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AvellanedaStoikovFinal.py
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AvellanedaStoikovFinal.py
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# -*- coding: utf-8 -*-
"""
Created on Thu Oct 12 16:40:52 2017
@author: Marco Dibo
"High-frequency trading in a limit order book"
by Marco Avellaneda and Sasha Stoikov"
"""
## Montecarlo simulation with numpy ##
import math
import numpy as np
import matplotlib.pyplot as plt
import random
#Parameters for mid price simulation:
S0 = 100. #initial price
T = 1.0 #time
sigma = 2 #volatility
M = 200 #number of time steps
dt = T/M #time step
Sim = 1000 #number of simulations
gamma = 0.1 #risk aversion
k = 1.5
A = 140
I = 1
#Results:
AverageSpread = []
Profit = []
Std = []
for i in range(1, Sim+1):
###reservation price:
### r(s,t) = s - q * gamma * sigma**2 * (T-t)
S = np.zeros((M+1,I))
Bid = np.zeros((M+1,I))
Ask = np.zeros((M+1,I))
ReservPrice = np.zeros((M+1,I))
spread = np.zeros((M+1,I))
deltaB = np.zeros((M+1,I))
deltaA = np.zeros((M+1,I))
q = np.zeros((M+1,I))
w = np.zeros((M+1,I))
equity = np.zeros((M+1,I))
reserve_relation = np.zeros((M+1,I))
S[0] = S0
ReservPrice[0] = S0
Bid[0] = S0
Ask[0] = S0
spread[0] = 0
deltaB[0] = 0
deltaA[0] = 0
q[0] = 0 #position
w[0] = 0 #wealth
equity[0] = 0
for t in range(1, M+1):
z = np.random.standard_normal(I)
S[t] = S[t-1] + sigma * math.sqrt(dt) * z
ReservPrice[t] = S[t] - q[t-1] * gamma * (sigma ** 2) * (T - t/float(M))
spread[t] = gamma * (sigma **2) * (T - t/float(M)) + (2/gamma) * math.log(1 + (gamma/k))
Bid[t] = ReservPrice[t] - spread[t]/2.
Ask[t] = ReservPrice[t] + spread[t]/2.
deltaB[t] = S[t] - Bid[t]
deltaA[t] = Ask[t] - S[t]
lambdaA = A * np.exp(-k * deltaA[t])
ProbA = lambdaA * dt
fa = random.random()
lambdaB = A * np.exp(-k * deltaB[t])
ProbB = lambdaB * dt
fb = random.random()
if ProbB > fb and ProbA < fa :
q[t] = q[t-1] + 1
w[t] = w[t-1] - Bid[t]
if ProbB < fb and ProbA > fa :
q[t] = q[t-1] - 1
w[t] = w[t-1] + Ask[t]
if ProbB < fb and ProbA < fa :
q[t] = q[t-1]
w[t] = w[t-1]
if ProbB > fb and ProbA > fa:
q[t] = q[t-1]
w[t] = w[t-1] - Bid[t]
w[t] = w[t] + Ask[t]
equity[t] = w[t] + q[t] * S[t]
AverageSpread.append(spread.mean())
Profit.append(equity[-1])
Std.append(equity[-1])
print (" Results ")
print ("----------------------------------------")
print ("%14s %21s" % ('statistic', 'value'))
print (40 * "-")
print ("%14s %20.5f" % ("Average spread :", np.array(AverageSpread).mean()))
print ("%16s %20.5f" % ("Profit :", np.array(Profit).mean()))
print ("%16s %20.5f" % ("Std(Profit) :", np.array(Std).std()))
#Plots:
x = np.linspace(0., T, num= (M+1))
fig=plt.figure(figsize=(10,8))
plt.subplot(2,1,1) # number of rows, number of columns, number of the subplot
plt.plot(x,S[:], lw = 1., label = 'S')
plt.plot(x,Ask[:], lw = 1., label = 'Ask')
plt.plot(x,Bid[:], lw = 1., label = 'Bid')
plt.grid(True)
plt.legend(loc=0)
plt.ylabel('P')
plt.title('Prices')
plt.subplot(2,1,2)
plt.plot(x,q[:], 'g', lw = 1., label = 'q') #plot 2 lines
plt.grid(True)
plt.legend(loc=0)
plt.axis('tight')
plt.xlabel('Time')
plt.ylabel('Position')
#Histogram of profit:
plt.figure(figsize = (7,5))
plt.hist(np.array(Profit), label = ['Inventory strategy'], bins = 100)
plt.legend(loc = 0)
plt.grid(True)
plt.xlabel('pnl')
plt.ylabel('number of values')
plt.title('Histogram')
#PNL:
plt.figure(figsize = (7,5))
plt.plot(np.array(equity), label = 'Inventory strategy')
plt.legend(loc = 0)
plt.grid(True)
plt.xlabel('pnl')
plt.ylabel('number of values')
plt.title('Profit')