Exogenous versus endogenous dynamics in price formation. Vladimir Filimonov Chair of Entrepreneurial Risks, D-MTEC, ETH Zurich

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1 Exogenous versus endogenous dynamics in price formation Vladimir Filimonov Chair of Entrepreneurial Risks, D-MTEC, ETH Zurich Chair of Quantitative Finance, École Centrale, Paris, France. May 16, 214

Fixed Income % 24 25 26 27 28 29 21 HFT trade volume as % of total

2 Algorithmic and High-Frequency Trading 6% 5% 4% 3% 2% 1% Adoption of algorithmic execution by asset classes Equities Futures Options FX Fixed Income % HFT trade volume as % of total market U.S. ~65% Asia ~19% Europe ~54% Source: Aite group Source: Aite group 2

3 Typical market makers reaction time Brent Crude WTI E mini S&P 5 1 sec 1 msec 1 msec Year Filimonov V., Sornette D. (214) La vie èconomique 1 msec Data source: TRTH 3

4 Financialization of commodities Increasing market share of commodity speculators Increasing market share of commodity speculators Traditional Speculator 16% Index Speculator 7% Physical Hedger 77% 28 Index Speculator 41% 1998 Physical Hedger 31% Traditional Speculator 28% S&P GSCI Spot Price Commodity Index Others DJ-AIG SP-GSCI S&P GSC March 28 $3 $25 $2 $15 $1 $5 $- Commodity Index Investment (Billions of Dollars) Source: CFTC figures charts by Mike Masters, Better Markets. Source: Goldman Sachs, Bloomberg, CFTC Commitments of Traders CIT Supplement 4

5 How does introduction and adoption of algorithmic (including HFT) trading affect price discovery mechanisms? Is it possible to quantify the interplay between exogeneity (external impact) and endogeneity (internal self-excitation) in price formation? How efficient are financial and financialized commodity markets? 5

6 Two views on the price discovery mechanism News Prices News Prices Efficient Markets (exogenous dynamics) Prices are just reflecting news: the market fully and instantaneously absorbs the flow of information and faithfully reflects it in asset prices. In particular, financial crashes are the signature of exogenous negative news of large impact. Reflexivity of markets (endogenous dynamics) Markets are subjected to internal feedback loops (e.g. created by collective behavior such as herding or informational cascades). Prices do influence the fundamentals and this newly-influenced set of fundamentals then proceed to change expectations, thus influencing prices. 6

7 Sources of reflexivity (endogeneity) in financial and financialized markets Behavioral mechanisms such imitation and informational cascades leading to herding; Speculation, based on technical analysis, including algorithmic trading; Hedging strategies (also increase cross-excitation between markets); Pricing of structured products such as ETFs (also contribute to cross-excitation) Methods of optimal portfolio execution and order splitting; Margin/leverage trading and margin-calls; High frequency trading (HFT) as a subset of algorithmic trading; Stop-loss orders and etc. 7

8 Bid The test subject: HF price dynamics Limit orders to sell Buy market order Price Limit orders to buy Last transaction price Best bid price Best ask price Mid-quote price Transaction Mid-quote price change Sell market order Ask Price Time 8

9 The model: Self-excited Hawkes process Self-excited Hawkes process is the point process whose intensity λt(t) is conditional on its history: (t F t )=µ + n X t i <t (t t i ) 12 Background intensity Self-excitation part 1 Intensity Time Applications of the Hawkes model: High-frequency price dynamics Order book construction Critical events and estimation of VaR Default times in a portfolio of companies Endogenous feedback Exogenous activity Triggered seismicity (earthquakes) Sequence of genes in DNA Epileptic seizures of brain Crime and violence propagation 9

10 Branching structure of Hawkes process n = Time Crucial parameter of the branching process is the branching ratio (n), which is defined as an average number of daughters per one mother For n < 1 system is subcritical (stationary evolution) For n = 1 system is critical (tipping point) For n > 1 system is supercritical (with prob.> will explode to infinity) In subcritical regime, the branching ratio (n) is equal to the fraction of endogenously generated events among the whole population. 1

11 Calibration of the model Maximum Likelihood method Estimation of the parameters can be performed by maximizing log-likelihood function, which is given by the expression: Z T! NX! log L(t 1,...,t N )= (t F t )dt + log i=1! Residual analysis (t i F ti ) Under the null hypothesis that the data ({ti}) was generated by the Hawkes process with given parameters, the following transformed point process ({τi}) should be Poisson with unit intensity: t i = Z ti (t F t )dt 11

12 Calibration issues. Kernel Exponential kernel! (t) = 1 e t/ (t)! Power law kernels (a) Omori-type kernel (t) = c (t + c) 1+ (t) (b) Power law kernel with cut-off (t) = c t 1+ (t c) (c) Approximate power law kernel (t) = 1 Z " M 1 X i= 1 1+ i exp t i S exp t 1 #,, i = cm i 12

13 Calibration issues. Kernel: sensitivity to outliers Empirical quantiles of inter-quote durations in E-mini S&P 5 Futures Contracts within RTH Date from Date to Q 9 Q 95 Q 99 Max Sensitivity of the estimation of branching ratio (n) to outliers in inter-event durations Data source: TRTH Theoretical quantiles of inter-event durations for Hawkes process with exponential kernel and µ=1 and n=.7 n est τ Q 9 Q 95 Q 99 Max Fraction of modified durations, % power law kernel (small outliers) power law kernel (large outliers) exponential kernel (large outliers) Filimonov V., Sornette D. (213) Working paper. arxiv:

14 Calibration issues. Kernel: regularization Sensitivity of the estimation of branching ratio (n) to the mis-specification of the power law kernel.9 (ii) Estimated branching ratio, n Branching ratio, n Filimonov V., Sornette D. (213) Working paper. arxiv: (iii) (i) Hawkes model with approximate power law kernel being calibrated on the data generated with Omori-type kernel Hawkes model with Omori-type kernel being calibrated on the data generated with approximate power law kernel 14

15 Calibration issues. Multiple extrema Surface of the reduced cost-function used for calibration of the Hawkes model on the midprice changes of E-mini S&P 5 Contracts in March 1 - April 3, 21, using the data randomized within millisecond intervals (see paper for details) Cost function µ =.15 n =1.154 c = θ = µ =.331 n =.751 c =.28 θ = θ c 1 2 Data source: TRTH Filimonov V., Sornette D. (213) Working paper. arxiv:

16 Calibration issues. RTH and overnight trading Fraction of total daily volume (left) and total daily mid-quote price changes (right) that is observed outside of Regular Trading Hours (9:3 to 16:15 CDT) on E-mini S&P 5 Futures Contracts. Overnight fraction of daily volume, % Year Overnight fraction of daily mid price changes, % Year Data source: TRTH Filimonov V., Sornette D. (213) Working paper. arxiv:

17 Calibration issues. Resolution of timestamps (I) Histograms of the time between consecutive FAST/ FIX packages (left panels) and overhead for the data processing (right panels) for E-mini S&P 5 Futures Contracts over RTH Time between FAST/FIX packages, msec Processing time, msec Filimonov V., Sornette D. (213) Working paper. arxiv: Data source: TRTH 17

18 Calibration issues. Resolution of timestamps (II) 1 second Events at the Exchange Packages at the Collection FAST/FIX Package 2 FAST/FIX Package 3 Illustration of the randomization procedure, when the resolution of timestamps is mis-specified. Events randomized Δ Branching ratio, n Bias in estimation of the branching ratio (n) that results from improper assumptions on the duration of randomization intervals, when real inter-packet time is 1 second.! exponential kernel (n=.5) power law kernel (n=.5) Poisson process (n=) , msec Filimonov V., Sornette D. (213) Working paper. arxiv:

19 Calibration issues. Intraday trends Sep 19 Sep 18 Sep 17 Sep Raw data After "detrending" Unconditional intensity of flow of mid-quote price changes of E-mini S&P 5 Futures Contracts on some dates of September October, 27.! Left panels present the raw data (black bars) and the average intensity over the period of September 1 October 3, 27 (red line).! Right panels present the unconditional intensity after detrending using the average intensity. Oct Oct : 12: 14: 16: 1: 12: 14: 16: Time (EST) Time (EST) Filimonov V., Sornette D. (213) Working paper. arxiv: Data source: TRTH 19

20 Calibration issues. Nonstationarity (I) Bias of the estimation of the branching ratio (n) in case of regime switch in background intensity (concatenation of 2 independent samples with µ1=1 and µ2, n=1) 1.1 Bias of the estimation of the branching ratio (n) in case of regime switch in branching ratio intensity (concatenation of 2 independent samples with n1=.5 and n2) Branching ratio, n Branching ratio, n µ n 2 Filimonov V., Sornette D. (213) Working paper. arxiv:

21 Calibration issues. Nonstationarity (II) Dynamics of daily numbers of mid-quote price changes counted over RTH for the Front Month Contract of the E-mini S&P 5 Futures (time period of February 1 to April 1 in three different years) Data source: TRTH Filimonov V., Sornette D. (213) Working paper. arxiv:

9 Nonfarm Payrolls -- June 1, 212 134 9 134 1 134 11 134 12 134 13 134 14 134 15 134 16 134 17 134 18 134 19 134 2 134 21 134 22 134 23 134 24 134 25 134 26 134 27 134 28 134 29 7:26: 7:27: 7:28:

22 9 Nonfarm Payrolls -- June 1, :26: 7:27: 7:28: 7:29: 7:3: 7:31: 7:32: 7:33: 7:34: CDT on Fri 1 Jun lots PCE Sept 1-yr Calibration issues. Nonstationarity (III). Scheduled macroeconomic announcements 22 Source: R. Almgren (212) Quantitative Brokers

23 Calibration issues. The choice of proxy Dynamics of bid (red), ask (blue), midquote price (green) and micro-price (black) Dynamics of last transaction price (red) and mid-quote price (blue) 23

24 Price Price Intensity Methodology March 23, 27 9: 1: 11: 12: 13: 14: Time 1:3 1:32 1:34 1:36 1:38 1:4 n =.43 We split the entire interval of the analysis (25-212) into 1 minutes intervals, rolling them with a step of 1 minute within the RTH In each of these windows we have calibrated the Hawkes model with the short-term exponential kernel on the timestamps of mid-quote price changes Each calibration resulted in a single estimation of the branching ration (n) We have performed residual analysis and rejected bad fits (using KS-test) Collecting all estimates for each month (~6-7 estimates) we have averaged them to construct the endogeneity index for the given month 24

25 Mechanisms of self-reflexivity milliseconds seconds minutes hours days weeks months years High-frequency trading Stop-loss orders Algorithmic trading Optimal execution Margin calls Imitation Long-term herding 25

26 Benchmark: Financial markets (E-mini S&P 5) Volume 1M 5M Monthly volume Number of events per month 4M 3M 2M 1M Number of events Trading activity proxied by volume and number of mid-price changes Volatility.1.5 Daily volatility Daily closing price 15 1 Price Dynamics of price and volatility Background activity Branching ratio Year 5 Rate of exogenous events (triggered by idiosyncratic news ) Branching ratio that quantifies endogeneity of the system (fraction of endogenous events in the system) Data source: TRTH Filimonov V., Sornette D. (212) Physical Review E 85(5), 5618 Filimonov V., Bicchetti D., Maystre N., Sornette D. (214) J. of Int. Money and Finance, 42,

27 Crude Oil: Brent and WTI Brent Crude (ICE Europe) Daily volatility Daily closing price 15 Daily volatility Daily closing price WTI (NYMEX) 15 Volatility Price Volatility Price 5M 1M 4M 8M Volume 3M 2M Volume 6M 4M 1M 2M.8.8 Branching ratio Branching ratio Year Year Data source: TRTH Filimonov V., Bicchetti D., Maystre N., Sornette D. (214) J. of Int. Money and Finance, 42,

Price Volume Total rate Branching ratio Exogenous vs endogenous shocks in HF 121 12 119 118 117 1K 8K 6K 4K 2K K 3 2.5 2 1.5 1.5.9.8.7 A1 B1 C1 D1 April 27, 21 21 116 114 112 11 18 16 1K 8K 6K 4K 2K K 7 6 5 4 3 2 1.

28 Price Volume Total rate Branching ratio Exogenous vs endogenous shocks in HF K 8K 6K 4K 2K K A1 B1 C1 D1 April 27, K 8K 6K 4K 2K K A2 B2 C2 D2 May May 6, 6, 21 April 27, 21: Significant fall of most of US markets following the cut of the credit rating of Greece and Portugal May 6, 21 ( flash-crash ): The activity of high-frequency traders of the S&P 5 E-mini futures contracts leaded to a dramatic fall in other markets Volume and Trading activity behave similar in both cases Branching ratio ( endogeneity index ) reveals fundamental difference between two shocks.6 9:3 1:3 11:3 12:3 13:3 14:3 15:3 Time, EST.6 9:3 1:3 11:3 12:3 13:3 14:3 15:3 Time, EST Source: V. Filimonov, D. Sornette (212) PRE 85 (5):

29 References Filimonov V., Sornette D. (212) Quantifying reflexivity in financial markets: Toward a prediction of flash crashes. Physical Review E, 85(5), doi:1.113/physreve , Filimonov V., Bicchetti D., Maystre N., Sornette D. (214) Quantification of the High Level of Endogeneity and of Structural Regime Shifts in Commodity Markets. Journal of International Money and Finance, 42, doi:1.116/j.jimonfin , Filimonov V., Sornette D. (213) Apparent criticality and calibration issues in the Hawkes self-excited point process model: application to high-frequency financial data. arxiv: Filimonov V., Wheatley S., Sornette D. (213) Effective measure of reflexivity of the self-excited Hawkes and Autoregressive Conditional Duration point processes. arxiv: Wheatley S., Filimonov V., Sornette D. (214) Estimation of the Hawkes Process with Renewal Process Immigration using an EM Algorithm. Working paper 29

Reflexivity in financialized commodity futures markets. The role of information

UNCTAD United Nations Conferenceence on Trade and Development Reflexivity in financialized commodity futures markets. The role of information Vladimir Filimonov ETH Zurich, D-MTEC, Chair of Entrepreneurial