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)
def impvol(cp, strike, premium):
try:
vol = blackFormulaImpliedStdDev(cp, strike,
forward=Fwd, blackPrice=premium, discount=discountFactor,
TTM=timeToMaturity)
except RuntimeError:
vol = np.nan
return vol/np.sqrt(timeToMaturity)
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)
