-
Notifications
You must be signed in to change notification settings - Fork 1
/
Copy pathoptions.py
200 lines (174 loc) · 9.67 KB
/
options.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
import pandas_market_calendars as mcal
import numpy as np
from scipy import optimize
from scipy import stats
# otype = Call or Put
# S0 = Underlying Price
# K = Strike
# T = days to expiration or date (YYYY-MM-DD)
# ls = Long or Short
# vol = Volatility
# marketPrice = Options Market Price
# q = Dividend Yield
# r = Risk Free Rate
class option():
def __init__(self, otype, S0, K, q=0, marketPrice=None, T=None, expDay=None, vol=None, r=0.025, ls='Long'):
self.S0=S0
self.K=K
self.r=r
self.otype=otype
self.daysInYear = 252
self.q=q
self.ls = ls
if T is None and expDay is None:
print('Please enter days to expiry or expiration day')
elif T is None:
self.expDayStr = expDay
expDay = np.datetime64(expDay)
nyse = mcal.get_calendar('NYSE')
self.T= (np.busday_count(np.datetime64('today'), expDay, holidays=nyse.holidays().holidays)+1)/self.daysInYear
else:
self.T=T
if marketPrice is None and vol is None:
print('Please enter either market price or implied vol of option')
elif marketPrice is None:
self.vol=vol
self.marketPrice=self.price()
elif vol is None:
self.marketPrice=marketPrice
self.vol=self.IV()
def inpcheck(self, S0=None, K=None, vol=None, r=None, T=None, q=0):
if S0 is None: S0 = self.S0
if K is None: K = self.K
if vol is None: vol = self.vol
if r is None: r = self.r
if T is None: T = self.T
return S0, K, vol, r, T, q
def d1d2(self, S0=None, K=None, vol=None, r=None, T=None, q=0):
S0, K, vol, r, T, q = self.inpcheck(S0, K, vol, r, T, q)
d1 = (np.log(S0/K)+(r - q + vol**2/2)*T)/(vol*np.sqrt(T))
d2 = d1-vol*np.sqrt(T)
return d1, d2
def price(self, S0=None, K=None, vol=None, r=None, T=None, q=0):
S0, K, vol, r, T, q = self.inpcheck(S0, K, vol, r, T, q)
d1, d2 = self.d1d2(S0, K, vol, r, T, q)
if self.otype == 'Call':
return S0*np.exp(-q*T)*stats.norm.cdf(d1)-K*np.exp(-r*T)*stats.norm.cdf(d2)
elif self.otype == 'Put':
return K*np.exp(-r*T)*stats.norm.cdf(-d2) - S0*np.exp(-q*T)*stats.norm.cdf(-d1)
def IV(self):
c = lambda x: (self.price(vol=x)-self.marketPrice)**2
x = 0.2
res = optimize.minimize(c, x)
return res.x[0]
def delta(self, S0=None, K=None, vol=None, r=None, T=None, q=0): #dV/dS
S0, K, vol, r, T, q = self.inpcheck(S0, K, vol, r, T, q)
d1, d2 = self.d1d2(S0, K, vol, r, T, q)
if self.otype == 'Call':
return np.exp(-q*T)*stats.norm.cdf(d1)
elif self.otype == 'Put':
return -np.exp(-q*T)*stats.norm.cdf(-d1)
def vega(self, S0=None, K=None, vol=None, r=None, T=None, q=0): #dV/dvol
S0, K, vol, r, T, q = self.inpcheck(S0, K, vol, r, T, q)
d1, d2 = self.d1d2(S0, K, vol, r, T, q)
return np.exp(-q*T)*S0*np.sqrt(T)*stats.norm.pdf(d1)
def theta(self, S0=None, K=None, vol=None, r=None, T=None, q=0): #-dV/dT
S0, K, vol, r, T, q = self.inpcheck(S0, K, vol, r, T, q)
d1, d2 = self.d1d2(S0, K, vol, r, T, q)
if self.otype == 'Call':
return -(np.exp(-q*T)*S0*stats.norm.pdf(d1)*vol)/(2*np.sqrt(T)) - r*K*np.exp(-r*T)*stats.norm.cdf(d2) + q*S0*np.exp(-q*T)*stats.norm.cdf(d1)
elif self.otype == 'Put':
return -(np.exp(-q*T)*S0*stats.norm.pdf(-d1)*vol)/(2*np.sqrt(T)) + r*K*np.exp(-r*T)*stats.norm.cdf(-d2) - q*S0*np.exp(-q*T)*stats.norm.cdf(-d1)
def rho(self, S0=None, K=None, vol=None, r=None, T=None, q=0): #dV.dr
S0, K, vol, r, T, q = self.inpcheck(S0, K, vol, r, T, q)
d1, d2 = self.d1d2(S0, K, vol, r, T, q)
if self.otype == 'Call':
return K*T*np.exp(-r*T)*stats.norm.cdf(d2)
elif self.otype == 'Put':
return -K*T*np.exp(-r*T)*stats.norm.cdf(-d2)
def omega(self, S0=None, K=None, vol=None, r=None, T=None, q=0): #aka lambda - leverage = dV/dS * S/V
S0, K, vol, r, T, q = self.inpcheck(S0, K, vol, r, T, q)
return self.delta(S0, K, vol, r, T, q) * (S0/self.price(S0, K, vol, r, T, q))
def gamma(self, S0=None, K=None, vol=None, r=None, T=None, q=0): #d^2V/dS^2
S0, K, vol, r, T, q = self.inpcheck(S0, K, vol, r, T, q)
d1, d2 = self.d1d2(S0, K, vol, r, T, q)
return np.exp(-q*T)*(stats.norm.pdf(d1)/(S0*vol*np.sqrt(T)))
def vanna(self, S0=None, K=None, vol=None, r=None, T=None, q=0): #d^2V/dSdvol
S0, K, vol, r, T, q = self.inpcheck(S0, K, vol, r, T, q)
d1, d2 = self.d1d2(S0, K, vol, r, T, q)
return -np.exp(-q*T)*stats.norm.pdf(d1)*d2/vol
def charm(self, S0=None, K=None, vol=None, r=None, T=None, q=0): #-d^2V/dTdS
S0, K, vol, r, T, q = self.inpcheck(S0, K, vol, r, T, q)
d1, d2 = self.d1d2(S0, K, vol, r, T, q)
if self.otype == 'Call':
return q*np.exp(-q*T)*stats.norm.cdf(d1) - np.exp(-q*T)*stats.norm.pdf(d1)*((2*(r-q)*T - d2*vol*np.sqrt(T))/(2*T*vol*np.sqrt(T)))
elif self.otype == 'Put':
return -q*np.exp(-q*T)*stats.norm.cdf(-d1) - np.exp(-q*T)*stats.norm.pdf(d1)*((2*(r-q)*T - d2*vol*np.sqrt(T))/(2*T*vol*np.sqrt(T)))
def vomma(self, S0=None, K=None, vol=None, r=None, T=None, q=0): #d^2V/dvol^2
S0, K, vol, r, T, q = self.inpcheck(S0, K, vol, r, T, q)
d1, d2 = self.d1d2(S0, K, vol, r, T, q)
return S0*np.exp(-q*T)*stats.norm.pdf(d1)*np.sqrt(T)*((d1*d2)/vol)
def veta(self, S0=None, K=None, vol=None, r=None, T=None, q=0): #d^2V/dvoldT
S0, K, vol, r, T, q = self.inpcheck(S0, K, vol, r, T, q)
d1, d2 = self.d1d2(S0, K, vol, r, T, q)
return -S0*np.exp(-q*T)*stats.norm.pdf(d1)*np.sqrt(T)*(q+(((r-q)*d1)/(vol*np.sqrt(T)))-(1+d1*d2)/(2*T))
def speed(self, S0=None, K=None, vol=None, r=None, T=None, q=0): #d^3V/dS^3
S0, K, vol, r, T, q = self.inpcheck(S0, K, vol, r, T, q)
d1, d2 = self.d1d2(S0, K, vol, r, T, q)
return -np.exp(-q*T)*((stats.norm.pdf(d1))/(S0**2*vol*np.sqrt(T)))*(d1/(vol*np.sqrt(T))+1)
def zomma(self, S0=None, K=None, vol=None, r=None, T=None, q=0): #d^3V/dS^2dvol
S0, K, vol, r, T, q = self.inpcheck(S0, K, vol, r, T, q)
d1, d2 = self.d1d2(S0, K, vol, r, T, q)
return np.exp(-q*T)*((stats.norm.pdf(d1)*(d1*d2-1))/(S0*vol**2*np.sqrt(T)))
def color(self, S0=None, K=None, vol=None, r=None, T=None, q=0): #d^3V/dS^2dT
S0, K, vol, r, T, q = self.inpcheck(S0, K, vol, r, T, q)
d1, d2 = self.d1d2(S0, K, vol, r, T, q)
return -np.exp(-q*T)*(stats.norm.pdf(d1)/(2*S0*T*vol*np.sqrt(T)))
def ultima(self, S0=None, K=None, vol=None, r=None, T=None, q=0): #d^3V/dvol^3
S0, K, vol, r, T, q = self.inpcheck(S0, K, vol, r, T, q)
d1, d2 = self.d1d2(S0, K, vol, r, T, q)
return (-self.vega(S0, K, vol, r, T, q)/vol**2)*(d1*d2*(1-d1*d2)+d1**2+d2**2)
def dualDelta(self, S0=None, K=None, vol=None, r=None, T=None, q=0): #dV/dK
S0, K, vol, r, T, q = self.inpcheck(S0, K, vol, r, T, q)
d1, d2 = self.d1d2(S0, K, vol, r, T, q)
if self.otype == 'Call':
return -np.exp(-r*T)*stats.norm.cdf(d2)
elif self.otype == 'Put':
return -np.exp(-r*T)*stats.norm.cdf(-d2)
def dualGamma(self, S0=None, K=None, vol=None, r=None, T=None, q=0): #d^2V/dK^2
S0, K, vol, r, T, q = self.inpcheck(S0, K, vol, r, T, q)
d1, d2 = self.d1d2(S0, K, vol, r, T, q)
return np.exp(-r*T)*(stats.norm.pdf(d2)/(K*vol*np.sqrt(T)))
#toSweep dictionary with variables to sweep as key and value as (min, max, steps)
def sweep(self, toSweep, toGrab):
inps = {'S0':self.S0, 'K':self.K, 'vol':self.vol, 'r':self.r, 'T':self.T, 'q':self.q}
vectors = dict([(k, np.linspace(toSweep[k][0], toSweep[k][1], toSweep[k][2])) for k in toSweep])
scalars = dict([(k, inps[k]) for k in inps if k not in vectors])
if len(toSweep) == 1:
out = np.array(list(vectors.values()))
if len(toSweep) == 2:
out = np.meshgrid(list(vectors.values())[0], list(vectors.values())[1])
if len(toSweep) == 3:
out = np.meshgrid(list(vectors.values())[0], list(vectors.values())[1], list(vectors.values())[2])
grids = dict([(k, out[i]) for i, k in enumerate(vectors)])
combined = {**grids, **scalars}
data = (combined['S0'], combined['K'], combined['vol'], combined['r'], combined['T'], combined['q'])
out = {}
if 'price' in toGrab: out['price'] = self.price(*data)
if 'delta' in toGrab: out['delta'] = self.delta(*data)
if 'vega' in toGrab: out['vega'] = self.vega(*data)
if 'theta' in toGrab: out['theta'] = self.theta(*data)
if 'rho' in toGrab: out['rho'] = self.rho(*data)
if 'omega' in toGrab: out['omega'] = self.omega(*data)
if 'gamma' in toGrab: out['gamma'] = self.gamma(*data)
if 'vanna' in toGrab: out['vanna'] = self.vanna(*data)
if 'charm' in toGrab: out['charm'] = self.charm(*data)
if 'vomma' in toGrab: out['vomma'] = self.vomma(*data)
if 'veta' in toGrab: out['veta'] = self.veta(*data)
if 'speed' in toGrab: out['speed'] = self.speed(*data)
if 'zomma' in toGrab: out['zomma'] = self.zomma(*data)
if 'color' in toGrab: out['color'] = self.color(*data)
if 'ultima' in toGrab: out['ultima'] = self.ultima(*data)
if 'dualDelta' in toGrab: out['dualDelta'] = self.dualDelta(*data)
if 'dualGamma' in toGrab: out['dualGamma'] = self.dualGamma(*data)
return {**combined, **out, **{'ls': self.ls}}