Profesor, MAF ITESO
En primer lugar, para poder bajar precios y información sobre opciones de Yahoo, es necesario cargar algunos paquetes de Python. En este caso, el paquete principal será Pandas. También, se usarán el Scipy y el Numpy para las matemáticas necesarias y, el Matplotlib y el Seaborn para hacer gráficos de las series de datos.
In [1]:
#importar los paquetes que se van a usar
import pandas as pd
import pandas_datareader.data as web
import numpy as np
from sklearn.neighbors import KernelDensity
import datetime
from datetime import datetime, timedelta
import scipy.stats as stats
import scipy as sp
import scipy.optimize as optimize
import scipy.cluster.hierarchy as hac
import matplotlib.pyplot as plt
import seaborn as sns
%matplotlib inline
#algunas opciones para Python
pd.set_option('display.notebook_repr_html', True)
pd.set_option('display.max_columns', 6)
pd.set_option('display.max_rows', 10)
pd.set_option('display.width', 78)
pd.set_option('precision', 3)
In [2]:
def get_historical_closes(ticker, start_date, end_date):
p = web.DataReader(ticker, "yahoo", start_date, end_date).sort_index('major_axis')
d = p.to_frame()['Adj Close'].reset_index()
d.rename(columns={'minor': 'Ticker', 'Adj Close': 'Close'}, inplace=True)
pivoted = d.pivot(index='Date', columns='Ticker')
pivoted.columns = pivoted.columns.droplevel(0)
return pivoted
In [3]:
data=get_historical_closes(['AAPL'], '2016-01-01', '2016-12-31')
data.plot(figsize=(8,6));
In [35]:
aapl = web.Options('AAPL', 'yahoo')
appl_opt = aapl.get_all_data().reset_index()
appl_opt
Out[35]:
In [46]:
appl_opt.JSON[0]['ask']
Out[46]:
In [5]:
def calc_daily_returns(closes):
return np.log(closes/closes.shift(1))[1:]
In [6]:
daily_returns=calc_daily_returns(data)
daily_returns.plot(figsize=(8,6));
In [7]:
mu=daily_returns.mean().AAPL
sigma=daily_returns.std().AAPL
ndays = 360
ntraj=10
dates=pd.date_range('20170101',periods=ndays)
simret = pd.DataFrame(sigma*np.random.randn(ndays,ntraj)+mu,index=dates)
simret
Out[7]:
In [8]:
simdata=(data.loc['2016-12-30',:].AAPL)*np.exp(simret.cumsum())
simdata
Out[8]:
In [9]:
simdata.plot(figsize=(8,6),legend=False);
In [10]:
K=160
mu=daily_returns.mean().AAPL
sigma=daily_returns.std().AAPL
ndays = 360
ntraj=100
dates=pd.date_range('20170101',periods=ndays)
simret = pd.DataFrame(sigma*np.random.randn(ndays,ntraj)+mu,index=dates)
simdata=(data.loc['2016-12-30',:].AAPL)*np.exp(simret.cumsum())
strike = pd.DataFrame({'Strike':K*np.ones(ndays)},index=dates)
simul=pd.concat([data.T,strike.T,simdata.T]).T
In [11]:
simul.plot(figsize=(8,6),legend=False);
In [12]:
strike = pd.DataFrame(K*np.ones(ndays*ntraj).reshape((ndays,ntraj)),index=dates)
call=pd.DataFrame({'Prima':np.exp(-mu*ndays)*np.fmax(simdata-strike,np.zeros(ndays*ntraj).reshape((ndays,ntraj))).T.mean()},index=dates)
call.plot();
In [13]:
call.loc['2017-06-10']
Out[13]:
In [14]:
put=pd.DataFrame({'Prima':np.exp(-mu*ndays)*np.fmax(strike-simdata,np.zeros(ndays*ntraj).reshape((ndays,ntraj))).T.mean()},index=dates)
put.plot();
In [15]:
put.loc['2017-06-10']
Out[15]:
In [16]:
ndays = 360
ntraj=10
#
values,indices=np.histogram(daily_returns,bins=250)
values=values.astype(np.float32)
weights=values/np.sum(values)
ret=np.random.choice(indices[1:],ndays*ntraj,p=weights)
#
dates=pd.date_range('20170101',periods=ndays)
simret = pd.DataFrame(ret.reshape((ndays,ntraj)),index=dates)
simret
Out[16]:
In [17]:
simdata=(data.loc['2016-12-30',:].AAPL)*np.exp(simret.cumsum())
simdata
Out[17]:
In [18]:
simdata.plot(figsize=(8,6),legend=False);
In [19]:
pd.concat([data,simdata]).plot(figsize=(8,6),legend=False);
In [20]:
K=160
ndays = 360
ntraj=1000
#
values,indices=np.histogram(daily_returns,bins=250)
values=values.astype(np.float32)
weights=values/np.sum(values)
ret=np.random.choice(indices[1:],ndays*ntraj,p=weights)
#
dates=pd.date_range('20170101',periods=ndays)
simret = pd.DataFrame(ret.reshape((ndays,ntraj)),index=dates)
simdata=(data.loc['2016-12-30',:].AAPL)*np.exp(simret.cumsum())
strike = pd.DataFrame({'Strike':K*np.ones(ndays)},index=dates)
simul=pd.concat([data.T,strike.T,simdata.T]).T
In [21]:
simul.plot(figsize=(8,6),legend=False);
In [22]:
strike = pd.DataFrame(K*np.ones(ndays*ntraj).reshape((ndays,ntraj)),index=dates)
call=pd.DataFrame({'Prima':np.exp(-mu*ndays)*np.fmax(simdata-strike,np.zeros(ndays*ntraj).reshape((ndays,ntraj))).T.mean()},index=dates)
call.plot();
In [23]:
call.loc['2017-06-10']
Out[23]:
In [24]:
put=pd.DataFrame({'Prima':np.exp(-mu*ndays)*np.fmax(strike-simdata,np.zeros(ndays*ntraj).reshape((ndays,ntraj))).T.mean()},index=dates)
put.plot();
In [25]:
put.loc['2017-06-10']
Out[25]:
In [26]:
kde = KernelDensity(kernel='gaussian', bandwidth=0.001).fit(daily_returns)
ndays = 360
ntraj=100
#
ret=kde.sample(n_samples=ndays*ntraj, random_state=None)
#
dates=pd.date_range('20170101',periods=ndays)
simret = pd.DataFrame(ret.reshape((ndays,ntraj)),index=dates)
simret
Out[26]:
In [27]:
simdata=(data.loc['2016-12-30',:].AAPL)*np.exp(simret.cumsum())
simdata
Out[27]:
In [28]:
pd.concat([data,simdata]).plot(figsize=(8,6),legend=False);
In [29]:
K=160
ndays = 360
ntraj=1000
#
ret=kde.sample(n_samples=ndays*ntraj, random_state=None)
#
dates=pd.date_range('20170101',periods=ndays)
simret = pd.DataFrame(ret.reshape((ndays,ntraj)),index=dates)
simdata=(data.loc['2016-12-30',:].AAPL)*np.exp(simret.cumsum())
strike = pd.DataFrame({'Strike':K*np.ones(ndays)},index=dates)
simul=pd.concat([data.T,strike.T,simdata.T]).T
In [30]:
simul.plot(figsize=(8,6),legend=False);
In [31]:
strike = pd.DataFrame(K*np.ones(ndays*ntraj).reshape((ndays,ntraj)),index=dates)
call=pd.DataFrame({'Prima':np.exp(-mu*ndays)*np.fmax(simdata-strike,np.zeros(ndays*ntraj).reshape((ndays,ntraj))).T.mean()},index=dates)
call.plot();
In [32]:
call.loc['2017-06-10']
Out[32]:
In [33]:
put=pd.DataFrame({'Prima':np.exp(-mu*ndays)*np.fmax(strike-simdata,np.zeros(ndays*ntraj).reshape((ndays,ntraj))).T.mean()},index=dates)
put.plot();
In [34]:
put.loc['2017-06-10']
Out[34]: