def __init__(self,symbol,interest,leg):
symbol = symbol
interest = float(interest)
self.qty = int(leg.q.get())
self.expiry = datetime.strptime(leg.ex.get()+' 2359',
'%m/%d/%y %H%M')
self.strike = float(leg.s.get())
self.option = leg.var.get()
self.price = float(leg.p.get())
sym_today = symbol+str(dt.today())
self.dte = (self.expiry - datetime.today()).days
if sym_today in prices_dict:
uprice = prices_dict[sym_today]
else:
uprice = si.get_live_price(symbol)
prices_dict[sym_today] = uprice
if leg.var.get() == 'Call':
v = mibian.BS([uprice,self.strike,interest,self.dte],
callPrice=self.price).impliedVolatility
if leg.var.get() == 'Put':
v = mibian.BS([uprice,self.strike,interest,self.dte],
putPrice=self.price).impliedVolatility
self.vol = v
def testBS(self):
'''Black-Scholes model tests'''
test = mibian.BS([81, 80, 6, 60], volatility=30)
self.assertEqual([test.callPrice, test.putPrice],
[4.8422936422068901, 3.0571309465072147])
self.assertEqual([test.callDelta, test.putDelta],
[0.5963986247019829, -0.4036013752980171])
self.assertEqual([test.callDelta2, test.putDelta2],
[-0.54332493698317152, 0.4468605293205825])
self.assertEqual([test.callTheta, test.putTheta],
[-0.038938157820841104, -0.025916540729723249])
self.assertEqual([test.callRho, test.putRho],
[0.07145095061696502, -0.05876522029421359])
self.assertEqual(test.vega, 0.12717225103657845)
self.assertEqual(test.gamma, 0.039304536595328565)
test = mibian.BS([52, 60, 5, 30], callPrice=3)
self.assertEqual(test.impliedVolatility, 95.703125)
test = mibian.BS([52, 60, 5, 30], putPrice=7.86)
self.assertEqual(test.impliedVolatility, 29.78515625)
test = mibian.BS([81, 80, 6, 60],
callPrice=4.8422936422068901,
putPrice=3.0571309465072147)
self.assertEqual(test.putCallParity, 0.02254482311879258)
def getOpionsChainPE(self, **kwargs):
Strike = int(0)
Length = int(0)
for key, value in kwargs.items():
print("%s == %s" % (key, value))
if (key == "Strike"):
Strike = int(value)
elif (key == "Length"):
Length = int(value)
else:
Strike = 0
Length = 0
if Strike == 0:
Strike = self.BankNiftyATMPrice
if Length == 0:
Length = 10
self.getBankNiftySpot()
self.getBankNiftyATM()
idx = self.BankNiftyPEInstruments[self.BankNiftyPEInstruments['strike']
== Strike].index
x = idx.item()
PE_Chain_DF = self.BankNiftyPEInstruments[(x -
Length):(x +
Length)].copy()
PE_Instrument_list = PE_Chain_DF['tradingsymbol'].tolist()
for i in range(len(PE_Instrument_list)):
PE_Instrument_list[i] = "NFO:" + PE_Instrument_list[i]
PEPrices = self.kconn.ltp(PE_Instrument_list)
print(PEPrices)
PE_Chain_DF['IV'] = np.nan
PE_Chain_DF['Delta'] = np.nan
for ind in PE_Chain_DF.index:
PE_Chain_DF["last_price"][ind] = PEPrices[
"NFO:" + PE_Chain_DF["tradingsymbol"][ind]]["last_price"]
voltyP = mibian.BS([
self.BankNiftySpotPrice, PE_Chain_DF["strike"][ind],
self.interestrates, (self.Expiry - date.today()).days
],
putPrice=PE_Chain_DF["last_price"][ind])
newVoltyP = float("{:.2f}".format(voltyP.impliedVolatility))
PE_Chain_DF["IV"][ind] = newVoltyP
p = mibian.BS([
self.BankNiftySpotPrice, PE_Chain_DF["strike"][ind],
self.interestrates, (self.Expiry - date.today()).days
],
volatility=newVoltyP)
PE_Chain_DF["Delta"][ind] = p.putDelta
return PE_Chain_DF
def y_today(self,row,int_rate=1.0):
x = self.x
dte = (row.Expiration - pd.Timestamp('today')).days
y=[]
for a in x:
if row.Option == 'Call':
y.append((mibian.BS([float(a),row.Strike,int_rate,dte],\
volatility=row.Vol).callPrice-row.Price)*row.Quantity*100)
if row.Option == 'Put':
y.append((mibian.BS([float(a),row.Strike,int_rate,dte],\
volatility=row.Vol).putPrice-row.Price)*row.Quantity*100)
return np.array(y)
def _get_odds_otm(current_price, strike, days_to_expiry, put_price):
cache_key = '_get_odds_otm' + str(current_price) + str(strike) + str(days_to_expiry) + str(put_price)
cached_result = cache.get(cache_key)
if cached_result is not None:
return cached_result
put_implied_volatility_calculator = mibian.BS([current_price, strike, INTEREST_RATE, days_to_expiry], putPrice=put_price)
# kinda silly, we need to construct another object to extract delta for a computation based on real put price
# Yahoo's volatility in interesting_put.impliedVolatility seems low, ~20% too low, so lets use the implied volatility
implied_volatility = put_implied_volatility_calculator.impliedVolatility
put_with_implied_volatility = mibian.BS([current_price, strike, INTEREST_RATE, days_to_expiry], volatility=implied_volatility)
result = 1 + put_with_implied_volatility.putDelta
cache.set(cache_key, result, YAHOO_FINANCE_CACHE_TIMEOUT)
return result
def _test_mibian():
underlying = 1.4565
strike = 1.45
interest = 1
days = 30
opt_info = [underlying, strike, interest, days]
c = mibian.BS(opt_info, volatility=20)
print(c.callPrice, c.putPrice, c.callDelta, c.putDelta, c.callDelta2,
c.putDelta2, c.callTheta, c.putTheta, c.callRho, c.putRho, c.vega,
c.gamma)
co = mibian.BS(opt_info, callPrice=c.callPrice)
co.impliedVolatility
def implied_vol(underlying_price: float,
strike_price: float,
interest: float,
expiry_date: date,
obs_date: date = None,
call_price: float = None,
put_price: float = None):
"""
It is used to find the implied volatility of the option.
Either call_price or put_price should be given.
If both are given then call is evaluated by default.
:param underlying_price: float
(S) Spot price
:param strike_price: float
(K) Strike price
:param interest: float
(r) Risk free interest rate
:param expiry_date: date
(T) Time to maturity i.e. expiry date
:param obs_date: date
Date of observation. By default present date.
:param call_price: float
Call option price for the strike.
:param put_price: float
Put option price for the strike.
:return: float
Implied volatility of the option
"""
days_expiry = days_to_expiry(expiry_date, obs_date=obs_date)
if days_expiry > 0:
if (call_price is None) & (put_price is None):
_logger.warning("Either call or put price need to be given")
else:
c = mibian.BS
if call_price is not None:
c = mibian.BS(
[underlying_price, strike_price, interest, days_expiry],
callPrice=call_price)
elif put_price is not None:
c = mibian.BS(
[underlying_price, strike_price, interest, days_expiry],
putPrice=put_price)
iv = c.impliedVolatility
# if iv == float("1e-05"):
# iv = 0.00001
return iv
else:
_logger.warning("Enter a date greater than today")
_logger.info("You entered: %s" % expiry_date)
return
def correct_IV_call(futures_price, data_buy, left_day, k): #修正call的隱波
import mibian
import pandas as pd
import numpy as np
import statsmodels.api as sm
IV_buy = []
for i in range(len(data_buy)):
try:
#先用真實價格套入BS模型回推隱波
a = mibian.BS(
[futures_price,
float(data_buy['履約價'][i]), 0.003, left_day],
callPrice=float(data_buy['結算價'][i]))
IV_buy.append(a.impliedVolatility)
except:
pass
weights_buy = np.polyfit(k, IV_buy, 6) #用6次式回歸修正
model_buy = np.poly1d(weights_buy)
b = list(range(min(data_buy['履約價']), max(data_buy['履約價']) + 100, 100))
pred_buy = model_buy(b) #套回修正過的回歸式回傳新的隱波
#print(pred_buy)
plt.plot(b, pred_buy)
#plt.xlim(10000,16000)
#plt.ylim(10,80)
plt.show()
return pred_buy, b
def correct_IV_put(futures_price,data_sell,left_day,k):#修正put的隱波
import mibian
import pandas as pd
import numpy as np
import statsmodels.api as sm
IV_sell = []
print('____執行correct_IV_put中回推隱波迴圈')
# def get_IV(row):
# return mibian.BS([futures_price, float(row['履約價']), 0.003, left_day], putPrice=float(row['結算價'])).impliedVolatility
for i in range(len(data_sell)):
try:
#先用真實價格套入BS模型回推隱波
print('結算價{}:'.format(i),float(data_sell['結算價'][i]))
a = mibian.BS([futures_price, float(data_sell['履約價'][i]), 0.003, left_day], putPrice= float(data_sell['結算價'][i]))
IV_sell.append(a.impliedVolatility)
except:
pass
# IV_sell = data_sell.apply(get_IV, axis=1)
print('____執行correct_IV_put中ployfit')
weights_sell = np.polyfit(k, IV_sell, 6)#用6次式回歸修正
print('____執行correct_IV_put中ploy1d')
model_sell = np.poly1d(weights_sell)
print('____執行correct_IV_put中List')
b = list(range(min(data_sell['履約價']),max(data_sell['履約價'])+100,100))
print('____執行correct_IV_put中model_sell')
pred_sell = model_sell(b)#套回修正過的回歸式回傳新的隱波
return pred_sell, b#回傳
def get_greeks(self, today, new_stock, new_vol):
'''Takes the date for today and the the current strike price
and returns the greeks as a dictionary'''
self.stock = new_stock
self.volatility = new_vol
days_left = (self.exDate - today).days
position = self.direction
c = m.BS([self.stock, self.strike, self.interest, days_left],
volatility=self.volatility)
if self.optiontype == "Call":
price = c.callPrice * position * 100
theta = c.callTheta * position * 100
delta = c.callDelta * position * 100
else:
price = c.putPrice * position * 100
theta = c.putTheta * position * 100
delta = c.putDelta * position * 100
options_dict = {"price": price, "theta": theta, "delta": delta}
return options_dict
def mibian_bs(row) -> pd.Series:
formula = mibian.BS(
[
row["underlying_price"],
row["strike"],
0,
row["days_to_expiry"],
],
volatility=row["volatility"],
)
if row["type"] == "CALL":
delta = formula.callDelta * row["amount"]
theta = formula.callTheta * row["amount"]
elif row["type"] == "PUT":
delta = formula.putDelta * row["amount"]
theta = formula.putTheta * row["amount"]
gamma = formula.gamma * row["amount"]
s = pd.Series({
"delta": delta,
"theta": theta,
"gamma": gamma,
})
return s
def predict_call_price(futures_price,data_buy,left_day,k):#修正新的call價格
pred_buy, b = correct_IV_call(futures_price,data_buy,left_day,k)#先尋找修正後的call隱波
whole_buy_price = []
for i in range(len(b)):
#用修正後的隱波套入BS模型得到價格並回傳
call_price = mibian.BS([futures_price,b[i],0.3,left_day],pred_buy[i]).callPrice
whole_buy_price.append(call_price)
return whole_buy_price
def greek_string(deets, iv):
#array deets needs [underlyingPrice, strikePrice, interestRate, daysToExpiration]
c = mibian.BS(deets, iv)
return ([
c.callPrice, c.putPrice, c.callDelta, c.putDelta, c.callDelta2,
c.putDelta2, c.callTheta, c.putTheta, c.callRho, c.putRho, c.vega,
c.gamma
])
def implied_vol(S, K, T, rfr, callprice=0.0, putprice=0.0):
"""
Calculates the implied volatility of the option.
"""
S1 = float(S)
K1 = float(K)
interest_rate = float(rfr * 100)
days_to_expiration = float(T * 365)
if callprice > 0.0:
bsc = mibian.BS([S1, K1, interest_rate, days_to_expiration],
callPrice=callprice)
elif putprice > 0.0:
bsc = mibian.BS([S1, K1, interest_rate, days_to_expiration],
putPrice=putprice)
implied_vol = round(bsc.impliedVolatility / 100, 6)
return implied_vol
def predict_put_price(futures_price,data_sell,left_day,k):#修正新的put價格
pred_sell,b = correct_IV_put(futures_price,data_sell,left_day,k)#先尋找修正後的put隱波
whole_sell_price = []
for i in range(len(b)):
#用修正後的隱波套入BS模型得到價格並回傳
put_price = mibian.BS([futures_price,b[i],0.3,left_day],pred_sell[i]).putPrice
whole_sell_price.append(put_price)
return whole_sell_price
def calc():
global TMX
global endTime
for K in prices:
c = mibian.BS([TMX, K, 0.0, (endTime - time.time()) / 15.0],
callPrice=C[K])
print c.impliedVolatility
print
def call_put_pricing_mibian(self, S_0, K, T, r, sigma, div, option='call'):
c = mibian.BS([S_0, K, r, T], volatility=sigma)
if option == 'call':
return c.callPrice
elif option == 'put':
return c.putPrice
else:
raise NameError('Option not defined correctly')
def y_days(self, row,int_rate=1.0,interval=0.0):
days = interval
x = self.x
y=[]
dte = (row.Expiration - pd.Timestamp('today')).days - days
if dte < 0:
return []
if dte == 0:
dte = .1
for a in x:
if row.Option == 'Call':
y.append((mibian.BS([float(a),row.Strike,int_rate,dte],volatility=row.Vol)
.callPrice-row.Price)*row.Quantity*100)
if row.Option == 'Put':
y.append((mibian.BS([float(a),row.Strike,int_rate,dte],volatility=row.Vol)
.putPrice-row.Price)*row.Quantity*100)
return np.array(y)
def compute_payoff(self, date=None, dte=None, iv_now=None):
day_of_exp = datetime.datetime.strptime(self.expiry, '%d%b%Y').date()
today = datetime.datetime.strptime(date, '%d%b%Y').date()
dte = np.max([(day_of_exp - today).days, 0]) + 0.000000001
if iv_now == None:
iv_now = self.iv
# If Call option...
if self.opt_type == 'C':
# If long self.calls...
if self.qty > 0:
# payoff = max(self.underlying_range- strike - premium, -premium) ???
self.payoff = (self.underlying_range.apply(lambda x: mibian.BS(
[x, self.strike, 6.47, dte], volatility=iv_now).callPrice)
- self.entry_price) * abs(self.qty)
# If short self.calls...
elif self.qty < 0:
# payoff = min(- self.underlying_range+ strike + premium, premium) ???
self.payoff = (self.entry_price - self.underlying_range.apply(
lambda x: mibian.BS([x, self.strike, 6.47, dte],
volatility=iv_now).callPrice)) * abs(
self.qty)
# If Put option...
elif self.opt_type == 'P':
# If long self.puts...
if self.qty > 0:
# payoff = max(strike - self.underlying_range- premium, -premium) ???
self.payoff = (self.underlying_range.apply(lambda x: mibian.BS(
[x, self.strike, 6.47, dte], volatility=iv_now).putPrice) -
self.entry_price) * abs(self.qty)
# If short self.puts...
elif self.qty < 0:
# payoff = min(- strike + self.underlying_range+ premium, premium) ???
self.payoff = (self.entry_price - self.underlying_range.apply(
lambda x: mibian.BS([x, self.strike, 6.47, dte],
volatility=iv_now).putPrice)) * abs(
self.qty)
# Set underlying price range as index
self.payoff.index = self.underlying_range
return self.payoff
def compute_expiry_payoff(self):
# If Call option...
if self.opt_type == 'C':
# If long self.calls...
if self.qty > 0:
# expiry_payoff = max(self.underlying_range- strike - premium, -premium) ???
self.expiry_payoff = (self.underlying_range.apply(
lambda x: mibian.BS([x, self.strike, 6.47, 0.00000001],
volatility=self.iv).callPrice) -
self.entry_price) * abs(self.qty)
# If short self.calls...
elif self.qty < 0:
# expiry_payoff = min(- self.underlying_range+ strike + premium, premium) ???
self.expiry_payoff = (
self.entry_price -
self.underlying_range.apply(lambda x: mibian.BS(
[x, self.strike, 6.47, 0.00000001], volatility=self.iv)
.callPrice)) * abs(self.qty)
# If Put option...
elif self.opt_type == 'P':
# If long self.puts...
if self.qty > 0:
# expiry_payoff = max(strike - self.underlying_range- premium, -premium) ???
self.expiry_payoff = (self.underlying_range.apply(
lambda x: mibian.BS([x, self.strike, 6.47, 0.00000001],
volatility=self.iv).putPrice) -
self.entry_price) * abs(self.qty)
# If short self.puts...
elif self.qty < 0:
# expiry_payoff = min(- strike + self.underlying_range+ premium, premium) ???
self.expiry_payoff = (
self.entry_price -
self.underlying_range.apply(lambda x: mibian.BS(
[x, self.strike, 6.47, 0.00000001], volatility=self.iv)
.putPrice)) * abs(self.qty)
# Set underlying price range as index
self.expiry_payoff.index = self.underlying_range
return self.expiry_payoff
def option_price(underlying_price: float,
strike_price: float,
interest: float,
expiry_date: date,
volatility: float,
obs_date: date = None):
"""
It is used to evaluate option's theoretical price and it's related greeks.
:param underlying_price: float
(S) Spot price
:param strike_price: float
(K) Strike price
:param interest: float
(r) Risk free interest rate
:param expiry_date: date
(T) Time to maturity i.e. expiry date
:param volatility: float
(v) (sigma) Volatility of the option
:param obs_date: date
Date of observation. By default present date.
:return: GreekValues
"""
days_to_exp = days_to_expiry(expiry_date, obs_date)
if days_to_exp > 0:
c = mibian.BS([underlying_price, strike_price, interest, days_to_exp],
volatility=volatility)
call = c.callPrice
call_delta = c.callDelta
call_dual_delta = c.callDelta2
call_theta = c.callTheta
call_rho = c.callRho
put = c.putPrice
put_delta = c.putDelta
put_dual_delta = c.putDelta2
put_theta = c.putTheta
put_rho = c.putRho
vega = c.vega
gamma = c.gamma
greek_values = GreekValues(call, call_delta, call_dual_delta,
call_theta, call_rho, put, put_delta,
put_dual_delta, put_theta, put_rho, vega,
gamma)
return greek_values
elif days_to_exp == 0:
greek_values = GreekValues(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
return greek_values
else:
_logger.warning("Enter a date greater than today")
_logger.info("You entered: %s" % expiry_date)
greek_values = GreekValues(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
return greek_values
def find_price(target_value, call_put, S, K, T, r, clicked):
if clicked and target_value and call_put and S and K and T and T >= 0 and r:
sigma = mibian.BS([S, K, r, T], volatility=target_value)
if call_put == 'c':
return sigma.callPrice
if call_put == 'p':
return sigma.putPrice
else:
return ''
def diagonal_spread(sT, interest_rate, front_strike, back_strike, front_future,
back_future, dte_front_opt, dte_back_opt):
'''
Diagonal spread (similar to a Calendar Spread) involves options of the same underlying but with different strike price & expiry
If a Call/Put is Sold with near-term expiration it is called "“front-month”"
If a Call/Put is Bought with long-term expiration it is called "“back-month”"
'''
net_premium = back_opt_premium - front_opt_premium
days_diff = dte_back_opt - dte_front_opt + 1
# Front-month IV
front_opt_iv = mibian.BS(
[front_future, front_strike, interest_rate, dte_front_opt],
callPrice=front_opt_premium).impliedVolatility
# Back-month IV
back_opt_iv = mibian.BS(
[back_future, back_strike, interest_rate, dte_back_opt],
callPrice=back_opt_premium).impliedVolatility
# Calendar Spread DataFrame
diagonal_spread = pd.DataFrame()
diagonal_spread['underlying_price'] = sT
diagonal_spread['front_opt_premium'] = np.nan
diagonal_spread['back_opt_premium'] = np.nan
for i in range(
0, len(diagonal_spread)
): # Calculating option price for different possible values of Future Contracts
diagonal_spread.loc[i, 'front_opt_premium'] = mibian.BS(
[
diagonal_spread.iloc[i]['underlying_price'], front_strike,
interest_rate, dte_front_opt
],
volatility=front_opt_iv).callPrice
diagonal_spread.loc[i, 'back_opt_premium'] = mibian.BS(
[
diagonal_spread.iloc[i]['underlying_price'] + days_diff,
back_strike, interest_rate, dte_back_opt
],
volatility=back_opt_iv).callPrice
diagonal_spread[
'payoff'] = diagonal_spread.back_opt_premium - diagonal_spread.front_opt_premium - net_premium
return diagonal_spread
def _test_py_vollib():
#CL,Q2019,560P,07/02/2019,0.6,1.61,0.54,1.54,1997,4465
F = 56.25
K = 56
sigma = .366591539
flag = 'p'
t = 15 / 365.0
r = .025
discounted_call_price = black.black(flag, F, K, t, r, sigma)
dcp = 1.54
ivpy = implied_volatility.implied_volatility(dcp, F, K, r, t, flag)
ivmn = mibian.BS([F, K, 2.5, 15], callPrice=dcp).impliedVolatility
discounted_call_price, ivpy, ivmn
def calculate_delta(dic, df, contract_type, curr_price):
df["Remaining Days"] = df["Expiration Date"] - datetime.now()
if contract_type == "Call":
delta_ls = [
mibian.BS([
curr_price, row["Strike"], dic["Interest Rate"],
row["Remaining Days"].days
], row["Volatility"][:-1]).callDelta
for index, row in df.iterrows()
]
elif contract_type == "Put":
delta_ls = [
mibian.BS([
curr_price, row["Strike"], dic["Interest Rate"],
row["Remaining Days"].days
], row["Volatility"][:-1]).putDelta
for index, row in df.iterrows()
]
else:
raise ValueError
df["Delta"] = pd.Series(delta_ls, index=df.index)
return df
def predict_call_price(futures_price, data_buy, left_day, k): #修正新的call價格
import mibian
import pandas as pd
import numpy as np
import statsmodels.api as sm
pred_buy, b = correct_IV_call(futures_price, data_buy, left_day,
k) #先尋找修正後的call隱波
whole_buy_price = []
for i in range(len(b)):
#用修正後的隱波套入BS模型得到價格並回傳
call_price = mibian.BS([futures_price, b[i], 0.3, left_day],
pred_buy[i]).callPrice
whole_buy_price.append(call_price)
return whole_buy_price
def predict_put_price(futures_price, data_sell, left_day, k): #修正新的put價格
import mibian
import pandas as pd
import numpy as np
import statsmodels.api as sm
pred_sell, b = correct_IV_put(futures_price, data_sell, left_day,
k) #先尋找修正後的put隱波
whole_sell_price = []
for i in range(len(b)):
#用修正後的隱波套入BS模型得到價格並回傳
put_price = mibian.BS([futures_price, b[i], 0.3, left_day],
pred_sell[i]).putPrice
whole_sell_price.append(put_price)
return whole_sell_price
def correct_IV_call(futures_price,data_buy,left_day,k):#修正call的隱波
IV_buy = []
for i in range(len(data_buy)):
try:
#先用真實價格套入BS模型回推隱波
print('結算價{}:'.format(i),float(data_buy['結算價'][i]))
a = mibian.BS([futures_price, float(data_buy['履約價'][i]), 0.003, left_day], callPrice= float(data_buy['結算價'][i]))
IV_buy.append(a.impliedVolatility)
except:
pass
weights_buy = np.polyfit(pd.to_numeric(k), pd.to_numeric(IV_buy), 6)#用6次式回歸修正
model_buy = np.poly1d(weights_buy)
b = list(range(min(data_buy['履約價']),max(data_buy['履約價'])+100,100))
pred_buy = model_buy(b)#套回修正過的回歸式回傳新的隱波
return pred_buy, b
def american_put_black_scholes(initial_stock_price, strike_price, rf_rate,
maturity, sigma, num_steps):
# Parameter initialization
deltaT = maturity / num_steps
up_factor = np.exp(sigma * np.sqrt(deltaT))
down_factor = 1.0 / up_factor
p = (np.exp(rf_rate * deltaT) - down_factor) / (up_factor - down_factor)
# Binomial Price Tree
stock_values = np.zeros((num_steps + 1, num_steps + 1))
stock_values[0, 0] = initial_stock_price
for i in range(1, num_steps + 1):
stock_values[i, 0] = stock_values[i - 1, 0] * up_factor
for j in range(1, i + 1):
stock_values[i, j] = stock_values[i - 1, j - 1] * down_factor
# savetxt('stock_values.csv', stock_values, delimiter=',')
# Option Price at Final Node
option_values = np.zeros((num_steps + 1, num_steps + 1))
for i in range(num_steps + 1):
option_values[num_steps,
i] = max(0, strike_price - stock_values[num_steps, i])
# Backward calculation for initial options price
for j in range(num_steps - 1):
option_values[num_steps, j] = mibian.BS([100, 105, 3, 365],
volatility=20).putPrice
for i in range(num_steps - 2, -1, -1):
for j in range(i + 1):
option_values[i, j] = max(
0, strike_price - stock_values[i, j],
np.exp(-rf_rate * deltaT) *
(p * option_values[i + 1, j] +
(1 - p) * option_values[i + 1, j + 1]))
# savetxt('option_values.csv', option_values, delimiter=',')
return option_values[0, 0]
def put_call_parity(underlying_price: float,
strike_price: float,
interest: float,
expiry_date: date,
obs_date: date = None,
call_price: float = None,
put_price: float = None):
"""
This is used to find the put call parity for the options.
Both call and put option price are required.
:param underlying_price: float
(S) Spot price
:param strike_price: float
(K) Strike price
:param interest: float
(r) Risk free interest rate
:param expiry_date: date
(T) Time to maturity i.e. expiry date
:param obs_date: date
Date of observation. By default present date.
:param call_price: float
Call option price for the strike.
:param put_price: float
Put option price for the strike.
:return: tuple(float, float)
Returns put call parity and implied volatility
"""
days_expiry = days_to_expiry(expiry_date, obs_date=obs_date)
if days_expiry > 0:
if (call_price is None) & (put_price is None):
_logger.warning("Both call and put price need to be given")
else:
c = mibian.BS(
[underlying_price, strike_price, interest, days_expiry],
callPrice=call_price,
putPrice=put_price)
return c.putCallParity, c.impliedVolatility
else:
_logger.warning("Enter a date greater than today")
_logger.info("You entered: %s" % expiry_date)
return