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@sebjai
Last active August 26, 2023 04:31
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Description\n",
"This notebook looks at some simple statistics of histortical intraday equity data. First we look at midprice and microprice, then order imbalance, stamped every 100 millisecond of the trading day. We will see that order imbalance tends to mean-revert, and has siginificant auto-correlation. Next, we look at the behaviour of order imbalance an instant before market order buys or sells arrive. The interesting aspect of this is that buy orders tend to arrive when the order imbalance is tilted to the buy side, while sell orders tend to arrive when the order imbalance is tilted to the sell side."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# import packages\n",
"\n",
"import scipy.io as sio # for loading matlab data\n",
"\n",
"import numpy as np # for numerical libs\n",
"\n",
"from matplotlib.ticker import FuncFormatter # for custom bar plot labels\n",
"\n",
"import matplotlib.pyplot as plt # for plotting\n",
"\n",
"import matplotlib.pylab as pylab\n",
"params = {'legend.fontsize': 'x-large',\n",
" 'figure.figsize': (15, 5),\n",
" 'axes.labelsize': 'x-large',\n",
" 'axes.titlesize':'x-large',\n",
" 'xtick.labelsize':'x-large',\n",
" 'ytick.labelsize':'x-large'}\n",
"pylab.rcParams.update(params)\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# load data"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"data = sio.loadmat('MSFT_20141103.mat')"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true,
"scrolled": true
},
"outputs": [],
"source": [
"LOB=data['LOB']\n",
"\n",
"t = (np.array((LOB['EventTime'][0][0][:,0]))-3600000*9.5)*1e-3\n",
"bid = np.array(LOB['BuyPrice'][0][0]*1e-4)\n",
"bidvol = np.array(LOB['BuyVolume'][0][0]*1.0)\n",
"ask = np.array(LOB['SellPrice'][0][0]*1e-4)\n",
"askvol = np.array(LOB['SellVolume'][0][0]*1.0)\n",
"MO=np.array(LOB['MO'][0][0]*1.0)\n",
"dt = t[1]-t[0]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Midprice, Microprice and Spread\n",
"\n",
"Let $P^b_t$ and $P_t^a$ denote the best bid and ask prices, and $V_t^b$ and $V_t^a$ denote the volume posted at the best bid and ask. Then,\n",
"\n",
"$$midprice_t=\\tfrac{1}{2}(P^b_t+P^a_t)$$\n",
"\n",
"$$microprice_t=\\frac{P^b_t\\,V^a_t+P^a_t\\,V^b_t}{V^a_t+V^b_t}$$\n",
"\n",
"$$spread_t=P_t^a-P_t^b$$"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"midprice = 0.5*(bid[:,0]+ask[:,0])\n",
"microprice= (bid[:,0]*askvol[:,0]+ask[:,0]*bidvol[:,0])/(bidvol[:,0]+askvol[:,0])\n",
"spread = ask[:,0]-bid[:,0]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"plot microprice"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
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J6ueHsvwfg0tmwMKvOjaqTlxUJB/e1YMRphTWJZYKof8Y1YYbujemQfWK3N67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\nSZK6ZPIoSZIkSerS/w9/uaFzWreiyAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1ea90043780>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(t, microprice)\n",
"plt.title('Microprice')\n",
"plt.ylabel('price')\n",
"plt.xlabel('time (seconds from trading start)')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"plot the difference between micro and mid prices"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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nk0iSRy3XEZEnEQg4/6aU2mm5olKDlFItlVIta9SoEcFLExERERERnXwSOeDcA6CW6bGa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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1ea909c32b0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(t, microprice-midprice)\n",
"plt.title('Microprice - Midprice')\n",
"plt.ylabel('diff')\n",
"plt.xlabel('time (seconds from trading start)')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that the difference is typically in the range $[-0.01, 0.01]$ while at the beginning of the day it is three times as large."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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YD7xmr5rtBrCpq5v9P1faXcw75z018y++dS5f/e3sftN+efwbmDF9l37TTvr5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\nRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1ea90a854a8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(t,spread)\n",
"plt.title('Spread')\n",
"plt.ylabel('spread')\n",
"plt.xlabel('time (seconds from trading start)')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This plot shows that the spread is about 0.13 in the morning, but quickly drops to 0.01 but sometimes spikes to 0.02 (mostly in the morning)."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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S1CsTT0mSJElSr6Yt8UxyapIa4/PcTsy+Sa5L8mCSFUnOSLLFUD1zk3wmyer2c3GSHYZi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\nP3tJkiRJmr2mc8b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QkGRPmtWyJtveTDLqsSfJscCFwO9O8B8g0NyX/wDrf3ZoJhv52I9h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\nSb0y8ZQkSZIk9crEU5IkSZLUq/8LJtY10rvXSvYAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1ea90c2f860>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.hist(spread,bins=[0.01,0.02,0.03], width=0.001,align='mid') \n",
"plt.title(\"Hist of spread\")\n",
"plt.xlabel(r'spread')\n",
"plt.ylabel('Freq')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Volume Imbalance\n",
"Now, let us look at how volume imbalance at the best bid and ask varies through the day\n",
"$$\\rho_t=\\frac{V_t^b-V_t^a}{V_t^b+V_t^a}\\in(-1,1)$$"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"rho = np.array((bidvol[:,0]-askvol[:,0])/(bidvol[:,0]+askvol[:,0]),ndmin=2).T"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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UVlZi3rx5mDp1Ku644w7dz0UQeuGxggj/dIQwCBI6CU08LOFr+bv5W/G3z3fh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\nS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yGalWUd8zUI1FnSluAXew6yJyTw8KC03fZONuHTT/lZFFndMB+C5M+MCxcMwfUrRgad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\nTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1ea90ab0898>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(t, rho)\n",
"plt.title('Imbalance')\n",
"plt.ylabel(r'$\\rho$')\n",
"plt.xlabel('time (seconds from trading start)')\n",
"\n",
"a = plt.axes([.65, .6, .2, .2])\n",
"idx = (t>3600) & (t<=3600+60)\n",
"plt.plot( t[idx], rho[idx])\n",
"plt.title('a')\n",
"plt.ylabel(r'$\\rho$')\n",
"plt.xlabel(r'$t$')\n",
"plt.xticks([3600,3630,3660])\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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SJK2cboaJXg2c3FZ2CrC9lHLzPOvsXz/e2VY+B6T78CRJkiRJg9BNMngRsCHJq5M8KMnp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\nRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1ea91171710>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.acorr(rho[:,0]-np.mean(rho[:,0]),maxlags=6000) # maximum one minute \n",
"plt.title('Autocorrelation of imbalance')\n",
"plt.xlim([0,6000])\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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kg1X18tbaV3exXZt43Z3BMVV1WpLTkuRRj3rUPHYDAACwvi3nkNcdSb4wSiZ72/rXR4/F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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1ea90aa94a8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.hist(rho, bins=np.linspace(-1, 1, num=50)) \n",
"plt.title(\"Hist of imbalance\")\n",
"plt.xlabel(r'$\\rho$')\n",
"plt.ylabel('Freq')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The raw imbalance"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"## transform imbalance using logit\n",
"y = -np.log(2/(1+rho)-1)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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SJEmSNPeMdY7n/wQ2H+wk+VGSbXpozwJg5VDZys6xNcUM4hYMxY5U1+DYFjSJ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\nVyaekiRJkqRe/f9okN2zWnVGVgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1ea90ab0e80>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.hist(y, bins=np.linspace(-5, 5, num=50)) \n",
"plt.title(\"Hist of transformed imbalance\")\n",
"plt.xlabel('y')\n",
"plt.ylabel('Freq')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Volume Imbalance at times of Market Orders"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"rho_MO = (MO[:,3]-MO[:,4])/(MO[:,3]+MO[:,4])"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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BwI3ABTT3rfwR8IKqmsp1lpIkSZKkSYxUD+UgVXUMcExf2XJgj0m2WwUcstYC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\nJpSSJEmSpE7+f9dKWUcciRAjAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1ea9381b828>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.hist(rho_MO[MO[:,7]==-1], bins=np.linspace(-1, 1, num=10),alpha=0.5)\n",
"plt.hist(rho_MO[MO[:,7]==+1], bins=np.linspace(-1, 1, num=10),alpha=0.5)\n",
"plt.title(\"Hist of imbalance conditional on MO type\")\n",
"plt.xlabel(r'$\\rho$')\n",
"plt.ylabel('Freq')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"# determine the rate of arrival of market orders conditional on order arrival in a specific bin \n",
"def MOActivity(MO,rho,a,b):\n",
" idx_rho = (rho>=a) & (rho<b)\n",
" idx_rho_MO = (rho_MO>=a) & (rho_MO<b)\n",
" idx_rho_MO_b = idx_rho_MO & (MO[:,7]==-1)\n",
" idx_rho_MO_s = idx_rho_MO & (MO[:,7]==+1)\n",
" \n",
" return [np.sum(idx_rho_MO_b), np.sum(idx_rho_MO_s)]/(dt*np.sum(idx_rho))"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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M4j6HG4BM8fw6YN1kjyVJkiRJg7eorlYqSZIkSZofJoeSJEmSJJNDSZIkSZLJoSRJkiQJ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\nl0rtrcByXf0AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1ea95d91a20>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"nbands=5\n",
"bands = np.array([-1+2*x/(nbands) for x in range(nbands+1)])\n",
"\n",
"MO_activity=np.zeros((nbands,2))\n",
"for i in range(nbands):\n",
" MO_activity[i,:] = MOActivity(MO,rho,bands[i],bands[i+1])\n",
"MO_activity=MO_activity.T\n",
"\n",
"plt.bar(bands[0:nbands],MO_activity[0,:],width=[(bands[j+1]-bands[j])*0.9 for j in range(nbands)],alpha=0.4)\n",
"plt.bar(bands[0:nbands],MO_activity[1,:],width=[(bands[j+1]-bands[j])*0.9 for j in range(nbands)],alpha=0.4)\n",
"plt.title(r'Rate of Arrival of MOs conditional on $\\rho\\in[a,b)$')\n",
"plt.xlabel(r'$\\rho\\in[a,b)$')\n",
"plt.ylabel(r'$\\lambda$')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [],
"source": [
"def GenerateRhoTransition(rho,bands):\n",
" rho_band = np.zeros((rho.size,1))\n",
"\n",
" for i in range(bands.size-1):\n",
" idx_i = (rho>=bands[i]) & (rho<bands[i+1])\n",
" rho_band[idx_i]=i\n",
"\n",
" rho_A = np.zeros((bands.size-1,bands.size-1))\n",
" norm = np.zeros(bands.size-1)\n",
" for i in range(bands.size-1):\n",
"\n",
" idx_i = (rho_band==i)\n",
"\n",
" idx_ip1 = idx_i\n",
" idx_ip1[1:idx_i.size-1] = idx_i[0:idx_i.size-2]\n",
"\n",
" for j in range(bands.size-1):\n",
" rho_A[i][j] = np.sum( rho_band[idx_ip1]==j )\n",
" norm[i]+=rho_A[i][j]\n",
"\n",
" for j in range(bands.size-1):\n",
" rho_A[i][j] /=norm[i]\n",
" \n",
" return rho_A"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [],
"source": [
"rho_A = GenerateRhoTransition(rho,bands)"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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ouSFjZtPTJLJpjqTtLevrI2J9vx/ba4e8IbcR+Bng9IgYe/TgiGtadr1V0tfI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\nA7kxZ2ZmZmZm1kBuzJmZmZmZmTXQ/wPSPC+o45dzMwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1eaa04e5c88>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, axarr = plt.subplots(1,3)\n",
"im = axarr[0].imshow(np.linalg.matrix_power(rho_A,int(np.round(1/dt))))\n",
"axarr[0].set_title(r'$\\rho$ transition 1s')\n",
"fig.colorbar(im, ax=axarr[0])\n",
"\n",
"im=axarr[1].imshow(np.linalg.matrix_power(rho_A,int(np.round(5/dt))))\n",
"axarr[1].set_title(r'$\\rho$ transition 5s')\n",
"fig.colorbar(im, ax=axarr[1])\n",
"\n",
"im=axarr[2].imshow(np.linalg.matrix_power(rho_A,int(np.round(60/dt))))\n",
"axarr[2].set_title(r'$\\rho$ transition 60s')\n",
"fig.colorbar(im, ax=axarr[2])\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
@HarmonicReflux
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Dear Sebastian,

Many thanks for sharing your analysis.

I yield an error in the second line as "MO" within 'MSFT_20141103.mat' is not defined.

data = sio.loadmat('MSFT_20141103.mat') # loads the data ok
MO=np.array(LOB['MO'][0][0]*1.0) # returns an error message as "MO" is not stored within data.

appearance_of_data_in_Matlab

Can you please share the link to the .mat file that you process in the notebook?

Many thanks,

Best,
Ben

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