def __init__(self, y, x, window_type='full_sample', window=None,
min_periods=None, intercept=True, nw_lags=None,
nw_overlap=False):
for attr in self.ATTRIBUTES:
setattr(self.__class__, attr, create_ols_attr(attr))
results = {}
for entity in y:
entity_y = y[entity]
entity_x = {}
for x_var in x:
entity_x[x_var] = x[x_var][entity]
from pandas.stats.interface import ols
results[entity] = ols(y=entity_y,
x=entity_x,
window_type=window_type,
window=window,
min_periods=min_periods,
intercept=intercept,
nw_lags=nw_lags,
nw_overlap=nw_overlap)
self.results = results
def __init__(self, y, x, window_type='full_sample', window=None,
min_periods=None, intercept=True, nw_lags=None,
nw_overlap=False):
import warnings
warnings.warn("The pandas.stats.plm module is deprecated and will be "
"removed in a future version. We refer to external packages "
"like statsmodels, see some examples here: "
"http://www.statsmodels.org/stable/mixed_linear.html",
FutureWarning, stacklevel=4)
for attr in self.ATTRIBUTES:
setattr(self.__class__, attr, create_ols_attr(attr))
results = {}
for entity in y:
entity_y = y[entity]
entity_x = {}
for x_var in x:
entity_x[x_var] = x[x_var][entity]
from pandas.stats.interface import ols
results[entity] = ols(y=entity_y,
x=entity_x,
window_type=window_type,
window=window,
min_periods=min_periods,
intercept=intercept,
nw_lags=nw_lags,
nw_overlap=nw_overlap)
self.results = results
def __init__(self, y, x, window_type=common.FULL_SAMPLE, window=None,
min_periods=None, intercept=True, nw_lags=None,
nw_overlap=False):
for attr in self.ATTRIBUTES:
setattr(self.__class__, attr, create_ols_attr(attr))
results = {}
for entity in y:
entity_y = y[entity]
entity_x = {}
for x_var in x:
entity_x[x_var] = x[x_var][entity]
from pandas.stats.interface import ols
results[entity] = ols(y=entity_y,
x=entity_x,
window_type=window_type,
window=window,
min_periods=min_periods,
intercept=intercept,
nw_lags=nw_lags,
nw_overlap=nw_overlap)
self.results = results
def __init__(self, y, x, window_type='full_sample', window=None,
min_periods=None, intercept=True, nw_lags=None,
nw_overlap=False):
import warnings
warnings.warn("The pandas.stats.plm module is deprecated and will be "
"removed in a future version. We refer to external packages "
"like statsmodels, see some examples here: "
"http://www.statsmodels.org/stable/mixed_linear.html",
FutureWarning, stacklevel=4)
for attr in self.ATTRIBUTES:
setattr(self.__class__, attr, create_ols_attr(attr))
results = {}
for entity in y:
entity_y = y[entity]
entity_x = {}
for x_var in x:
entity_x[x_var] = x[x_var][entity]
from pandas.stats.interface import ols
results[entity] = ols(y=entity_y,
x=entity_x,
window_type=window_type,
window=window,
min_periods=min_periods,
intercept=intercept,
nw_lags=nw_lags,
nw_overlap=nw_overlap)
self.results = results
def Compute_IV(optionDataFrame,
tMin=0,
nMin=0,
QDMin=0,
QDMax=1,
keepOTMData=True):
"""
Pre-processing of a standard European option quote file.
- Calculation of implied risk-free rate and dividend yield
- Calculation of implied volatility
- Estimate ATM volatility for each expiry
- Compute implied volatility and Quick Delta for each quote
Options for filtering the input data set:
- maturities with less than nMin strikes are ignored
- maturities shorter than tMin (ACT/365 daycount) are ignored
- strikes with Quick Delta < qdMin or > qdMax are ignored
"""
grouped = optionDataFrame.groupby('dtExpiry')
isFirst = True
for spec, group in grouped:
print('processing group %s' % spec)
# implied vol for this type/expiry group
indx = group.index
dtTrade = group['dtTrade'][indx[0]]
dtExpiry = group['dtExpiry'][indx[0]]
spot = group['Spot'][indx[0]]
daysToExpiry = (dtExpiry - dtTrade).days
timeToMaturity = daysToExpiry / 365.0
# exclude groups with too short time to maturity
if timeToMaturity < tMin:
continue
# exclude groups with too few data points
df_call = group[group['Type'] == 'C']
df_put = group[group['Type'] == 'P']
if (len(df_call) < nMin) | (len(df_put) < nMin):
continue
# calculate forward, implied interest rate and implied div. yield
df_C = DataFrame((df_call['PBid'] + df_call['PAsk']) / 2,
columns=['PremiumC'])
df_C.index = df_call['Strike']
df_P = DataFrame((df_put['PBid'] + df_put['PAsk']) / 2,
columns=['PremiumP'])
df_P.index = df_put['Strike']
# use 'inner' join because some strikes are not quoted for C and P
df_all = df_C.join(df_P, how='inner')
df_all['Strike'] = df_all.index
df_all['C-P'] = df_all['PremiumC'] - df_all['PremiumP']
model = ols(y=df_all['C-P'], x=df_all['Strike'])
b = model.beta
# intercept is last coef
iRate = -np.log(-b[0]) / timeToMaturity
dRate = np.log(spot / b[1]) / timeToMaturity
discountFactor = np.exp(-iRate * timeToMaturity)
Fwd = spot * np.exp((iRate - dRate) * timeToMaturity)
print('Fwd: %f int rate: %f div yield: %f' % (Fwd, iRate, dRate))
# mid-market ATM volatility
def impvol(cp, strike, premium):
try:
vol = blackFormulaImpliedStdDev(cp,
strike,
forward=Fwd,
blackPrice=premium,
discount=discountFactor,
TTM=timeToMaturity)
except:
vol = np.nan
return vol / np.sqrt(timeToMaturity)
# implied bid/ask vol for all options
df_call['IVBid'] = [
impvol('C', strike, price)
for strike, price in zip(df_call['Strike'], df_call['PBid'])
]
df_call['IVAsk'] = [
impvol('C', strike, price)
for strike, price in zip(df_call['Strike'], df_call['PAsk'])
]
df_call['IVMid'] = (df_call['IVBid'] + df_call['IVAsk']) / 2
df_put['IVBid'] = [
impvol('P', strike, price)
for strike, price in zip(df_put['Strike'], df_put['PBid'])
]
df_put['IVAsk'] = [
impvol('P', strike, price)
for strike, price in zip(df_put['Strike'], df_put['PAsk'])
]
df_put['IVMid'] = (df_put['IVBid'] + df_put['IVAsk']) / 2
f_call = interp1d(df_call['Strike'].values, df_call['IVMid'].values)
f_put = interp1d(df_put['Strike'].values, df_put['IVMid'].values)
atmVol = (f_call(Fwd) + f_put(Fwd)) / 2
print('ATM vol: %f' % atmVol)
# Quick Delta, computed with ATM vol
rv = norm()
df_call['QuickDelta'] = [rv.cdf(np.log(Fwd/strike)/(atmVol*np.sqrt(timeToMaturity))) \
for strike in df_call['Strike']]
df_put['QuickDelta'] = [rv.cdf(np.log(Fwd/strike)/(atmVol*np.sqrt(timeToMaturity))) \
for strike in df_put['Strike']]
# keep data within QD range
df_call = df_call[(df_call['QuickDelta'] >= QDMin) & \
(df_call['QuickDelta'] <= QDMax) ]
df_put = df_put[ (df_put['QuickDelta'] >= QDMin) & \
(df_put['QuickDelta'] <= QDMax) ]
# final assembly...
df_cp = df_call.append(df_put, ignore_index=True)
df_cp['iRate'] = iRate
df_cp['iDiv'] = dRate
df_cp['ATMVol'] = atmVol
df_cp['Fwd'] = Fwd
df_cp['TTM'] = timeToMaturity
df_cp['CP'] = [1 if t == 'C' else -1 for t in df_cp['Type']]
# keep only OTM data ?
if keepOTMData:
df_cp = df_cp[((df_cp['Strike'] >= Fwd) & (df_cp['Type'] == 'C')) |
((df_cp['Strike'] < Fwd) & (df_cp['Type'] == 'P'))]
if isFirst:
df_final = df_cp
isFirst = False
else:
df_final = df_final.append(df_cp, ignore_index=True)
return df_final
def ATM_Vol(premium, discountFactor, forward, strike):
"""
Aproximate std dev, for calls close to the money
"""
vol = (premium/discountFactor - .5*(forward-strike))*5.0/(forward+strike)
return vol
# get spot and option data frame
(spot, optionDataFrame) = read_SPX_file(option_data_file)
grouped = optionDataFrame.groupby('dtExpiry')
isFirst = True
for spec, group in grouped:
print('processing group %s' % spec)
# implied vol for this type/expiry group
indx = group.index
dtTrade = group['dtTrade'][indx[0]]
dtExpiry = group['dtExpiry'][indx[0]]
daysToExpiry = (dtExpiry-dtTrade).days
timeToMaturity = daysToExpiry/365.0
# exclude groups with too few data points
# or too short maturity
if timeToMaturity < tMin:
continue
# valid call and put quotes
df_call = group[(group['Type'] == 'C') & (group['Bid']>0) \
& (group['Ask']>0)]
df_put = group[(group['Type'] == 'P') & (group['Bid']>0) \
& (group['Ask']>0)]
if (len(df_call) == 0) | (len(df_put) == 0):
continue
# calculate forward, implied interest rate and implied div. yield
df_call['Mid'] = (df_call['Bid']+df_call['Ask'])/2
df_put['Mid'] = (df_put['Bid']+df_put['Ask'])/2
df_C = DataFrame.filter(df_call, items=['Strike', 'Mid'])
df_C.columns = ['Strike', 'PremiumC']
to_join = DataFrame(df_put['Mid'], index=df_put['Strike'],
columns=['PremiumP'])
# use 'inner' join because some strikes are not quoted for C and P
df_all = df_C.join(to_join, on='Strike', how='inner')
df_all['C-P'] = df_all['PremiumC'] - df_all['PremiumP']
model = ols(y=df_all['C-P'], x=df_all.ix[:,'Strike'])
b = model.beta
# intercept is last coef
iRate = -np.log(-b[0])/timeToMaturity
dRate = np.log(spot/b[1])/timeToMaturity
discountFactor = np.exp(-iRate*timeToMaturity)
Fwd = spot * np.exp((iRate-dRate)*timeToMaturity)
print('Fwd: %f int rate: %f div yield: %f' % (Fwd, iRate, dRate))
# interpolate ATM premium and vol: used to compute Quick Delta
f_call = interp1d(df_all['Strike'].values, df_all['PremiumC'].values)
f_put = interp1d(df_all['Strike'].values, df_all['PremiumP'].values)
atmPremium = (f_call(Fwd)+f_put(Fwd))/2
atmVol = blackFormulaImpliedStdDev('C', strike=Fwd,
forward=Fwd, blackPrice=atmPremium,
discount=discountFactor,
TTM=timeToMaturity)/np.sqrt(timeToMaturity)
print('ATM vol: %f' % atmVol)
# Quick Delta, computed with ATM vol
rv = norm()
df_call['QuickDelta'] = [rv.cdf(np.log(Fwd/strike)/(atmVol*np.sqrt(timeToMaturity))) \
for strike in df_call['Strike']]
df_put['QuickDelta'] = [rv.cdf(np.log(Fwd/strike)/(atmVol*np.sqrt(timeToMaturity))) \
for strike in df_put['Strike']]
# implied bid/ask vol for all options
def impvol(strike, premium):
try:
vol = blackFormulaImpliedStdDev(cp, strike,
forward=Fwd, blackPrice=premium, discount=discountFactor,
TTM=timeToMaturity)
except:
vol = np.nan
return vol/np.sqrt(timeToMaturity)
cp = 'C'
df_call['IVBid'] = [impvol(strike, price) for strike, price in zip(df_call['Strike'], df_call['Bid'])]
df_call['IVAsk'] = [impvol(strike, price) for strike, price in zip(df_call['Strike'], df_call['Ask'])]
# QD computed with ATM vol
cp = 'P'
df_put['IVBid'] = [impvol(strike, price) for strike, price in zip(df_put['Strike'], df_put['Bid'])]
df_put['IVAsk'] = [impvol(strike, price) for strike, price in zip(df_put['Strike'], df_put['Ask'])]
# keep OTM data for options within QD range
df_call = df_call[ (df_call['Strike'] >= Fwd) & \
(df_call['QuickDelta'] >= QDMin) & \
(df_call['QuickDelta'] <= QDMax) ]
df_put = df_put[ (df_put['Strike'] < Fwd) & \
(df_put['QuickDelta'] >= QDMin) & \
(df_put['QuickDelta'] <= QDMax) ]
# final assembly...
df_cp = df_call.append(df_put, ignore_index=True)
df_cp['R'] = iRate
df_cp['D'] = dRate
df_cp['ATMVol'] = atmVol
df_cp['F'] = Fwd
df_cp['T'] = timeToMaturity
df_cp = df_cp.rename(columns=
{'IVBid': 'VB',
'IVAsk': 'VA',
'Strike': 'K'})
df_cp['CP'] = [1 if t == 'C' else -1 for t in df_cp['Type']]
if isFirst:
df_final = df_cp
isFirst = False
else:
df_final = df_final.append(df_cp, ignore_index=True)
def Compute_IV(optionDataFrame, tMin=0, nMin=0, QDMin=0, QDMax=1, keepOTMData=True):
"""
Pre-processing of a standard European option quote file.
- Calculation of implied risk-free rate and dividend yield
- Calculation of implied volatility
- Estimate ATM volatility for each expiry
- Compute implied volatility and Quick Delta for each quote
Options for filtering the input data set:
- maturities with less than nMin strikes are ignored
- maturities shorter than tMin (ACT/365 daycount) are ignored
- strikes with Quick Delta < qdMin or > qdMax are ignored
"""
grouped = optionDataFrame.groupby('dtExpiry')
isFirst = True
for spec, group in grouped:
print('processing group %s' % spec)
# implied vol for this type/expiry group
indx = group.index
dtTrade = group['dtTrade'][indx[0]]
dtExpiry = group['dtExpiry'][indx[0]]
spot = group['Spot'][indx[0]]
daysToExpiry = (dtExpiry-dtTrade).days
timeToMaturity = daysToExpiry/365.0
# exclude groups with too short time to maturity
if timeToMaturity < tMin:
continue
# exclude groups with too few data points
df_call = group[group['Type'] == 'C']
df_put = group[group['Type'] == 'P']
if (len(df_call) < nMin) | (len(df_put) < nMin):
continue
# calculate forward, implied interest rate and implied div. yield
df_C = DataFrame((df_call['PBid']+df_call['PAsk'])/2,
columns=['PremiumC'])
df_C.index = df_call['Strike']
df_P = DataFrame((df_put['PBid']+df_put['PAsk'])/2,
columns=['PremiumP'])
df_P.index = df_put['Strike']
# use 'inner' join because some strikes are not quoted for C and P
df_all = df_C.join(df_P, how='inner')
df_all['Strike'] = df_all.index
df_all['C-P'] = df_all['PremiumC'] - df_all['PremiumP']
model = ols(y=df_all['C-P'], x=df_all['Strike'])
b = model.beta
# intercept is last coef
iRate = -np.log(-b[0])/timeToMaturity
dRate = np.log(spot/b[1])/timeToMaturity
discountFactor = np.exp(-iRate*timeToMaturity)
Fwd = spot * np.exp((iRate-dRate)*timeToMaturity)
print('Fwd: %f int rate: %f div yield: %f' % (Fwd, iRate, dRate))
# mid-market ATM volatility
def impvol(cp, strike, premium):
try:
vol = blackFormulaImpliedStdDev(cp, strike,
forward=Fwd, blackPrice=premium, discount=discountFactor,
TTM=timeToMaturity)
except:
vol = np.nan
return vol/np.sqrt(timeToMaturity)
# implied bid/ask vol for all options
df_call['IVBid'] = [impvol('C', strike, price) for strike, price
in zip(df_call['Strike'], df_call['PBid'])]
df_call['IVAsk'] = [impvol('C', strike, price) for strike, price
in zip(df_call['Strike'], df_call['PAsk'])]
df_call['IVMid'] = (df_call['IVBid'] + df_call['IVAsk'])/2
df_put['IVBid'] = [impvol('P', strike, price) for strike, price
in zip(df_put['Strike'], df_put['PBid'])]
df_put['IVAsk'] = [impvol('P', strike, price) for strike, price
in zip(df_put['Strike'], df_put['PAsk'])]
df_put['IVMid'] = (df_put['IVBid'] + df_put['IVAsk'])/2
f_call = interp1d(df_call['Strike'].values, df_call['IVMid'].values)
f_put = interp1d(df_put['Strike'].values, df_put['IVMid'].values)
atmVol = (f_call(Fwd)+f_put(Fwd))/2
print('ATM vol: %f' % atmVol)
# Quick Delta, computed with ATM vol
rv = norm()
df_call['QuickDelta'] = [rv.cdf(np.log(Fwd/strike)/(atmVol*np.sqrt(timeToMaturity))) \
for strike in df_call['Strike']]
df_put['QuickDelta'] = [rv.cdf(np.log(Fwd/strike)/(atmVol*np.sqrt(timeToMaturity))) \
for strike in df_put['Strike']]
# keep data within QD range
df_call = df_call[(df_call['QuickDelta'] >= QDMin) & \
(df_call['QuickDelta'] <= QDMax) ]
df_put = df_put[ (df_put['QuickDelta'] >= QDMin) & \
(df_put['QuickDelta'] <= QDMax) ]
# final assembly...
df_cp = df_call.append(df_put, ignore_index=True)
df_cp['iRate'] = iRate
df_cp['iDiv'] = dRate
df_cp['ATMVol'] = atmVol
df_cp['Fwd'] = Fwd
df_cp['TTM'] = timeToMaturity
df_cp['CP'] = [1 if t == 'C' else -1 for t in df_cp['Type']]
# keep only OTM data ?
if keepOTMData:
df_cp = df_cp[((df_cp['Strike']>=Fwd) & (df_cp['Type'] == 'C')) |
((df_cp['Strike']<Fwd) & (df_cp['Type'] == 'P'))]
if isFirst:
df_final = df_cp
isFirst = False
else:
df_final = df_final.append(df_cp, ignore_index=True)
return df_final
