def plot_price_model(seed=0, num_days=1000):
# Create a simulation environment
env = sca.MarketEnvironment()
# Reset the enviroment with the given seed
env.reset(seed)
# Create an array to hold the daily stock price for the given number of days
price_hist = np.zeros(num_days)
# Get the simulated stock price movement from the environment
for i in range(num_days):
_, _, _, info = env.step(i)
price_hist[i] = info.price
# Print Average and Standard Deviation in Stock Price
print('Average Stock Price: ${:,.2f}'.format(price_hist.mean()))
print('Standard Deviation in Stock Price: ${:,.2f}'.format(
price_hist.std()))
# print('Standard Deviation of Random Noise: {:,.5f}'.format(np.sqrt(env.singleStepVariance * env.tau)))
# Plot the price history for the given number of days
price_df = pd.DataFrame(data=price_hist,
columns=['Stock'],
dtype='float64')
ax = price_df.plot(colormap='cool', grid=False)
ax.set_facecolor(color='k')
ax = plt.gca()
yNumFmt = mticker.StrMethodFormatter('${x:,.2f}')
ax.yaxis.set_major_formatter(yNumFmt)
plt.ylabel('Stock Price')
plt.xlabel('days')
plt.show()
def get_optimal_vals(lq_time=60, nm_trades=60, tr_risk=1e-6, title=''):
# Create a simulation environment
env = sca.MarketEnvironment()
# Reset the enviroment with the given parameters
env.reset(liquid_time=lq_time, num_trades=nm_trades, lamb=tr_risk)
# Set the title for the AC Optimal Strategy table
if title == '':
title = 'AC Optimal Strategy'
else:
title = 'AC Optimal Strategy for ' + title
# Get the AC optimal values from the environment
E = env.get_AC_expected_shortfall(env.total_shares)
V = env.get_AC_variance(env.total_shares)
U = env.compute_AC_utility(env.total_shares)
left_col = [('Number of Days to Sell All the Shares:',
['{}'.format(env.liquidation_time)]),
('Half-Life of The Trade:', ['{:,.1f}'.format(1 / env.kappa)]),
('Utility:', ['${:,.2f}'.format(U)])]
right_col = [('Initial Portfolio Value:',
['${:,.2f}'.format(env.total_shares * env.startingPrice)]),
('Expected Shortfall:', ['${:,.2f}'.format(E)]),
('Standard Deviation of Shortfall:',
['${:,.2f}'.format(np.sqrt(V))])]
# Generate the table with the AC optimal values
val_table = generate_table(left_col, right_col, title)
return val_table
def get_av_std(lq_time=60, nm_trades=60, tr_risk=1e-6, trs=100):
# Create simulation environment
env = sca.MarketEnvironment()
# Reset the enviroment
env.reset(liquid_time=lq_time, num_trades=nm_trades, lamb=tr_risk)
# Get the trading list
trl = env.get_trade_list()
# Since we are not selling fractional shares we round up the shares in the trading list
trade_list = round_trade_list(trl)
# Set the initial shortfall to zero
shortfall_hist = np.array([])
for episode in range(trs):
# Print current episode every 100 episodes
if (episode + 1) % 100 == 0:
print('Episode [{}/{}]'.format(episode + 1, trs),
end='\r',
flush=True)
# Reset the enviroment
env.reset(seed=episode,
liquid_time=lq_time,
num_trades=nm_trades,
lamb=tr_risk)
# set the environment to make transactions
env.start_transactions()
for trade in trade_list:
action = trade / env.shares_remaining
_, _, _, info = env.step(action)
if info.done:
shortfall_hist = np.append(shortfall_hist,
info.implementation_shortfall)
break
print('Average Implementation Shortfall: ${:,.2f}'.format(
shortfall_hist.mean()))
print(
'Standard Deviation of the Implementation Shortfall: ${:,.2f}'.format(
shortfall_hist.std()))
plt.plot(shortfall_hist, 'cyan', label='')
plt.xlim(0, trs)
ax = plt.gca()
ax.set_facecolor('k')
ax.set_xlabel('Episode', fontsize=15)
ax.set_ylabel('Implementation Shortfall (US $)', fontsize=15)
ax.axhline(shortfall_hist.mean(), 0, 1, color='m', label='Average')
yNumFmt = mticker.StrMethodFormatter('${x:,.0f}')
ax.yaxis.set_major_formatter(yNumFmt)
plt.legend()
plt.show
def implement_trade_list(seed=0, lq_time=60, nm_trades=60, tr_risk=1e-6):
# Create simulation environment
env = sca.MarketEnvironment()
# Reset the environment with the given parameters
env.reset(seed=seed,
liquid_time=lq_time,
num_trades=nm_trades,
lamb=tr_risk)
# Get the trading list from the environment
trl = env.get_trade_list()
# Since we are not selling fractional shares we round up the shares in the trading list
trade_list = round_trade_list(trl)
# set the environment to make transactions
env.start_transactions()
# Create an array to hold the impacted stock price
price_hist = np.array([])
# Implement the trading list in our similation environment
for trade in trade_list:
# Convert the number of shares to sell in each trade into an action
action = trade / env.shares_remaining
# Take a step in the environment my selling the number of shares in the current trade
_, _, _, info = env.step(action)
# Get the impacted price from the environment
price_hist = np.append(price_hist, info.exec_price)
# If all shares have been sold, stop making transactions and get the implementation sortfall
if info.done:
print('Implementation Shortfall: ${:,.2f} \n'.format(
info.implementation_shortfall))
break
# Plot the impacted price
price_df = pd.DataFrame(data=price_hist,
columns=['Stock'],
dtype='float64')
ax = price_df.plot(colormap='cool', grid=False)
ax.set_facecolor(color='k')
ax.set_title('Impacted Stock Price')
ax = plt.gca()
yNumFmt = mticker.StrMethodFormatter('${x:,.2f}')
ax.yaxis.set_major_formatter(yNumFmt)
plt.plot(price_hist, 'o')
plt.ylabel('Stock Price')
plt.xlabel('Trade Number')
plt.show()
def plot_efficient_frontier(tr_risk = 1e-6):
# Create a simulation environment
env = sca.MarketEnvironment()
# Reset the enviroment with the given trader's risk aversion
env.reset(lamb = tr_risk)
# Get the expected shortfall and corresponding variance for the given trader's risk aversion
tr_E = env.get_AC_expected_shortfall(env.total_shares)
tr_V = env.get_AC_variance(env.total_shares)
# Create empty arrays to hold our values of E, V, and U
E = np.array([])
V = np.array([])
U = np.array([])
# Set the number of plot points for our frontier
num_points = 7000
# Set the values of the trader's risk aversion to plot
lambdas = np.linspace(1e-7, 1e-4, num_points)
# Calclate E, V, U for each value of llambda
for llambda in lambdas:
env.reset(lamb = llambda)
E = np.append(E, env.get_AC_expected_shortfall(env.total_shares))
V = np.append(V, env.get_AC_variance(env.total_shares))
U = np.append(U, env.compute_AC_utility(env.total_shares))
# Plot E vs V and use U for the colorbar
cm = plt.cm.get_cmap('gist_rainbow')
sc = plt.scatter(V, E, s = 20, c = U, cmap = cm)
plt.colorbar(sc, label = 'AC Utility', format = mticker.StrMethodFormatter('${x:,.0f}'))
ax = plt.gca()
ax.set_facecolor('k')
ymin = E.min() * 0.7
ymax = E.max() * 1.1
plt.ylim(ymin, ymax)
yNumFmt = mticker.StrMethodFormatter('${x:,.0f}')
xNumFmt = mticker.StrMethodFormatter('{x:,.0f}')
ax.yaxis.set_major_formatter(yNumFmt)
ax.xaxis.set_major_formatter(xNumFmt)
plt.xlabel('Variance of Shortfall')
plt.ylabel('Expected Shortfall')
# Get the annotation label and the correction factors
an_st, xcrf, ycrf, scrf = get_crfs(tr_risk)
# Plot the annotation in the above plot
plt.annotate(an_st, xy = (tr_V, tr_E), xytext = (tr_V * xcrf, tr_E * ycrf), color = 'w', size = 'large',
arrowprops = dict(facecolor = 'cyan', shrink = scrf, width = 3, headwidth = 10))
plt.show()
def get_env_param():
# Create a simulation environment
env = sca.MarketEnvironment()
# Set the title for the financial parameters table
fp_title = 'Financial Parameters'
# Get the default financial parameters from the simulation environment
fp_left_col = [('Annual Volatility:', ['{:.0f}%'.format(env.anv * 100)]),
('Daily Volatility:', ['{:.1f}%'.format(env.dpv * 100)])]
fp_right_col = [('Bid-Ask Spread:', ['{:.3f}'.format(env.basp)]),
('Daily Trading Volume:', ['{:,.0f}'.format(env.dtv)])]
# Set the title for the Almgren and Chriss Model parameters table
acp_title = 'Almgren and Chriss Model Parameters'
# Get the default Almgren and Chriss Model Parameters from the simulation environment
acp_left_col = [('Total Number of Shares for Agent1 to Sell:',
['{:,}'.format(env.total_shares1)]),
('Total Number of Shares for Agent2 to Sell:',
['{:,}'.format(env.total_shares2)]),
('Starting Price per Share:',
['${:.2f}'.format(env.startingPrice)]),
('Price Impact for Each 1% of Daily Volume Traded:',
['${}'.format(env.eta)]),
('Number of Days to Sell All the Shares:',
['{}'.format(env.liquidation_time)]),
('Number of Trades:', ['{}'.format(env.num_n)])]
acp_right_col = [
('Fixed Cost of Selling per Share:', ['${:.3f}'.format(env.epsilon)]),
('Trader\'s Risk Aversion for Agent 1:', ['{}'.format(env.llambda1)]),
('Trader\'s Risk Aversion for Agent 2:', ['{}'.format(env.llambda2)]),
('Permanent Impact Constant:', ['{}'.format(env.gamma)]),
('Single Step Variance:', ['{:.3f}'.format(env.singleStepVariance)]),
('Time Interval between trades:', ['{}'.format(env.tau)])
]
# Generate tables with the default financial and AC Model parameters
fp_table = generate_table(fp_left_col, fp_right_col, fp_title)
acp_table = generate_table(acp_left_col, acp_right_col, acp_title)
return fp_table, acp_table
def plot_trade_list(lq_time=60, nm_trades=60, tr_risk=1e-6, show_trl=False):
# Create simulation environment
env = sca.MarketEnvironment()
# Reset the environment with the given parameters
env.reset(liquid_time=lq_time, num_trades=nm_trades, lamb=tr_risk)
# Get the trading list from the environment
trade_list = env.get_trade_list()
# Add a zero at the beginning of the trade list to indicate that at time 0 we don't sell any stocks
new_trl = np.insert(trade_list, 0, 0)
# We create a dataframe with the trading list and trading trajectory
df = pd.DataFrame(data=list(range(nm_trades + 1)),
columns=['Trade Number'],
dtype='float64')
df['Stocks Sold'] = new_trl
df['Stocks Remaining'] = (np.ones(nm_trades + 1) *
env.total_shares) - np.cumsum(new_trl)
# Create a figure with 2 plots in 1 row
fig, axes = plt.subplots(nrows=1, ncols=2)
# Make a scatter plot of the trade list
df.iloc[1:].plot.scatter(x='Trade Number',
y='Stocks Sold',
c='Stocks Sold',
colormap='gist_rainbow',
alpha=1,
sharex=False,
s=50,
colorbar=False,
ax=axes[0])
# Plot a line through the points of the scatter plot of the trade list
axes[0].plot(df['Trade Number'].iloc[1:],
df['Stocks Sold'].iloc[1:],
linewidth=2.0,
alpha=0.5)
axes[0].set_facecolor(color='k')
yNumFmt = mticker.StrMethodFormatter('{x:,.0f}')
axes[0].yaxis.set_major_formatter(yNumFmt)
axes[0].set_title('Trading List')
# Make a scatter plot of the number of stocks remaining after each trade
df.plot.scatter(x='Trade Number',
y='Stocks Remaining',
c='Stocks Remaining',
colormap='gist_rainbow',
alpha=1,
sharex=False,
s=50,
colorbar=False,
ax=axes[1])
# Plot a line through the points of the scatter plot of the number of stocks remaining after each trade
axes[1].plot(df['Trade Number'],
df['Stocks Remaining'],
linewidth=2.0,
alpha=0.5)
axes[1].set_facecolor(color='k')
yNumFmt = mticker.StrMethodFormatter('{x:,.0f}')
axes[1].yaxis.set_major_formatter(yNumFmt)
axes[1].set_title('Trading Trajectory')
# Set the spacing between plots
plt.subplots_adjust(wspace=0.4)
plt.show()
print('\nNumber of Shares Sold: {:,.0f}\n'.format(new_trl.sum()))
if show_trl:
# Since we are not selling fractional shares we round up the shares in the trading list
rd_trl = round_trade_list(new_trl)
# rd_trl = new_trl
# We create a dataframe with the modified trading list and trading trajectory
df2 = pd.DataFrame(data=list(range(nm_trades + 1)),
columns=['Trade Number'],
dtype='float64')
df2['Stocks Sold'] = rd_trl
df2['Stocks Remaining'] = (np.ones(nm_trades + 1) *
env.total_shares) - np.cumsum(rd_trl)
df2.set_index('Trade Number', inplace=True)
# return df2.style.hide_index().format({'Trade Number': '{:.0f}', 'Stocks Sold': '{:,.0f}', 'Stocks Remaining': '{:,.0f}'})
return df2.style.format({
'Stocks Sold': '{:,.0f}',
'Stocks Remaining': '{:,.0f}'
})
import utils # Get the default financial and AC Model parameters financial_params, ac_params = utils.get_env_param() financial_params ac_params import numpy as np import syntheticChrissAlmgren as sca from ddpg_agent import Agent from collections import deque # Create simulation environment env = sca.MarketEnvironment() # Initialize Feed-forward DNNs for Actor and Critic models. agent = Agent(state_size=env.observation_space_dimension(), action_size=env.action_space_dimension(), random_seed=0) # Set the liquidation time lqt = 60 # Set the number of trades n_trades = 60 # Set trader's risk aversion tr = 1e-6 # Set the number of episodes to run the simulation episodes = 10000
