def test_analytical_vega(self):
while self.tdi.has_next():
row = self.tdi.next_row()
S, K, t, r, sigma = row['S'], row['K'], row['t'], row['R'], row[
'v']
self.assertAlmostEqual(analytical.vega('c', S, K, t, r, sigma),
row['CV'] * .01,
delta=0.000001)
self.assertAlmostEqual(analytical.vega('p', S, K, t, r, sigma),
row['PV'] * .01,
delta=0.000001)
def test_analytical_vega(self):
S = 49
K = 50
sigma = .2
r = .05
t = 0.3846
flag = 'p'
c_put = c_analytical.vega(flag, S, K, t, r, sigma)
py_put = py_analytical.vega(flag, S, K, t, r, sigma)
self.assertTrue(almost_equal(c_put, py_put))
flag = 'c'
c_call = c_analytical.vega(flag, S, K, t, r, sigma)
py_call = py_analytical.vega(flag, S, K, t, r, sigma)
self.assertTrue(almost_equal(c_call, py_call))
def test_vega(self):
vegas = [
vega(flag, S, K, t, r, sigma)
for flag, S, K, t, r, sigma in self.arg_combinations
]
nvegas = [
nvega(flag, S, K, t, r, sigma)
for flag, S, K, t, r, sigma in self.arg_combinations
]
self.assertTrue(self.diff_mean(vegas, nvegas) < self.epsilon)
def Calculate_vega(each_row):
if each_row['Implied_Volatility'] == 0:
measure= 0
else:
try:
measure = bs_a.vega(flag=each_row['CallOrPut'], S=each_row['Spot'], K=each_row['Strike_Price'],
t=each_row['Days_to_Expiry']/365, r=.1,sigma=each_row['Implied_Volatility'])
except:
measure = 0
print("Vega", end=" ")
return measure
def calc_all(self, b):
h = self.all_set(b)
if not h: return False
if not h.get("sigma"): self.civ(h)
if not h.get("sigma"): return False
a = (h["flag"], h["F"], h["K"], h["t"], h["r"], h["sigma"])
r = self.rounding
h["price"] = round(oprice(*a), r)
h["delta"] = round(delta(*a), r)
h["gamma"] = round(gamma(*a) * 100, r)
h["vega"] = round(vega(*a), r)
return h
def vega(self, option_obj, asset_price, timestamp, expiration,
call_put_flag):
flag = call_put_flag
S = asset_price
K = option_obj.strike
t = self.time_2_expiration(timestamp, expiration)
r = self.risk_free_rate
sigma = option_obj.sigma
vega = vollib_greeks.vega(flag, S, K, t, r, sigma)
return vega
def update_vega(self, asset_code):
flag = asset_code[0].lower()
S = self.mid_dict['IDX#PHX']
if len(asset_code) == 6:
K = int(asset_code[1:3])
elif len(asset_code) == 7:
K = int(asset_code[1:4])
t = (63 - (time.time() - self.start_time) /
(900 / 21)) / 252 #time to expiration in years
r = 0
price = self.mid_dict[asset_code]
sigma = IV(price, S, K, r, t, flag) * np.sqrt(252)
return bsga.vega(flag, S, K, t, r, sigma)
def calculateAllGreeks(ticker, date, type, strike):
S = si.get_live_price(ticker)
K = strike
sigma = calculateAnnualizedVolatility(ticker)
t = optionExpiration(date)
r = calculateTreasuryYield(date)
if type == 'Call' or type == "call" or type == "C" or type == 'c':
flag = 'c'
else:
flag = 'p'
dlta = delta(flag, S, K, t, r, sigma)
gam = gamma(flag, S, K, t, r, sigma)
thta = theta(flag, S, K, t, r, sigma)
vga = vega(flag, S, K, t, r, sigma)
rh = rho(flag, S, K, t, r, sigma)
return ({"delta": dlta, "gamma": gam, "theta": thta, "vega": vga, "rho": rh})
def calculateGreek(ticker, date, type, strike, greek):
grk = 0
S = si.get_live_price(ticker)
K = strike
sigma = calculateAnnualizedVolatility(ticker)
t = optionExpiration(date)
r = calculateTreasuryYield(date)
flag = ''
if type == 'Call' or type == "call" or type == "C" or type == 'c':
flag = 'c'
flag = 'p'
if greek == "Delta" or greek == "delta":
grk = delta(flag, S, K, t, r, sigma)
elif greek == "Gamma" or greek == "gamma":
grk = gamma(flag, S, K, t, r, sigma)
elif greek == "Theta" or greek == "theta":
grk = theta(flag, S, K, t, r, sigma)
elif greek == "Vega" or greek == "vega":
grk = vega(flag, S, K, t, r, sigma)
else:
grk = rho(flag, S, K, t, r, sigma)
return grk
def precompute(table, computedate, underlying, include_riskfree):
db = psycopg2.connect(host="localhost",
user=settings.db_username,
password=settings.db_password,
database="optiondata")
cur2 = db.cursor()
underlying_fragment = ""
if (underlying != "*"):
underlying_fragment = "underlying_symbol = '" + underlying + "' AND "
date_fragment = ""
if (computedate != "*"):
date_fragment = "quote_date = '" + str(computedate) + "' AND "
query = "SELECT id, quote_date, underlying_mid_1545, mid_1545, expiration, strike, option_type FROM " + \
table + " WHERE " + underlying_fragment + date_fragment + "iv IS NULL"
cur2.execute(query)
result = cur2.fetchall()
print(
str(computedate) + " " + str(underlying) + ": " + str(len(result)) +
" results")
bulkrows = []
if (len(result) > 0):
for row in result:
rowid = row[0]
quote_date = row[1]
underlying_mid_1545 = float(row[2])
mid_1545 = float(row[3])
expiration = row[4]
strike = float(row[5])
option_type = row[6]
expiration_time = datetime.datetime.combine(
expiration, datetime.time(16, 0))
remaining_time_in_years = util.remaining_time(
quote_date, expiration_time)
rf = util.interest
if include_riskfree:
rf = util.get_riskfree_libor(quote_date,
remaining_time_in_years)
try:
iv = implied_volatility.implied_volatility(
mid_1545, underlying_mid_1545, int(strike),
remaining_time_in_years, rf, option_type)
except:
iv = 0.001
try:
bs_price_bid_ask = black_scholes(option_type,
underlying_mid_1545, strike,
remaining_time_in_years, rf,
iv)
except:
bs_price_bid_ask = 0.001
try:
delta = analytical.delta(option_type, underlying_mid_1545,
strike, remaining_time_in_years, rf,
iv) * 100
except:
delta = 0.001
try:
theta = analytical.theta(option_type, underlying_mid_1545,
strike, remaining_time_in_years, rf,
iv) * 100
except:
theta = 0.001
try:
vega = analytical.vega(option_type, underlying_mid_1545,
strike, remaining_time_in_years, rf,
iv) * 100
except:
vega = 0.001
bulkrows.append({
'iv': iv,
'bs_price_bid_ask': bs_price_bid_ask,
'delta': delta,
'theta': theta,
'vega': vega,
'rowid': rowid
})
psycopg2.extras.execute_batch(
cur2,
"""UPDATE """ + table +
""" SET iv=%(iv)s, bs_price_bid_ask=%(bs_price_bid_ask)s, delta=%(delta)s, theta=%(theta)s, vega=%(vega)s WHERE id=%(rowid)s""",
bulkrows,
page_size=100)
db.commit()
db.close()
def weighted_iv(cls, options, term, flag='c'):
if flag == 'c':
# Call fields
bid = 'CallBid'
ask = 'CallAsk'
last_sale = 'CallLastSale'
else:
# Put fields
bid = 'PutBid'
ask = 'PutAsk'
last_sale = 'PutLastSale'
option_iv = pd.Series(pd.np.zeros(len(options.data.index)),
index=options.data.index,
name='OptionImpliedVolatility')
for i in options.data.index:
t = options.data.Expiration[i] / 365.0
price = (options.data[bid][i] + options.data[ask][i]) / 2.0
option_iv[i] = cls.calculate(options.underlying_price,
options.data.Strike[i],
t,
price,
flag=flag)
data = options.data.join(option_iv)
def _find_expiration_dates(df, term):
"""
Find two expiration dates closest to given number of days, front and back month.
"""
expirations = df[['Expiration'
]].drop_duplicates().reset_index(drop=True)
back_expirations = expirations[(expirations.Expiration >
term)].copy()
front_expirations = expirations[(expirations.Expiration <
term)].copy()
if back_expirations.size > 0 and front_expirations.size > 0:
front_back_values = []
for frame in [
front_expirations,
back_expirations,
]:
frame['Difference'] = frame['Expiration'].apply(
lambda value: abs(value - term))
front_back_values.append(
frame.sort_values(
by=['Difference']).head(1)['Expiration'].values[0])
return front_back_values
return None, None
front, back = _find_expiration_dates(data, term)
if not front or not back:
return 0.0
def _find_closest_strikes(df,
front,
back,
underlying_price,
number_of_strikes=4):
"""
We take 4 (number_of_strikes) options contracts with strikes
nearest to current stock price. We'll use this list to
calculate IV Index for the front and back months.
"""
strike_expiration_df = df[(df.Expiration == front) |
(df.Expiration == back)][[
'Strike', 'Expiration'
]].drop_duplicates().reset_index(
drop=True)
front_back_lists = []
for value in (
front,
back,
):
s1 = strike_expiration_df[(
strike_expiration_df.Expiration == value)]['Strike'].apply(
lambda item: abs(item - underlying_price)).reset_index(
drop=True)
s2 = df[(df.Expiration == value
)]['Strike'].drop_duplicates().reset_index(drop=True)
front_back_lists.append(
pd.DataFrame({
'Difference': s1,
'Strike': s2
}).reset_index(drop=True).sort_values(by='Difference').
head(number_of_strikes)['Strike'].values)
return front_back_lists
front_strikes, back_strikes = _find_closest_strikes(
data, front, back, options.underlying_price)
# data = data[(data.OptionImpliedVolatility > .01) & (data.OptionImpliedVolatility < 1) &
# TODO: Removed IV < 1 filter. IV can be greater than 100%. Looking at you AyyMD ;)
data = data[(data.OptionImpliedVolatility > .01) & ((
(data.Expiration == front) & (data.Strike.isin(front_strikes))) | (
(data.Expiration == back) & (data.Strike.isin(back_strikes))))
& ((data[bid] > 0) | (data[ask] > 0))]
# ) & (data[last_sale] > 0) & (data[bid] > 0) & (data[ask] > 0)]
# TODO: Do we care about filtering out options that are not active (last_sale == 0). For example,
# if we keep only last_sale > 0 strikes we may end up without options to process. This will
# cause vega weights calculations to fail.
# TODO: Sometimes bid or ask are 0, so make sure average is calculated correctly.
df = pd.DataFrame()
for index, items in data[[
'Strike', 'Expiration'
]].drop_duplicates().reset_index(drop=True).iterrows():
values = data[(data.Strike == items['Strike'])
& (data.Expiration == items['Expiration'])][[
'OptionImpliedVolatility', ask, bid
]].mean()
values['Strike'] = items['Strike']
values['Expiration'] = items['Expiration']
values['Price'] = (
values[bid] + values[ask]
) / 2.0 if values[ask] > 0 and values[bid] > 0 else max(
values[ask], values[bid])
values['Vega'] = vega(flag, options.underlying_price,
items['Strike'], items['Expiration'] / 365.0,
RISK_FREE_INTEREST_RATE,
values['OptionImpliedVolatility'])
df = df.append(values, ignore_index=True)
# Liquidity considerations in estimating implied volatility (Rohini Grover and Susan Thomas)
#
# Interpolation scheme:
#
# vix = 100 * [ weight_t1 * ( (Nc2 - 30) / (Nc2 - Nc1) ) + weight_t2 * ( (30 - Nc1) / (Nc2 - Nc1) ) ]
#
# Where weight_ti are implied volatilities and Nci is the number of calendar days to
# expiration. Here, i = 1, 2 for the near and next month respectively.
def _front_vega_weights(df, front, back, term):
"""
This function will calculate weighted average for the front month,
where weighting is done by Vega (option price sensitivity to a
change in Implied Volatility).
"""
vegas_ivs = 0.0
vegas = 0.0
for index, items in df[(df.Expiration == front)].iterrows():
vegas_ivs += items['Vega'] * items['OptionImpliedVolatility']
vegas += items['Vega']
vw = vegas_ivs / vegas
expiry_sqrt = (math.sqrt(back) - math.sqrt(term)) / (
math.sqrt(back) - math.sqrt(front))
return vw, expiry_sqrt
def _back_vega_weights(df, front, back, term):
"""
This function will calculate weighted average for the back month,
where weighting is done by Vega (option price sensitivity to a
change in Implied Volatility).
"""
vegas_ivs = 0.0
vegas = 0.0
for index, items in df[(df.Expiration == back)].iterrows():
vegas_ivs += items['Vega'] * items['OptionImpliedVolatility']
vegas += items['Vega']
vw = vegas_ivs / vegas
expiry_sqrt = (math.sqrt(term) - math.sqrt(front)) / (
math.sqrt(back) - math.sqrt(front))
return vw, expiry_sqrt
vw1, i1 = _front_vega_weights(df, front, back, term)
vw2, i2 = _back_vega_weights(df, front, back, term)
return i1 * vw1 + i2 * vw2
def precompute(underlying, include_riskfree):
done = False
bulksize = 100000
counter = 0
print("precompute: " + str(underlying))
print()
while not done:
db = psycopg2.connect(host="localhost",
user=settings.db_username,
password=settings.db_password,
database="optiondata")
cur2 = db.cursor()
print("Query for next " + str(bulksize) + " items to precompute ")
query = "SELECT id, quote_date, underlying_mid_1545, mid_1545, expiration, strike, option_type FROM optiondata WHERE underlying_symbol = '" + underlying + "' AND iv IS NULL LIMIT " + str(
bulksize)
cur2.execute(query)
result = cur2.fetchall()
print(str(len(result)) + " items to precompute")
if len(result) == 0:
done = True
print("Done precomputing")
print()
bulkrows = []
for row in result:
rowid = row[0]
quote_date = row[1]
underlying_mid_1545 = float(row[2])
mid_1545 = float(row[3])
expiration = row[4]
strike = float(row[5])
option_type = row[6]
expiration_time = datetime.datetime.combine(
expiration, datetime.time(16, 0))
remaining_time_in_years = util.remaining_time(
quote_date, expiration_time)
rf = util.interest
if include_riskfree:
rf = util.get_riskfree_libor(quote_date,
remaining_time_in_years)
try:
iv = implied_volatility.implied_volatility(
mid_1545, underlying_mid_1545, int(strike),
remaining_time_in_years, rf, option_type)
delta = analytical.delta(option_type, underlying_mid_1545,
strike, remaining_time_in_years, rf,
iv) * 100
theta = analytical.theta(option_type, underlying_mid_1545,
strike, remaining_time_in_years, rf,
iv) * 100
vega = analytical.vega(option_type, underlying_mid_1545,
strike, remaining_time_in_years, rf,
iv) * 100
except:
iv = 0.001
delta = 0.001
theta = 0.001
vega = 0.001
bulkrows.append({
'iv': iv,
'delta': delta,
'theta': theta,
'vega': vega,
'rowid': rowid
})
counter += 1
if (((counter % 1000) == 0) or ((len(result) < bulksize) and
(counter == len(result)))):
try:
cur2.executemany(
"""UPDATE optiondata SET iv=%(iv)s, delta=%(delta)s, theta=%(theta)s, vega=%(vega)s WHERE id=%(rowid)s""",
bulkrows)
db.commit()
print("inserted: " + str(counter))
bulkrows = []
time.sleep(1)
except Exception as e:
print("an exception occurred")
print(e)
if (len(result) < bulksize) and (counter == len(result)):
done = True
print("Done precomputing")
print()
db.close()
def precompute(underlying):
print("precompute: " + str(underlying))
print
db = pgdb.connect(host="localhost",
user=settings.db_username,
password=settings.db_password,
database="optiondata")
cur2 = db.cursor()
query = "SELECT id, quote_date, underlying_bid_1545, underlying_ask_1545, bid_1545, ask_1545, expiration, strike, option_type FROM optiondata WHERE underlying_symbol = '" + underlying + "' AND iv IS NULL ORDER BY id asc"
cur2.execute(query)
result = cur2.fetchall()
print(str(len(result)) + " items to precompute")
for row in result:
rowid = row[0]
quote_date = row[1]
underlying_bid_1545 = row[2]
underlying_ask_1545 = row[3]
bid_1545 = row[4]
ask_1545 = row[5]
expiration = row[6]
strike = float(row[7])
option_type = row[8].lower()
current_quote = float((underlying_bid_1545 + underlying_ask_1545) / 2)
midprice = float((bid_1545 + ask_1545) / 2)
expiration_time = datetime.combine(expiration, time(16, 0))
remaining_time_in_years = util.remaining_time(quote_date,
expiration_time)
iv = 0.001
delta = 0.001
theta = 0.001
vega = 0.001
if remaining_time_in_years > 0:
try:
iv = implied_volatility.implied_volatility(
midprice, current_quote, int(strike),
remaining_time_in_years, util.interest, option_type)
except:
iv = 0.001
delta = analytical.delta(option_type, current_quote, strike,
remaining_time_in_years, util.interest,
iv) * 100
theta = analytical.theta(option_type, current_quote, strike,
remaining_time_in_years, util.interest,
iv) * 100
vega = analytical.vega(option_type, current_quote, strike,
remaining_time_in_years, util.interest,
iv) * 100
updateQuery = "UPDATE optiondata SET iv=%s, delta=%s, theta=%s, vega=%s WHERE id=%s" % (
iv, delta, theta, vega, rowid)
try:
cur2.execute(updateQuery)
db.commit()
except:
print("Except")
print(rowid)
print(current_quote)
print(midprice)
print(iv)
print(delta)
print(theta)
print(vega)
print(updateQuery)
db.close()