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main.py
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main.py
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import numpy as np
import matplotlib.pyplot as pp
from src.hjb_solvers import (
MM_Model_Parameters,
AS2P_Finite_Difference_Solver,
AS3P_Finite_Difference_Solver,
ASAS_Finite_Difference_Solver
)
def create_as2p_model_solutions():
lambda_m = 50
lambda_p = 50
kappa_m = 10
kappa_p = 10
epsilon_m = 0
epsilon_p = 0
delta = 0
phi = 0.0001
alpha = 0.00001
q_min = -25
q_max = 25
cost = 0.000
rebate = 0.0025
tick = 0.5
T = 1 # minutes
n = 5 * 500 # one step per second
parameters = MM_Model_Parameters(lambda_m, lambda_p, kappa_m, kappa_p, delta, epsilon_m, epsilon_p,
phi, alpha, q_min, q_max, T, cost, rebate, tick)
solution = AS2P_Finite_Difference_Solver.solve(parameters, N_steps=n)
fig, ax = pp.subplots(1, 2, figsize=(12, 4))
ax[0].plot(solution.t_grid, solution.get_l_plus(20))
ax[0].plot(solution.t_grid, solution.get_l_plus(10))
ax[0].plot(solution.t_grid, solution.get_l_plus(0))
ax[0].plot(solution.t_grid, solution.get_l_plus(-10))
ax[0].plot(solution.t_grid, solution.get_l_plus(-20))
ax[0].set_title("Ask skews")
ax[0].set_ylabel("Skew")
ax[0].set_xlabel("Time")
ax[1].plot(solution.t_grid, solution.get_l_minus(20))
ax[1].plot(solution.t_grid, solution.get_l_minus(10))
ax[1].plot(solution.t_grid, solution.get_l_minus(0))
ax[1].plot(solution.t_grid, solution.get_l_minus(-10))
ax[1].plot(solution.t_grid, solution.get_l_minus(-20))
ax[1].set_title("Bid skews")
ax[1].set_ylabel("Skew")
ax[1].set_xlabel("Time")
pp.show()
def create_as3p_model_solutions():
lambda_m = 50
lambda_p = 50
kappa_m = 100
kappa_p = 100
delta = 0
epsilon_m = 0
epsilon_p = 0
phi = 0.000001
alpha = 0.0001
q_min = -5
q_max = 5
cost = 0.005
rebate = 0.0025
tick = 0.5
T = 5 # minutes
n = 5*60 # one step per second
d_grid = np.linspace(0, 0.1, 100)
fig, ax = pp.subplots(figsize=[3.5, 3]);
pp.plot(d_grid, lambda_p*np.exp(-kappa_p*d_grid),
color='blue', lw=3)
ax.set_xlabel('distance from mid')
ax.set_ylabel('fill rate (fills/minute)')
parameters = MM_Model_Parameters(lambda_m, lambda_p, kappa_m, kappa_p, delta, epsilon_m, epsilon_p,
phi, alpha, q_min, q_max, T, cost, rebate, tick)
impulses, model = AS3P_Finite_Difference_Solver.solve(parameters, N_steps=n)
# Plot the value function
Y = model.q_grid
X = model.t_grid
X, Y = np.meshgrid(X,Y)
f = pp.figure(figsize=[5, 4]);
pp3d = pp.axes(projection="3d", elev=20, azim=50);
pp3d.set_title("Value function");
pp3d.set_xlabel("Minute");
pp3d.set_ylabel("Inventory");
pp3d.set_zlabel("Value");
pp3d.plot_surface(X, Y, model.h, cmap='magma');
#f.savefig("./graphs/value_function.pdf", bbox_inches='tight')
# Plot the impulse regions
from matplotlib import colors
import matplotlib.patches as mpatches
mycolors = ['white', 'blue', 'red']
cmap = colors.ListedColormap(mycolors)
f, ax = pp.subplots(figsize=[4, 4])
ax.imshow(impulses, cmap=cmap, aspect='auto')
ax.set_xticks([0, 0.5*n, n])
ax.set_xticklabels([0, int(0.5*n), n],fontsize=8);
ax.set_yticks(np.arange(0, len(model.q_grid), 2));
ax.set_yticklabels(model.q_grid[::2],fontsize=8);
ax.set_ylabel('Inventory')
ax.set_xlabel('Second')
#f.savefig("./graphs/impulse_regions.pdf", bbox_inches='tight')
# Plot the ask spread for continuation region
f, ax = pp.subplots(figsize=[5, 4])
for q in range(3, -4, -1):
ax.plot(model.l_p[q], label=f'q={q}')
ax.set_title("Ask to mid spread")
pp.legend()
#f.savefig("./graphs/ask_to_mid_spread.pdf", bbox_inches='tight')
# Plot the bid spread for continuation region
fig, ax = pp.subplots(figsize=[5, 4])
for q in range(3, -4, -1):
ax.plot(model.l_m[q], label=f'q={q}')
ax.set_title("Bid to mid spread")
pp.legend()
#f.savefig("./graphs/bid_to_mid_spread.pdf", bbox_inches='tight')
pp.show()
def create_asas_model_solutions():
lambda_m = 40
lambda_p = 40
kappa_m = 1.0/10
kappa_p = 1.0/10
epsilon_m = 30
epsilon_p = 30
delta = 0
phi = 0.01
alpha = 0.01
q_min = -6
q_max = 6
cost = 0.000
rebate = 0.0025
tick = 0.5
T = 10 # minutes
n = 500 # one step per second
parameters = MM_Model_Parameters(lambda_m, lambda_p, kappa_m, kappa_p, delta, epsilon_m, epsilon_p,
phi, alpha, q_min, q_max, T, cost, rebate, tick)
solution = ASAS_Finite_Difference_Solver.solve(parameters, N_steps=n)
fig, ax = pp.subplots(1, 2, figsize=(12, 4))
ax[0].plot(solution.t_grid, solution.get_l_plus(2))
ax[0].plot(solution.t_grid, solution.get_l_plus(1))
ax[0].plot(solution.t_grid, solution.get_l_plus(0))
ax[0].plot(solution.t_grid, solution.get_l_plus(-1))
ax[0].plot(solution.t_grid, solution.get_l_plus(-2))
ax[0].set_title("Ask skews")
ax[0].set_ylabel("Skew")
ax[0].set_xlabel("Time")
ax[1].plot(solution.t_grid, solution.get_l_minus(2))
ax[1].plot(solution.t_grid, solution.get_l_minus(1))
ax[1].plot(solution.t_grid, solution.get_l_minus(0))
ax[1].plot(solution.t_grid, solution.get_l_minus(-1))
ax[1].plot(solution.t_grid, solution.get_l_minus(-2))
ax[1].set_title("Bid skews")
ax[1].set_ylabel("Skew")
ax[1].set_xlabel("Time")
pp.show()
if __name__ == '__main__':
#create_as2p_model_solutions()
#create_as3p_model_solutions()
create_asas_model_solutions()