Large events on the stock market: A study of high resolution data Kertész János Institute of Physics, BME with Adam Zawadowski (BME) Tóth Bence (BME) György Andor (BME) Doyne Farmer (Santa Fe, Rome)

LARGE PRICE CHANGES ON SMALL SCALES BUX index, Nov 12, :17 AA 587 crashes in New York

GM

LARGE CHANGES, SCALES, CAUSES Prices fluctuate – large events happen unusually often In a Gaussian world the Black Tuesday 1929, Black Monday 1987, etc. should practically never happen Similarly (or even more so): Large events on small scales are significantly frequent (fat tails in price distributions). Correlations (esp. in the volatility) are present. Large price changes (LPC-s) are of major interest: Prediction (???): Free lunch (but Efficient Market Hypothesis (EMH)) Understanding mechanism  Stabilizing markets

Why large price moves? Price changes due to “news”: response to external force “Internal” market mechanism affects fluctuation Often “no basic reason”.

OTHER STUDIES ON LARGE PRICE CHANGES Average shape around LPC-s Mostly daily price changes of  10%,  20 days Abnormal returns calculated using  analysis (takes into account the general trend by relating price to an index). AMEX, NYSE, TSE, Johannesburg studied by dif. groups Overshooting found Up-down asymmetry: Either no or weaker overreaction for increases Cox et al. and Atkins et al. compared the overreaction to the bid-ask spread and concluded that no profit could be gained Overshooting does not necessarily contradict EMH.

Omori law for market crashes (Lillo & Mantegna, 2002): There are aftershocks in the volatility described by a power law. Three events (1987, 1997, 1998), daily data, no universal behavior, no signature of internal/external origin. Exogenous vs. endogenous LPC-s (Sornette and Helmstetter, 2003) Three events (1987, 1991, 2001). Black Monday endo, Gorbachev, 9.11 exo Power law decay of excess volatility with larger exponent for exo.

Intraday price changes > (4%  8  ) Significant overreaction in the first 20 min-s. After drop 1.2% in 50 trading minutes at 99% significance level 2.1% %! (Too long!) Smaller but significant in the first 10 mins Buy at event, sell after 400 mins and gain 1.3% with 95% conf where the B/AS was taken into account. Be careful, no transaction costs were considered!

NYSENASDAQ

Relaxation function (characteristic for response): Autocorrelation function (characteristic for steady state): Response decays significantly faster than autocorrelations

Stock Markets: Double auction, where buyers and sellers put public limit orders in arbitrary sequence into the Limit Order Book (LOB). Orders immediately executed are the market orders. The rules of execution are regulated in detail. These are the microscopic laws of the market, and the LOB contains the microscopic dynamics.

32 days GSK January 2002 Data from the London Stock Exchange to

variable exponent volatility 0.38 bid-ask spread 0.38 limit orders placed - bid 0.37 limit orders placed - ask 0.40 cancelations - bid 0.30 cancelations - ask 0.42 Is slow decay due to „psychology” or intrinsic to the market? Simple zero intelligence model leads to power law decay in excess volatility and spread with larger exponent (~1/2).

SUMMARY Large event in high resolution financial data Often overreaction in intraday data. The decay of the volatility autocorrelation function is slower than that of the response Empirics: „Power law” decay of relaxation functions of volatility and bid/ask spread, imbalance, number of cancellations etc. Mysterious 0.4 exponent… Differenciating between human and intrinsic The NASDAQ puzzle (B/A spread) Large events are mostly due to liquidity problems and not caused by volume (not discussed here but our data reinforce this view)