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monte_carlo.py
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from numpy.random import normal
from numpy import array
import numpy
import math
def plotstock(ticker='PG', time_intervals=1000, iterations=10, start='2007-1-1'):
# Load data for 'ticker'
data = pd.DataFrame()
data[ticker] = wb.DataReader(ticker, data_source='yahoo', start=start)['Adj Close']
# Estimate historical log returns
log_returns = np.log(1 + data.pct_change())
#data.plot(figsize=(10, 6));
#log_returns.plot(figsize=(10, 6));
# Calculate brownian motion --> r = drift + stdev * e**r
u = log_returns.mean()
var = log_returns.var()
drift = u - (0.5 * var)
stdev = log_returns.std()
daily_returns = np.exp(drift.values + stdev.values * norm.ppf(np.random.rand(time_intervals, iterations)))
# Fill matrix of dims time_intervals x iterations
price_list = np.zeros_like(daily_returns)
# stock price in new list must be last one in data set to
# make reasonable predictions, also must be first in list
# for all iterations
price_list[0] = data.iloc[-1]
for t in range(1, t_intervals):
price_list[t] = price_list[t - 1] * daily_returns[t]
# Combine historical data with predicted data
pred_date = pd.date_range(start = data.index.max().date(),
periods = time_intervals)
#preds = pd.DataFrame(price_list)
#preds['Date'] = pred_date
#preds = preds.set_index('Date')
#combined_data = data.append(preds, sort=False)
#return combined_data
sim = []
for i in range(len(price_list)):
for j in range(len(price_list[i])):
v = {'Date':pred_date[i].date(), ticker:price_list[i][j]}
sim.append(v)
sim = pd.DataFrame(sim).set_index('Date')
means = sim.reset_index().groupby('Date')[[ticker]].mean()
data_dates = data.reset_index().Date.apply(lambda x: datetime.datetime.strftime(x, "%x")).values
sim_dates = sim.reset_index().Date.apply(lambda x: datetime.datetime.strftime(x, "%x")).values
mean_dates = means.reset_index().Date.apply(lambda x: datetime.datetime.strftime(x, "%x")).values
dd = {'actual': [data_dates, data[ticker].values],
'simulated': [sim_dates, sim[ticker].values],
'means': [mean_dates, means[ticker].values]}
return dd
# Make plotly plot
# trace0 = go.Scatter(
# x=dd['actual'][0],
# y=dd['actual'][1]
# )
# trace1 = go.Scatter(
# x=dd['simulated'][0],
# y=combo['simulated'][1]
# )
# trace2 = go.Scatter(
# x=dd['means'][0],
# y=dd['means'][1]
# )
# plotdata = [trace0, trace1, trace2]
# plotty = py.plot(plotdata, filename=f'{ticker}-line', auto_open=False)
# return plotty
# return tls.get_embed(plotty)
# return dd
def pyplotstock(ticker='PG', time_intervals=1000, iterations=10, start='2007-1-1'):
# Load data for 'ticker'
data = pd.DataFrame()
data[ticker] = wb.DataReader(ticker, data_source='yahoo', start=start)['Adj Close']
# Estimate historical log returns
log_returns = np.log(1 + data.pct_change())
#data.plot(figsize=(10, 6));
#log_returns.plot(figsize=(10, 6));
# Calculate brownian motion --> r = drift + stdev * e**r
u = log_returns.mean()
var = log_returns.var()
drift = u - (0.5 * var)
stdev = log_returns.std()
daily_returns = np.exp(drift.values + stdev.values * norm.ppf(np.random.rand(time_intervals, iterations)))
# Fill matrix of dims time_intervals x iterations
price_list = np.zeros_like(daily_returns)
# stock price in new list must be last one in data set to
# make reasonable predictions, also must be first in list
# for all iterations
price_list[0] = data.iloc[-1]
for t in range(1, t_intervals):
price_list[t] = price_list[t - 1] * daily_returns[t]
# Combine historical data with predicted data
pred_date = pd.date_range(start = data.index.max().date(),
periods = time_intervals)
preds = pd.DataFrame(price_list)
preds['Date'] = pred_date
preds = preds.set_index('Date')
combined_data = data.append(preds, sort=False)
sim = []
for i in range(len(price_list)):
for j in range(len(price_list[i])):
v = {'Date':pred_date[i].date(), ticker:price_list[i][j]}
sim.append(v)
sim = pd.DataFrame(sim).set_index('Date')
means = sim.reset_index().groupby('Date')[[ticker]].mean()
# Plot data
plt.figure(figsize=(10,6))
plt.title(ticker)
plt.plot(data)
plt.plot(sim, alpha=0.5);
plt.plot(means);
# plt.plot(combined_data);
plt.savefig(f'static/img/{ticker}-{datetime.datetime.now().date()}.png')
return combined_data
def monte_carlo_step(previous, rate, stdv):
return previous * math.exp(normal(rate, stdv))
def build_monte_carlo_array(previous, rate, stdv, depth):
sim_series = [monte_carlo_step(previous, rate, stdv)]
for i in range(depth):
sim_series.append(monte_carlo_step(sim_series[i], rate, stdv))
return array([sim_series])