-
Notifications
You must be signed in to change notification settings - Fork 11
/
feature_functions.py
314 lines (246 loc) · 9.63 KB
/
feature_functions.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
# -*- coding: utf-8 -*-
"""
Created on Mon Sep 18 11:55:53 2023
@author: Local User
"""
import numpy as np
import math
import pandas as pd
import scipy.optimize as optimize
from scipy.stats import norm
def binomial_option_price(S, K, T, r, sigma, n, option_type):
dt = T / n
u = math.exp(sigma * math.sqrt(dt))
d = 1 / u
p = (math.exp(r * dt) - d) / (u - d)
option_tree = [[0 for j in range(n+1)] for i in range(n+1)]
# Calculate option values at expiration (n periods)
for j in range(n+1):
if option_type == 'call':
option_tree[n][j] = max(0, S * (u ** (n-j)) * (d ** j) - K)
elif option_type == 'put':
option_tree[n][j] = max(0, K - S * (u ** (n-j)) * (d ** j))
# Backward induction to calculate option values at earlier nodes
for i in range(n-1, -1, -1):
for j in range(i+1):
if option_type == 'call':
option_tree[i][j] = max(0, math.exp(-r * dt) * (p * option_tree[i+1][j] + (1-p) * option_tree[i+1][j+1]))
elif option_type == 'put':
option_tree[i][j] = max(0, math.exp(-r * dt) * (p * option_tree[i+1][j] + (1-p) * option_tree[i+1][j+1]))
return option_tree[0][0]
def bjerksund_stensland_greeks(S, K, T, r, sigma, option_type):
if option_type == "call":
option_type = 0
elif option_type == "put":
option_type = 1
d1 = (np.log(S / K) + (r + (sigma**2) / 2) * T) / (sigma * np.sqrt(T))
d2 = d1 - sigma * np.sqrt(T)
alpha = (r * (1 - option_type) - 0.5 * (sigma**2)) / (sigma**2)
beta = (r * (1 - option_type) + 0.5 * (sigma**2)) / (sigma**2)
if option_type == 0:
# Calculate Delta for a call option
delta = norm.cdf(d1)
# Calculate Gamma for a call option
gamma = norm.pdf(d1) / (S * sigma * np.sqrt(T))
# Calculate Theta for a call option
theta = (r * K * np.exp(-r * T) * norm.cdf(d2) -
(r - beta * sigma**2) * S * norm.cdf(d1) -
(1 - option_type) * (r - beta * sigma**2) * S * norm.pdf(d1) / (2 * np.sqrt(T)))
# Calculate Vega for a call option
vega = S * np.sqrt(T) * norm.pdf(d1)
return delta, gamma, theta, vega
elif option_type == 1:
# Calculate Delta for a put option
delta = -norm.cdf(-d1)
# Calculate Gamma for a put option
gamma = norm.pdf(d1) / (S * sigma * np.sqrt(T))
# Calculate Theta for a put option
theta = (r * K * np.exp(-r * T) * norm.cdf(-d2) -
(r - beta * sigma**2) * S * norm.cdf(-d1) +
(1 - option_type) * (r - beta * sigma**2) * S * norm.pdf(-d1) / (2 * np.sqrt(T)))
# Calculate Vega for a put option
vega = S * np.sqrt(T) * norm.pdf(d1)
return delta, gamma, theta, vega
def Binarizer(number):
if number <= 0:
return 0
elif number > 0:
return 1
def return_proba(prediction_dataset):
probabilities = []
for row in prediction_dataset.index:
prediction_data = prediction_dataset[prediction_dataset.index == row]
prediction = prediction_data["prediction"].iloc[0]
if prediction == 0:
probabilities.append(prediction_data["probability_0"].iloc[0])
elif prediction == 1:
probabilities.append(prediction_data["probability_1"].iloc[0])
return probabilities
def round_to_multiple(number, multiple):
return multiple * round(number / multiple)
def butterfly_cost(x):
return (x.iloc[1] * 2) - (x.iloc[0] + x.iloc[2])
def get_non_one(row):
if row['price_below_strike_prob'] != 1:
return row['price_below_strike_prob']
elif row['price_above_strike_prob'] != 1:
return row['price_above_strike_prob']
else:
return None
def premium_discount(row):
if row["last_quote.bid"] - row["intrinsic_value"] < 0:
return 0
else:
return row["last_quote.bid"] - row["intrinsic_value"]
def intrinsic_value_call(row):
if row["underlying_asset.price"] - row["details.strike_price"] < 0:
return 0
else:
return row["underlying_asset.price"] - row["details.strike_price"]
def intrinsic_value_put(row):
if row["details.strike_price"] - row["underlying_asset.price"] < 0:
return 0
else:
return row["details.strike_price"] - row["underlying_asset.price"]
def black_scholes(option_type, S, K, t, r, q, sigma):
"""
Calculate the Black-Scholes option price.
:param option_type: 'call' for call option, 'put' for put option.
:param S: Current stock price.
:param K: Strike price.
:param t: Time to expiration (in years).
:param r: Risk-free interest rate (annualized).
:param q: Dividend yield (annualized).
:param sigma: Stock price volatility (annualized).
:return: Option price.
"""
d1 = (math.log(S / K) + (r - q + 0.5 * sigma ** 2) * t) / (sigma * math.sqrt(t))
d2 = d1 - sigma * math.sqrt(t)
if option_type == 'call':
return S * math.exp(-q * t) * norm.cdf(d1) - K * math.exp(-r * t) * norm.cdf(d2)
elif option_type == 'put':
return K * math.exp(-r * t) * norm.cdf(-d2) - S * math.exp(-q * t) * norm.cdf(-d1)
else:
raise ValueError("Option type must be either 'call' or 'put'.")
def black_scholes_greeks(S, K, T, r, sigma, option_type):
"""
Computes the Black-Scholes Greeks: Delta, Gamma, Theta, Vega, Rho
Parameters:
S (float): Current price of the underlying asset
K (float): Strike price of the option
T (float): Time to expiration (in years)
r (float): Risk-free interest rate (annualized)
sigma (float): Volatility of the underlying asset (annualized)
option_type (str): 'call' for call option, 'put' for put option
Returns:
dict: A dictionary containing the Black-Scholes Greeks
"""
d1 = (math.log(S / K) + (r + 0.5 * sigma**2) * T) / (sigma * math.sqrt(T))
d2 = d1 - sigma * math.sqrt(T)
if option_type == 'call':
delta = norm.cdf(d1)
theta = - (S * norm.pdf(d1) * sigma / (2 * math.sqrt(T)) + r * K * math.exp(-r * T) * norm.cdf(d2))
rho = K * T * math.exp(-r * T) * norm.cdf(d2)
elif option_type == 'put':
delta = norm.cdf(d1) - 1
theta = - (S * norm.pdf(d1) * sigma / (2 * math.sqrt(T)) - r * K * math.exp(-r * T) * norm.cdf(-d2))
rho = -K * T * math.exp(-r * T) * norm.cdf(-d2)
else:
raise ValueError("Invalid option type. Use 'call' or 'put'.")
gamma = norm.pdf(d1) / (S * sigma * math.sqrt(T))
vega = S * norm.pdf(d1) * math.sqrt(T) / 100 # Dividing by 100 to scale vega to 1% change in volatility
greeks = {
'Delta': delta,
'Gamma': gamma,
'Theta': theta,
'Vega': vega,
'Rho': rho
}
return pd.Series(greeks)
def seconds_to_days(seconds):
"""
Converts seconds to days.
Parameters:
seconds (int or float): The number of seconds.
Returns:
float: The number of days.
"""
seconds_per_day = 24 * 60 * 60 # Number of seconds in a day
days = seconds / seconds_per_day
return days
def call_implied_vol(row):
S = row["underlying_price"]
K = row["strike_price"]
t = row["time_to_exp"]
r = .05
q = 0.015
option_type = "call"
def f_call(sigma):
return black_scholes(option_type, S, K, t, r, q, sigma) - row["call_c"]
try:
call_newton_vol = optimize.newton(f_call, x0=0.15, tol=0.05, maxiter=50)
except:
call_newton_vol = np.nan
return call_newton_vol
def put_implied_vol(row):
S = row["underlying_price"]
K = row["strike_price"]
t = row["time_to_exp"]
r = .05
q = 0.015
option_type = "put"
def f_put(sigma):
return black_scholes(option_type, S, K, t, r, q, sigma) - row["put_c"]
try:
put_newton_vol = optimize.newton(f_put, x0=0.15, tol=0.05, maxiter=50)
except:
put_newton_vol = np.nan
return put_newton_vol
def call_fair_value(row):
S = row["underlying_price"]
K = row["strike_price"]
t = row["time_to_exp"]
sigma = row["call_implied_vol"]
r = .05
q = 0.015
option_type = "call"
if np.isnan(sigma):
return np.nan
else:
return black_scholes(option_type, S, K, t, r, q, sigma)
def put_fair_value(row):
S = row["underlying_price"]
K = row["strike_price"]
t = row["time_to_exp"]
sigma = row["put_implied_vol"]
r = .05
q = 0.015
option_type = "put"
if np.isnan(sigma):
return np.nan
else:
return black_scholes(option_type, S, K, t, r, q, sigma)
def call_greeks(row):
S = row["underlying_price"]
K = row["strike_price"]
T = row["time_to_exp"]
sigma = row["call_implied_vol"]
r = .05
q = 0.015
option_type = "call"
if np.isnan(sigma):
return np.nan
else:
return black_scholes_greeks(S, K, T, r, sigma, option_type)
def put_greeks(row):
S = row["underlying_price"]
K = row["strike_price"]
T = row["time_to_exp"]
sigma = row["put_implied_vol"]
r = .05
q = 0.015
option_type = "put"
if np.isnan(sigma):
return np.nan
else:
return black_scholes_greeks(S, K, T, r, sigma, option_type)