Options Pricing

Code/portfolio_optimizer.py

@@ -0,0 +1,8 @@
+import pandas as pd 
+import matplotlib.pyplot as plt
+import seaborn as sns
+import numpy as np
+import statsmodels.api as sm 
+import time 
+import math
+import datetime

options-fair-price-valuation/blackScholes.py

@@ -0,0 +1,42 @@
+import numpy as np
+import datetime
+import scipy.stats as si
+import numpy as np
+import scipy.stats as si
+import yfinance as yf
+
+def black_scholes_calc(S, K, T, r, sigma, option = 'call'): 
+	#S: Current Stock Price
+    #K: Strike price
+    #T: Time to maturity in Years
+    #r: Risk Free interest rate
+    #sigma: Volatility of underlying asset
+
+    d1 = (np.log(S / K) + (r + 0.5 * sigma ** 2) * T) / (sigma * np.sqrt(T))
+    d2 = (np.log(S / K) + (r - 0.5 * sigma ** 2) * T) / (sigma * np.sqrt(T))
+
+    if option == 'call':
+        result = (S * si.norm.cdf(d1, 0.0, 1.0) - K * np.exp(-r * T) * si.norm.cdf(d2, 0.0, 1.0))
+    if option == 'put':
+        result = (K * np.exp(-r * T) * si.norm.cdf(-d2, 0.0, 1.0) - S * si.norm.cdf(-d1, 0.0, 1.0))
+
+    return result
+
+'''
+Sample Run
+'''
+s = yf.Ticker('AAPL')
+opt = s.option_chain('2020-08-21')
+call= opt.calls 
+S = s.history(period = "max")['Close'].iloc[-1]
+T = (datetime.date(2020,11,20) - datetime.date(2020,7,24)).days / 365.0
+print(S, T)
+for i in range(len(call)):
+	v = call.iloc[i]['impliedVolatility']
+	r = 0.17900 
+	K = call.iloc[i]['strike']
+	print(K)
+	print ('Price: %.4f' % black_scholes_calc(S, K, T, 0.014, v))
+
+
+

options-fair-price-valuation/monteCarlo.py

@@ -0,0 +1,40 @@
+import datetime
+from random import gauss
+from math import exp,sqrt
+import yfinance as yf
+import pandas as pd
+
+
+def monterCarloPriceGenerator(sP, vol, rfi, time_diff):
+	price = sP*exp((rfi - 0.5*vol**2)*time_diff+ vol*sqrt(time_diff)*gauss(0,1.0))
+	return price
+
+def call_payoff(sT, k):
+	return max(sT-k, 0)
+#Stock
+s = yf.Ticker('AAPL')
+opt = s.option_chain('2020-08-21')
+call= opt.calls 
+
+def finalPrice(S,v,r,T,K):
+	simulations = 900000
+	payoffs = []
+	discount_factor = exp(-r * T)
+
+	for i in range(simulations):
+	    S_T = monterCarloPriceGenerator(S,v,r,T)
+	    payoffs.append(call_payoff(S_T, K))
+	price = discount_factor * (sum(payoffs) / float(simulations))
+	print ('Price: %.4f' % price)
+
+#print(call.iloc[30]['impliedVolatility'])
+#print(call.head(40))
+S = s.history(period = "max")['Close'].iloc[-1]
+r = 0.17900  # rate of 0.14%
+T = (datetime.date(2020,8,21) - datetime.date(2020,7,24)).days / 365.0
+for i in range(len(call)):
+	v = call.iloc[i]['impliedVolatility']
+	K = call.iloc[i]['strike']
+	print(K)
+	finalPrice(S,v,r,T,K)
+