in finance
We could then accept the 18$ and do the following: we buy ½ of the stock today for 50$ and wait until tomorrow. If the stock goes up we have to deliver one stock for the price of 100$, so we have to buy another ½ for 65$. Having spent a total of 115$ and received a total of 118$ we make a profit of 3$. If the stock goes down we don’t have to deliver the stock and can sell our ½ stock for 35$, adding the 18$ we got for the contract and subtracting the 50$ we paid for the ½ stock at t = 0 again gives us a profit of 3$.
Money spent Money received Profit
130$ » Buy ½ stock at t = 0: -50$ » Initial contract: 18$ » Buy ½ stock at t = 1: -65$ » Delivery of 1 stock: 100$ » Total -115$ » Total 118$ 3$
100$
» Buy ½ stock at t = 0: -50$ » Initial contract: 18$ » Sell ½ stock at t = 1: 35$
70$ » Total -50$ » Total 53$ 3$
We make a profit of 3$, no matter what happens tomorrow!
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (36/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 48 Options in finance
We could then accept the 18$ and do the following: we buy ½ of the stock today for 50$ and wait until tomorrow. If the stock goes up we have to deliver one stock for the price of 100$, so we have to buy another ½ for 65$. Having spent a total of 115$ and received a total of 118$ we make a profit of 3$. If the stock goes down we don’t have to deliver the stock and can sell our ½ stock for 35$, adding the 18$ we got for the contract and subtracting the 50$ we paid for the ½ stock at t = 0 again gives us a profit of 3$.
Money spent Money received Profit
130$ » Buy ½ stock at t = 0: -50$ » Initial contract: 18$ » Buy ½ stock at t = 1: -65$ » Delivery of 1 stock: 100$ » Total -115$ » Total 118$ 3$
100$
» Buy ½ stock at t = 0: -50$ » Initial contract: 18$ » Sell ½ stock at t = 1: 35$
70$ » Total -50$ » Total 53$ 3$
We make a profit of 3$, no matter what happens tomorrow!
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (37/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 49 Options in finance
We could then accept the 18$ and do the following: we buy ½ of the stock today for 50$ and wait until tomorrow. If the stock goes up we have to deliver one stock for the price of 100$, so we have to buy another ½ for 65$. Having spent a total of 115$ and received a total of 118$ we make a profit of 3$. If the stock goes down we don’t have to deliver the stock and can sell our ½ stock for 35$, adding the 18$ we got for the contract and subtracting the 50$ we paid for the ½ stock at t = 0 again gives us a profit of 3$.
Money spent Money received Profit
130$ Expected values based on empirical » Buy ½ stock at t = 0: -50$ » Initial contract: 18$ probabilities» Buy ½ stock at t =do 1: not-65$ give» theDelivery fair of 1 stock: price! 100$ » Total -115$ » Total 118$ 3$
100$
» Buy ½ stock at t = 0: -50$ » Initial contract: 18$ » Sell ½ stock at t = 1: 35$
70$ » Total -50$ » Total 53$ 3$
We make a profit of 3$, no matter what happens tomorrow!
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (38/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 50 One thousand scenarios for the U.S. treasury curve
Distribution of 1 Year Government Bond Yields, USA, 1962 - 2015
» 23,117 daily observations on 1 year government yields in the USA and Japan show that rates bunch near the zero yield level and can go negative. » 1,000 scenario simulation benchmarked in today's yields so that the Monte Carlo simulation correctly prices the entire current Treasury curve.
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (39/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 51 One thousand scenarios for the U.S. treasury curve
Good models are the essence of strategy and planning!
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (40/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 52 One thousand scenarios for the U.S. treasury curve
Money spent Money received
130$ » Buy ½ stock at t = 0: -50$ » Initial contract: 18$ » Buy ½ stock at t = 1: -65$ » Delivery of 1 stock: 100$ » Total -115$ » Total 118$ 3$
100$
» Buy ½ stock at t = 0: -50$ » Initial contract: 18$ » Sell ½ stock at t = 1: 35$
70$ » Total -50$ » Total 53$ 3$
Good models are the essence of strategy and planning!
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (41/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 53 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 statistical physics approach
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (42/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 54 Physical models applied to financial markets - Hamiltonians
https://www.flickr.com/photos/bankenverband/9930916773, Jochen Zick
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (43/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 55 Physical models applied to financial markets - Hamiltonians
» Toy model of a stock market based on the following assumptions: › Our market consists of L traders exchanging a single kind of share; › The total number of shares, N, is fixed in time; › A trader can only interact with a single other trader: i.e. the traders feel only a two-body interaction; › The traders can only buy or sell one share in any single transaction; › The price of the share changes with discrete steps, multiples of a given monetary unit; › When the tendency of the market to sell a share, i.e. the market supply, increases then the price of the share decreases; › For our convenience the supply is expressed in term of natural numbers; › To simplify the notation, we take the monetary unit equal to 1.
Article: F. Bagarello, J. Phys. A, 6823-6840 (2006)
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (44/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 56 Physical models applied to financial markets - Hamiltonians
» The formal Hamiltonian of the model is the following operator:
푯 = 푯ퟎ + 푯풍, 풘풉풆풓풆 푳 푳 † † † † 푯ퟎ = 풂풍 풂풍 풂풍 + 휷풍 풄풍 풄풍 + 풐 풐 + 풑 풑 풍=ퟏ 풍=ퟏ
푳 푷 푷 † † † † † † 푯풍 = 풑풊풋 풂풊 풂풋 풄풊풄풋 + 풂풊풂풋 풄풋풄풊 + 풐 풑 + 풑 풐 풊,풋=ퟏ » where 푷 = 풑 † 풑 and the following commutation rules are used: † † † † » 풂 풍, 풂풏 = 풄풍, 풄풏 = 휹풍풏푰 풑, 풑 = 풐, 풐 = 푰 » All other commutators are zero.
» We further assume that 풑풊풊 = ퟎ ⌗ ⌗ ⌗ ⌗ » Number, price, cash and supply operators: 풂풍 , 풑 , 풄풍 , 풐
» The states of the market are: 흎 풏 ; 풌 ;푶;푴 . = 흋 풏 ; 풌 ;푶;푴, 흋 풏 ; 풌 ;푶;푴
» where 풏 = 풏ퟏ, 풏 ퟐ, … , 풏푳, 풌 = 풌ퟏ, 풌ퟐ, … , 풌 푳 and 푛 푛 푘 푘 † 1 † 퐿 † 1 † 퐿 † 푶 † 푴 풂ퟏ … 풂푳 풄ퟏ … 풄푳 풐 … 풑 흋 풏 ; 풌 ;푶;푴 = 흋ퟎ 풏ퟏ! … 풏푳! 풌ퟏ! … 풌푳! 푶! 푴! 풂 흋 = 풄 흋 = 풑흋 = 풐흋 = ퟎ, 풇풐풓 풋 = ퟏ, ퟐ, … , 푳 » 휑0 is the vacuum of the model: 풋 ퟎ 풋 ퟎ ퟎ ퟎ
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (45/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 57 Physical models applied to financial markets - Hamiltonians
» The time evolution for the observables, e.g., the price 푑푋(푡) = 푖푒푖퐻푡 퐻, 푋 푒−푖퐻푡 = 푖 퐻, 푋(푡) 푑푡
Article: F. Bagarello, J. Phys. A, 6823-6840 (2006), Foto: https://www.flickr.com/photos/bankenverband/9930916773, Jochen Zick
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (46/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 58 How to “explain” the curves – different approaches
The combinatorial approach
Pictures from O. Racorean, Geometry and Topology of the Stock Market, 2013
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (47/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 59 Physical models applied to financial markets - A string model in phynance
The “cosmological” approach
Article Physica A 391 (2012) 5172-5188
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (48/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 60 Physical models applied to financial markets – Selected books
R. Mantegna, H. Stanley L. Wille M. Small F. Abergel, B. Chakrabarti, A. Chakraborti, A.Ghosh (Ed) Correlations and Complexity in New Directions in Statistical Applied Nonlinear Time Series Finance Physics Econophysics of Systemic Risk Applications in Physics, and Network Dynamice Cambridge University Press Econophysics, Bioinformatics, Physiology and Finance and Pattern Recognition Systemic Risk and Network World Scientific Series on Dynamics Springer Nonlinear Science, Series A Vol. 52 Springer
B. Mandelbrot O. Racorean H. Kleinert B. Baaquie Fractals and Scaling in Finance Geometry and Topology of the Path Integrals in Quantum Quantum Finance Stock Market Mechanics, Statistics, Polymer Discontinuity, Concentration, Path Integrals and Hamiltonians Physics, and Financial Markets Risk Quantum Computer generation for Options and Interest rates of quants World Scientific Springer Cambridge CreateSpace
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (49/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 61 Known models in different domains of science
Chapman, Hall Computational Neuroscience A Comprehensive Approach CRC Mathematical Biology and Mediscience Series
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (50/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 62 Mathematical/physical models in finance – The “patient” financial markets
Parallels between Earthquakes, Financial crashes and epileptic seizures Didier Sornette
Didier Sornette Neuron Reviews on Cognitive Architectures, Vol. 86, Number 1, Oct. 2015
See also:
I. Osorio, H. Zaveri, M. Frei, S.Arthurs (Ed.) Epilepsy The Intersection of Neurosciences, Biology, Mathematics, Enginieering, and Physics CRC Press
Our models “fit” in different areas of research – mathematical structures can by analysed by analogies
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (51/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 63 The “patient” financial markets
Our models “fit” in various fields of science
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (52/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 64 The “patient” financial markets
Our models “fit” in various fields of science
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (53/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 65 The “patient” financial markets
Our models “fit” in various fields of science – exploring mathematical structures via analogy
Photo source: © NH1977 / PIXELIO
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (54/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 66 Physical models applied to financial markets – Implementation
2016-10-10 | From Physics to Finance | Time series in finance – non-linearity and prediction of the future (55/55) © d-fine © d —-fine All —rights All rightsreserved reserved | 67 The mechanics of the balance sheet – an engineers approach
2016-10-10 | From Physics to Finance | The mechanics of the balance sheet – an engineers approach © d-fine © d —-fine All —rights All rightsreserved reserved | 68 Inflows and outflows
2016-10-10 | From Physics to Finance | The mechanics of the balance sheet – an engineers approach (1/7) © d-fine © d —-fine All —rights All rightsreserved reserved | 69 Counting and labelling monetary units in time
2016-10-10 | From Physics to Finance | The mechanics of the balance sheet – an engineers approach (2/7) © d-fine © d —-fine All —rights All rightsreserved reserved | 70 The “bow wave” of the balance sheet
2016-10-10 | From Physics to Finance | The mechanics of the balance sheet – an engineers approach (3/7) © d-fine © d —-fine All —rights All rightsreserved reserved | 71 The “bow wave” of the balance sheet
2016-10-10 | From Physics to Finance | The mechanics of the balance sheet – an engineers approach (4/7) © d-fine © d —-fine All —rights All rightsreserved reserved | 72 Cost reduction via canceling “waves”
» How can we achieve an optimal match between business structure, liquidity structure, and interest rate structure while taking into account their dynamics?
Photo source: www.Rudis-Fotoseite.de / pixelio.de
2016-10-10 | From Physics to Finance | The mechanics of the balance sheet – an engineers approach (5/7) © d-fine © d —-fine All —rights All rightsreserved reserved | 73 Cost reduction via canceling “waves”
» How can we achieve an optimal match between business structure, liquidity structure, and interest rate structure while taking into account their dynamics?
Photo source: FotoHiero / pixelio.de
2016-10-10 | From Physics to Finance | The mechanics of the balance sheet – an engineers approach (6/7) © d-fine © d —-fine All —rights All rightsreserved reserved | 74 Cost reduction via canceling “waves”
» How can we achieve an optimal match between business structure, liquidity structure, and interest rate structure while taking into account their dynamics?
Photo source: FotoHiero / pixelio.de
2016-10-10 | From Physics to Finance | The mechanics of the balance sheet – an engineers approach (7/7) © d-fine © d —-fine All —rights All rightsreserved reserved | 75 The costs of the crisis
2016-10-10 | From Physics to Finance | The costs of the crisis © d-fine © d —-fine All —rights All rightsreserved reserved | 76 SoFFin (Sonderfonds Finanzmarktstabilisierung)
Financial Market Stabilization Fund 296,5 billion EUR in 2014 guarantees of up to 400bn Euros recapitalize or purchase assets for up to 80bn Euros
Accumulated losses of the SoFFin: » 2009: 4.3 billion Euros » 2010: 4.8 billion Euros » 2011: 13.1 billion Euros » 2012: 23 billion Euros » 2013: 21.5 billion Euros » 2014: 21.9 billion Euros
Equity recapitalizations (30.06.2012) : » Aareal Bank AG: 0.3 » Commerzbank AG: 6.7 » Hypo Real Estate: 9.8 » WestLB AG: 3.0
Source: SoFFin Jahresberichte, http://www.fmsa.de/de/fmsa/soffin/Berichte/index.html Source: Bundesministerium für Finanzen, Auf den Punkt - Bundeshaushalt 2014, August 2014
2016-10-10 | From Physics to Finance | The costs of the crisis (1/11) © d-fine © d —-fine All —rights All rightsreserved reserved | 77 Visualizing US debt – 1
100 dollars
Source: Die Welt / August 2011
2016-10-10 | From Physics to Finance | The costs of the crisis (2/11) © d-fine © d —-fine All —rights All rightsreserved reserved | 78 Visualizing US debt – 2
10.000 dollars – average years income world wide
Source: Die Welt / August 2011
2016-10-10 | From Physics to Finance | The costs of the crisis (3/11) © d-fine © d —-fine All —rights All rightsreserved reserved | 79 Visualizing US debt – 3
1 million dollars
Source: Die Welt / August 2011
2016-10-10 | From Physics to Finance | The costs of the crisis (4/11) © d-fine © d —-fine All —rights All rightsreserved reserved | 80 Visualizing US debt – 4
100 million dollars – This amount can be transported on a europallet
Source: Die Welt / August 2011
2016-10-10 | From Physics to Finance | The costs of the crisis (5/11) © d-fine © d —-fine All —rights All rightsreserved reserved | 81 Visualizing US debt – 5
1 billion dollars – 10 europallets, not easy to transport
Source: Die Welt / August 2011
2016-10-10 | From Physics to Finance | The costs of the crisis (6/11) © d-fine © d —-fine All —rights All rightsreserved reserved | 82 Visualizing US debt – 6
1 trillion dollars – in comparison to an American Football field or a Boeing 747
Source: Die Welt / August 2011
2016-10-10 | From Physics to Finance | The costs of the crisis (7/11) © d-fine © d —-fine All —rights All rightsreserved reserved | 83 Visualizing US debt – 7
15 trillion dollars – represents the forecasted national debt of the USA at the end of 2011
Source: Die Welt / August 2011
2016-10-10 | From Physics to Finance | The costs of the crisis (8/11) © d-fine © d —-fine All —rights All rightsreserved reserved | 84 Visualizing US debt – 8
114,5 trillion dollars – sum of all unsecured obligations of the USA – i.e. national debt, including pensions, social services and private debt
15 trillion dollars (5 trillion dollars held by foreigners, 1,2 trillion dollars held by China)
Source: Die Welt / August 2011
2016-10-10 | From Physics to Finance | The costs of the crisis (9/11) © d-fine © d —-fine All —rights All rightsreserved reserved | 85 Visualizing US debt – 8
114,5 trillion dollars – sumThere of areall unsecured 1011 stars inobligations the galaxy. of Thatthe usedUSA to –be i.e. a hugenational number. debt, includingBut it’s only a pensions,hundred socialbillion. services It’s less thanand private the national debt deficit! We used to call them astronomical numbers. Now we should call them economical numbers.
Richard Feynman (1918–1988) 15 trillion dollars (5 trillion dollars held by foreigners, 1,2 trillion dollars held by China)
Source: Die Welt / August 2011
2016-10-10 | From Physics to Finance | The costs of the crisis (10/11) © d-fine © d —-fine All —rights All rightsreserved reserved | 86 Cost of science (budget)
Spektrum der Wissenschaft April 2016
2016-10-10 | From Physics to Finance | The costs of the crisis (11/11) © d-fine © d —-fine All —rights All rightsreserved reserved | 87 Is the financial complexity manageable?
2016-10-10 | From Physics to Finance | Is the financial complexity manageable? © d-fine © d —-fine All —rights All rightsreserved reserved | 88 High frequency trading
» HFT incorporates proprietary trading strategies carried out by computers » Electronic exchanges were first authorized by the U.S. Securities and Exchange Commission in 1998 » Execution times have fallen from several seconds in the year 2000 to milliseconds on modern systems
Source: Handelsblatt 2012
2016-10-10 | From Physics to Finance | Is the financial complexity manageable? (1/22) © d-fine © d —-fine All —rights All rightsreserved reserved | 89 Volume of high frequency trading
Number of transactions in » Portion of HFT in U.S. equity trades DAX titles has increased from less than 10 % in 2000 to over 70% in 2010 » About 40% of Xetra transactions are 41 billion carried out by HFT systems 1 billion 1993 2011
Portion of U.S. Portion of equity trading firms order volume these engaging in HFT firms account for
Source: Handelsblatt 2012
2016-10-10 | From Physics to Finance | Is the financial complexity manageable? (2/22) © d-fine © d —-fine All —rights All rightsreserved reserved | 90 Role of high frequency trading in the crisis
» In 2010 the Dow Jones Index experienced its largest one- day point decline in history “Flash Crash” » The U.S. Securities and Exchange Commission and the Commodity Futures Trading Commission concluded in a joint investigation that the actions of HFT firms largely contributed to volatility during the crash.
Source: Handelsblatt 2012
2016-10-10 | From Physics to Finance | Is the financial complexity manageable? (3/22) © d-fine © d —-fine All —rights All rightsreserved reserved | 91 Role of high frequency trading in the crisis
» In 2010 the Dow Jones Index experienced its largest one- day point decline in history “Flash Crash” S. Patterson M. Lewis » The U.S. SecuritiesDark Pools and Flash Boys ExchangeCrown Commission Business and Norton & Company the Commodity Futures Trading Commission concluded in a joint investigation that the actions of HFT firms largely contributed to volatility during the crash.
Source: Handelsblatt 2012
2016-10-10 | From Physics to Finance | Is the financial complexity manageable? (4/22) © d-fine © d —-fine All —rights All rightsreserved reserved | 92 Network topologies of interbank payments
CHAPS: Clearing House Automated Payment System CHAPS offers same-day sterling fund transfers Many flows are routed through settlement banks
Source: Becher, Millard, and Soramäki, The network topology of CHAPS Sterling, Bank of England, Working Paper 355
2016-10-10 | From Physics to Finance | Is the financial complexity manageable? (5/22) © d-fine © d —-fine All —rights All rightsreserved reserved | 93 Network topologies of interbank payments
CHAPS: Clearing House Automated Payment System CHAPS offers same-day sterling fund transfers Many flows are routed through settlement banks
» The settlement banks form a complete network » 4 settlement banks account for almost 80% of the payments, measured by value or volume!
Source: Becher, Millard, and Soramäki, The network topology of CHAPS Sterling, Bank of England, Working Paper 355
2016-10-10 | From Physics to Finance | Is the financial complexity manageable? (6/22) © d-fine © d —-fine All —rights All rightsreserved reserved | 94 Network topologies of interbank payments
CHAPS: Clearing House Automated Payment System CHAPS offers same-day sterling fund transfers Many flows are routed through settlement banks
» The settlement banks form a complete network » 4 settlement banks account for almost 80% of the payments, measured by value or volume!
Source: Becher, Millard, and Soramäki, The network topology of CHAPS Sterling, Bank of England, Working Paper 355
2016-10-10 | From Physics to Finance | Is the financial complexity manageable? (7/22) © d-fine © d —-fine All —rights All rightsreserved reserved | 95 Economics and banking – a complex network of dependencies
Expenses Profitability P&L Earnings Growth Off-balance Capital positions Cash flow Rating / Balance sheet Solvency positions Balance Downside sheet Derivative risk Optionalities Hedge Investor opinion
Risk Cash flow Liquidity External funding levels Investment Liquidity opportunities risk
From: Managing Liquidity in Banks, R. Duttweiler, 2009
2016-10-10 | From Physics to Finance | Is the financial complexity manageable? (8/22) © d-fine © d —-fine All —rights All rightsreserved reserved | 96 Complexity and networks: Economy and insurance companies
Income
Tr
Government T Insurance companies IntG Int S In G Households SF Capital Market Firms G SHH I C
Insurance companies form a vital part of the macroeconomic flow chart
2016-10-10 | From Physics to Finance | Is the financial complexity manageable? (9/22) © d-fine © d —-fine All —rights All rightsreserved reserved | 97 Complexity and networks: All of us are affected
Source: bild, Handelsblatt
2016-10-10 | From Physics to Finance | Is the financial complexity manageable? (10/22) © d-fine © d —-fine All —rights All rightsreserved reserved | 98 Complexity and networks: All of us are affected
Source: bild, Handelsblatt, FAZ
2016-10-10 | From Physics to Finance | Is the financial complexity manageable? (11/22) © d-fine © d —-fine All —rights All rightsreserved reserved | 99 Collecting and processing information
Digital economy is founded on data
Photo source: en.wikipedia.org
2016-10-10 | From Physics to Finance | Is the financial complexity manageable? (12/22) © d-fine © —d- fineAll rights — All reserved rights reserved | 100 Combating the crisis: Is the financial and European debt crisis over?
» CISS = Composite Indicator of Systemic Stress
Source: European Systemic Risk Board (ESRB) Risk Dashboard Notes: The CISS comprises 15 raw, mainly market-based raw financial stress measures that are split equally into five categories, namely the financial intermediaries sector, money markets, equity markets, bond markets and foreign exchange markets. The raw stress indicators are homogenised by replacing each individual observation with its function value from the indicators’ empirical cumulative distribution function. The five segment-specific sub-indices of financial stress are computed as averages of their three constituent transformed stress measures. The CISS aggregates the five sub-indices based on portfolio theoretical principles, i.e. by taking into account the time-varying cross-correlations between the sub-indices. The CISS thus places relatively more weight on situations in which stress prevails simultaneously in several market segments. It is unit-free and constrained to lie within the interval (0, 1). For further details see Hollo, D., Kremer, M. and Lo Duca, M., “CISS - A composite indicator of systemic stress in the financial system”, Working Paper Series, No 1426, ECB, March 2012. The Sovereign CISS aims to measure the level of stress in euro area sovereign bond markets and applies the same methodological concept of the CISS.
2016-10-10 | From Physics to Finance | Is the financial complexity manageable? (13/22) © d-fine © —d- fineAll rights — All reserved rights reserved | 101 Watson, we need your help!
Source: WELT KOMPAKT, March 2012
2016-10-10 | From Physics to Finance | Is the financial complexity manageable? (14/22) © d-fine © —d- fineAll rights — All reserved rights reserved | 102 Watson, we need your help!
Source: ZEIT Online
2016-10-10 | From Physics to Finance | Is the financial complexity manageable? (15/22) © d-fine © —d- fineAll rights — All reserved rights reserved | 103 Has physics caused the crisis?
» Risk management depends heavily on sophisticated models » Developed models were too complex to be understood intuitively » Computer experts construct “financial hydrogen bombs” as already suspected by Felix Rohatyn in 1998
2016-10-10 | From Physics to Finance | Is the financial complexity manageable? (16/22) © d-fine © —d- fineAll rights — All reserved rights reserved | 104 Physical models applied to financial markets
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.
2016-10-10 | From Physics to Finance | Is the financial complexity manageable? (17/22) © d-fine © —d- fineAll rights — All reserved rights reserved | 105 When things fall apart
Vienna, May 9th, 1873
New York, October 25th, 1929
Northern Rock, September 18th, 2007
Photo source: en.wikipedia.org
2016-10-10 | From Physics to Finance | Is the financial complexity manageable? (18/22) © d-fine © —d- fineAll rights — All reserved rights reserved | 106 Economics and banking – a complex network of dependencies
2016-10-10 | From Physics to Finance | Is the financial complexity manageable? (19/22) © d-fine © —d- fineAll rights — All reserved rights reserved | 107 Can human brains handle the amount of information?
From: Managing Liquidity in Banks, R. Duttweiler, 2009; European Systemic Risk Board (ESRB) Risk Dashboard; Didier Sornette, Neuron, Reviews on Cognitive Architectures, Vol. 86, Number 1, Oct. 2015
, 2016-10-10 | From Physics to Finance | Is the financial complexity manageable? (20/22) © d-fine © —d- fineAll rights — All reserved rights reserved | 108 The four “business dimensions”
Business Acumen
Global bank Liquidity risk management
Greed Fear
Modelling Interest rate risk
Risk duty of due care
2016-10-10 | From Physics to Finance | Is the financial complexity manageable? (21/22) © d-fine © —d- fineAll rights — All reserved rights reserved | 109 Has physics caused the crisis?
» Risk management depends heavily on sophisticated models » Developed models were too complex to be understood intuitively » Computer experts construct “financial hydrogen bombs” as already suspected by Felix Rohatyn in 1998
Physics has not caused the crisis
Ignoramus et ignorabimus versus We have to know. We will know. D. Hilbert
Everything which is not forbidden is compulsory. M. Gell-Mann
2016-10-10 | From Physics to Finance | Is the financial complexity manageable? (22/22) © d-fine © —d- fineAll rights — All reserved rights reserved | 110 Contact
Dr Oliver Hein d-fine Partner Frankfurt Tel +49 69-90737-324 Munich Mobile +49 151-148 19-324 London E-Mail [email protected] Vienna Zurich
Headquarters d-fine GmbH An der Hauptwache 7 60313 Frankfurt/Main Germany
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© d-fine © —d- fineAll rights — All reserved rights reserved | 111 d-fine
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