Large events on the stock market: A study of high resolution data

Kertész JánosInstitute of Physics, BME

withAdam Zawadowski (BME)Tóth Bence (BME)György Andor (BME)Doyne Farmer (Santa Fe, Rome)

LARGE PRICE CHANGES ON SMALL SCALES

BUX index, Nov 12, 200115:17 AA 587 crashes inNew York

GM

LARGE CHANGES, SCALES, CAUSES

Prices fluctuate – large events happen unusually oftenIn 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 fluctuationOften “no basic reason”.

• 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 level2.1% 400 99%! (Too long!)

Smaller but significant in the first 10 mins

Buy at event, sell after 400 mins and gain 1.3% with 95% confwhere the B/AS was taken into account.

Be careful, no transaction costs were considered!

NYSE NASDAQ

Relaxation function (characteristic for response):

Autocorrelation function (characteristic for steady state):

Response decayssignificantly 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 daysGSKJanuary 2002

Data from the London Stock Exchange 05.2000 to 12.2002

variable exponentvolatility 0.38bid-ask spread 0.38limit orders placed - bid 0.37limit orders placed - ask 0.40cancelations - bid 0.30cancelations - 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)