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
|
# <nbformat>2</nbformat>
# <markdowncell>
# # Parallel Monto-Carlo options pricing
# <markdowncell>
# ## Problem setup
# <codecell>
from __future__ import print_function
import sys
import time
from IPython.parallel import Client
import numpy as np
from mckernel import price_options
from matplotlib import pyplot as plt
# <codecell>
cluster_profile = "default"
price = 100.0 # Initial price
rate = 0.05 # Interest rate
days = 260 # Days to expiration
paths = 10000 # Number of MC paths
n_strikes = 6 # Number of strike values
min_strike = 90.0 # Min strike price
max_strike = 110.0 # Max strike price
n_sigmas = 5 # Number of volatility values
min_sigma = 0.1 # Min volatility
max_sigma = 0.4 # Max volatility
# <codecell>
strike_vals = np.linspace(min_strike, max_strike, n_strikes)
sigma_vals = np.linspace(min_sigma, max_sigma, n_sigmas)
# <markdowncell>
# ## Parallel computation across strike prices and volatilities
# <markdowncell>
# The Client is used to setup the calculation and works with all engines.
# <codecell>
c = Client(profile=cluster_profile)
# <markdowncell>
# A LoadBalancedView is an interface to the engines that provides dynamic load
# balancing at the expense of not knowing which engine will execute the code.
# <codecell>
view = c.load_balanced_view()
# <codecell>
print("Strike prices: ", strike_vals)
print("Volatilities: ", sigma_vals)
# <markdowncell>
# Submit tasks for each (strike, sigma) pair.
# <codecell>
t1 = time.time()
async_results = []
for strike in strike_vals:
for sigma in sigma_vals:
ar = view.apply_async(price_options, price, strike, sigma, rate, days, paths)
async_results.append(ar)
# <codecell>
print("Submitted tasks: ", len(async_results))
# <markdowncell>
# Block until all tasks are completed.
# <codecell>
c.wait(async_results)
t2 = time.time()
t = t2-t1
print("Parallel calculation completed, time = %s s" % t)
# <markdowncell>
# ## Process and visualize results
# <markdowncell>
# Get the results using the `get` method:
# <codecell>
results = [ar.get() for ar in async_results]
# <markdowncell>
# Assemble the result into a structured NumPy array.
# <codecell>
prices = np.empty(n_strikes*n_sigmas,
dtype=[('ecall',float),('eput',float),('acall',float),('aput',float)]
)
for i, price in enumerate(results):
prices[i] = tuple(price)
prices.shape = (n_strikes, n_sigmas)
# <markdowncell>
# Plot the value of the European call in (volatility, strike) space.
# <codecell>
plt.figure()
plt.contourf(sigma_vals, strike_vals, prices['ecall'])
plt.axis('tight')
plt.colorbar()
plt.title('European Call')
plt.xlabel("Volatility")
plt.ylabel("Strike Price")
# <markdowncell>
# Plot the value of the Asian call in (volatility, strike) space.
# <codecell>
plt.figure()
plt.contourf(sigma_vals, strike_vals, prices['acall'])
plt.axis('tight')
plt.colorbar()
plt.title("Asian Call")
plt.xlabel("Volatility")
plt.ylabel("Strike Price")
# <markdowncell>
# Plot the value of the European put in (volatility, strike) space.
# <codecell>
plt.figure()
plt.contourf(sigma_vals, strike_vals, prices['eput'])
plt.axis('tight')
plt.colorbar()
plt.title("European Put")
plt.xlabel("Volatility")
plt.ylabel("Strike Price")
# <markdowncell>
# Plot the value of the Asian put in (volatility, strike) space.
# <codecell>
plt.figure()
plt.contourf(sigma_vals, strike_vals, prices['aput'])
plt.axis('tight')
plt.colorbar()
plt.title("Asian Put")
plt.xlabel("Volatility")
plt.ylabel("Strike Price")
# <codecell>
plt.show()
|
