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Fixing parallel options pricing example.
Brian E. Granger -
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1 def price_options(S=100.0, K=100.0, sigma=0.25, r=0.05, days=260, paths=10000):
2 """
3 Price European and Asian options using a Monte Carlo method.
4
5 Parameters
6 ----------
7 S : float
8 The initial price of the stock.
9 K : float
10 The strike price of the option.
11 sigma : float
12 The volatility of the stock.
13 r : float
14 The risk free interest rate.
15 days : int
16 The number of days until the option expires.
17 paths : int
18 The number of Monte Carlo paths used to price the option.
19
20 Returns
21 -------
22 A tuple of (E. call, E. put, A. call, A. put) option prices.
23 """
24 import numpy as np
25 from math import exp,sqrt
26
27 h = 1.0/days
28 const1 = exp((r-0.5*sigma**2)*h)
29 const2 = sigma*sqrt(h)
30 stock_price = S*np.ones(paths, dtype='float64')
31 stock_price_sum = np.zeros(paths, dtype='float64')
32 for j in range(days):
33 growth_factor = const1*np.exp(const2*np.random.standard_normal(paths))
34 stock_price = stock_price*growth_factor
35 stock_price_sum = stock_price_sum + stock_price
36 stock_price_avg = stock_price_sum/days
37 zeros = np.zeros(paths, dtype='float64')
38 r_factor = exp(-r*h*days)
39 euro_put = r_factor*np.mean(np.maximum(zeros, K-stock_price))
40 asian_put = r_factor*np.mean(np.maximum(zeros, K-stock_price_avg))
41 euro_call = r_factor*np.mean(np.maximum(zeros, stock_price-K))
42 asian_call = r_factor*np.mean(np.maximum(zeros, stock_price_avg-K))
43 return (euro_call, euro_put, asian_call, asian_put)
44
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@@ -1,2053 +1,2054 b''
1 <?xml version="1.0" encoding="utf-8"?>
1 <?xml version="1.0" encoding="utf-8"?>
2 <notebook>
2 <notebook>
3 <name>mcpricer</name>
3 <name>mcpricer</name>
4 <nbformat>2</nbformat>
4 <nbformat>2</nbformat>
5 <worksheets>
5 <worksheets>
6 <worksheet>
6 <worksheet>
7 <cells>
7 <cells>
8 <markdowncell>
8 <markdowncell>
9 <source># Parallel Monto-Carlo options pricing</source>
9 <source># Parallel Monto-Carlo options pricing</source>
10 </markdowncell>
10 </markdowncell>
11 <markdowncell>
11 <markdowncell>
12 <source>## Problem setup</source>
12 <source>## Problem setup</source>
13 </markdowncell>
13 </markdowncell>
14 <codecell>
14 <codecell>
15 <input>import sys
15 <input>import sys
16 import time
16 import time
17 from IPython.parallel import Client
17 from IPython.parallel import Client
18 import numpy as np
18 import numpy as np
19 from mcpricer import price_options
19 from mckernel import price_options
20 from matplotlib import pyplot as plt</input>
20 from matplotlib import pyplot as plt</input>
21 <language>python</language>
21 <language>python</language>
22 <prompt_number>27</prompt_number>
22 <prompt_number>1</prompt_number>
23 <collapsed>1</collapsed>
23 <collapsed>1</collapsed>
24 <outputs />
24 <outputs />
25 </codecell>
25 </codecell>
26 <codecell>
26 <codecell>
27 <input>cluster_profile = "default"
27 <input>cluster_profile = "default"
28 price = 100.0 # Initial price
28 price = 100.0 # Initial price
29 rate = 0.05 # Interest rate
29 rate = 0.05 # Interest rate
30 days = 260 # Days to expiration
30 days = 260 # Days to expiration
31 paths = 10000 # Number of MC paths
31 paths = 10000 # Number of MC paths
32 n_strikes = 5 # Number of strike values
32 n_strikes = 5 # Number of strike values
33 min_strike = 90.0 # Min strike price
33 min_strike = 90.0 # Min strike price
34 max_strike = 110.0 # Max strike price
34 max_strike = 110.0 # Max strike price
35 n_sigmas = 5 # Number of volatility values
35 n_sigmas = 5 # Number of volatility values
36 min_sigma = 0.1 # Min volatility
36 min_sigma = 0.1 # Min volatility
37 max_sigma = 0.4 # Max volatility</input>
37 max_sigma = 0.4 # Max volatility</input>
38 <language>python</language>
38 <language>python</language>
39 <prompt_number>28</prompt_number>
39 <prompt_number>2</prompt_number>
40 <collapsed>1</collapsed>
40 <collapsed>1</collapsed>
41 <outputs />
41 <outputs />
42 </codecell>
42 </codecell>
43 <codecell>
43 <codecell>
44 <input>strike_vals = np.linspace(min_strike, max_strike, n_strikes)
44 <input>strike_vals = np.linspace(min_strike, max_strike, n_strikes)
45 sigma_vals = np.linspace(min_sigma, max_sigma, n_sigmas)</input>
45 sigma_vals = np.linspace(min_sigma, max_sigma, n_sigmas)</input>
46 <language>python</language>
46 <language>python</language>
47 <prompt_number>29</prompt_number>
47 <prompt_number>3</prompt_number>
48 <collapsed>1</collapsed>
48 <collapsed>1</collapsed>
49 <outputs />
49 <outputs />
50 </codecell>
50 </codecell>
51 <markdowncell>
51 <markdowncell>
52 <source>## Parallel computation across strike prices and volatilities</source>
52 <source>## Parallel computation across strike prices and volatilities</source>
53 </markdowncell>
53 </markdowncell>
54 <markdowncell>
54 <markdowncell>
55 <source>The Client is used to setup the calculation and works with all engines.</source>
55 <source>The Client is used to setup the calculation and works with all engines.</source>
56 </markdowncell>
56 </markdowncell>
57 <codecell>
57 <codecell>
58 <input>c = Client(profile=cluster_profile)</input>
58 <input>c = Client(profile=cluster_profile)</input>
59 <language>python</language>
59 <language>python</language>
60 <prompt_number>30</prompt_number>
60 <prompt_number>4</prompt_number>
61 <collapsed>1</collapsed>
61 <collapsed>1</collapsed>
62 <outputs />
62 <outputs />
63 </codecell>
63 </codecell>
64 <markdowncell>
64 <markdowncell>
65 <source>A LoadBalancedView is an interface to the engines that provides dynamic load
65 <source>A LoadBalancedView is an interface to the engines that provides dynamic load
66 balancing at the expense of not knowing which engine will execute the code.</source>
66 balancing at the expense of not knowing which engine will execute the code.</source>
67 </markdowncell>
67 </markdowncell>
68 <codecell>
68 <codecell>
69 <input>view = c.load_balanced_view()</input>
69 <input>view = c.load_balanced_view()</input>
70 <language>python</language>
70 <language>python</language>
71 <prompt_number>31</prompt_number>
71 <prompt_number>5</prompt_number>
72 <collapsed>1</collapsed>
72 <collapsed>1</collapsed>
73 <outputs />
73 <outputs />
74 </codecell>
74 </codecell>
75 <codecell>
75 <codecell>
76 <input>print "Strike prices: ", strike_vals
76 <input>print "Strike prices: ", strike_vals
77 print "Volatilities: ", sigma_vals</input>
77 print "Volatilities: ", sigma_vals</input>
78 <language>python</language>
78 <language>python</language>
79 <prompt_number>32</prompt_number>
79 <prompt_number>6</prompt_number>
80 <collapsed>0</collapsed>
80 <collapsed>0</collapsed>
81 <outputs>
81 <outputs>
82 <output>
82 <output>
83 <output_type>stream</output_type>
83 <output_type>stream</output_type>
84 <text>Strike prices: [ 90. 95. 100. 105. 110.]
84 <text>Strike prices: [ 90. 95. 100. 105. 110.]
85 Volatilities: [ 0.1 0.175 0.25 0.325 0.4 ]</text>
85 Volatilities: [ 0.1 0.175 0.25 0.325 0.4 ]</text>
86 </output>
86 </output>
87 </outputs>
87 </outputs>
88 </codecell>
88 </codecell>
89 <markdowncell>
89 <markdowncell>
90 <source>Submit tasks for each (strike, sigma) pair.</source>
90 <source>Submit tasks for each (strike, sigma) pair.</source>
91 </markdowncell>
91 </markdowncell>
92 <codecell>
92 <codecell>
93 <input>t1 = time.time()
93 <input>t1 = time.time()
94 async_results = []
94 async_results = []
95 for strike in strike_vals:
95 for strike in strike_vals:
96 for sigma in sigma_vals:
96 for sigma in sigma_vals:
97 ar = view.apply_async(price_options, price, strike, sigma, rate, days, paths)
97 ar = view.apply_async(price_options, price, strike, sigma, rate, days, paths)
98 async_results.append(ar)</input>
98 async_results.append(ar)</input>
99 <language>python</language>
99 <language>python</language>
100 <prompt_number>33</prompt_number>
100 <prompt_number>7</prompt_number>
101 <collapsed>1</collapsed>
101 <collapsed>1</collapsed>
102 <outputs />
102 <outputs />
103 </codecell>
103 </codecell>
104 <codecell>
104 <codecell>
105 <input>print "Submitted tasks: ", len(async_results)</input>
105 <input>print "Submitted tasks: ", len(async_results)</input>
106 <language>python</language>
106 <language>python</language>
107 <prompt_number>34</prompt_number>
107 <prompt_number>8</prompt_number>
108 <collapsed>0</collapsed>
108 <collapsed>0</collapsed>
109 <outputs>
109 <outputs>
110 <output>
110 <output>
111 <output_type>stream</output_type>
111 <output_type>stream</output_type>
112 <text>Submitted tasks: 25</text>
112 <text>Submitted tasks: 25</text>
113 </output>
113 </output>
114 </outputs>
114 </outputs>
115 </codecell>
115 </codecell>
116 <markdowncell>
116 <markdowncell>
117 <source>Block until all tasks are completed.</source>
117 <source>Block until all tasks are completed.</source>
118 </markdowncell>
118 </markdowncell>
119 <codecell>
119 <codecell>
120 <input>c.wait(async_results)
120 <input>c.wait(async_results)
121 t2 = time.time()
121 t2 = time.time()
122 t = t2-t1
122 t = t2-t1
123
123
124 print "Parallel calculation completed, time = %s s" % t</input>
124 print "Parallel calculation completed, time = %s s" % t</input>
125 <language>python</language>
125 <language>python</language>
126 <prompt_number>35</prompt_number>
126 <prompt_number>9</prompt_number>
127 <collapsed>0</collapsed>
127 <collapsed>0</collapsed>
128 <outputs>
128 <outputs>
129 <output>
129 <output>
130 <output_type>stream</output_type>
130 <output_type>stream</output_type>
131 <text>Parallel calculation completed, time = 1.8046438694 s</text>
131 <text>Parallel calculation completed, time = 2.57819604874 s</text>
132 </output>
132 </output>
133 </outputs>
133 </outputs>
134 </codecell>
134 </codecell>
135 <markdowncell>
135 <markdowncell>
136 <source>## Process and visualize results</source>
136 <source>## Process and visualize results</source>
137 </markdowncell>
137 </markdowncell>
138 <markdowncell>
138 <markdowncell>
139 <source>Get the results using the `get` method:</source>
139 <source>Get the results using the `get` method:</source>
140 </markdowncell>
140 </markdowncell>
141 <codecell>
141 <codecell>
142 <input>results = [ar.get() for ar in async_results]
142 <input>results = [ar.get() for ar in async_results]
143 </input>
143 </input>
144 <language>python</language>
144 <language>python</language>
145 <prompt_number>36</prompt_number>
145 <prompt_number>10</prompt_number>
146 <collapsed>1</collapsed>
146 <collapsed>1</collapsed>
147 <outputs />
147 <outputs />
148 </codecell>
148 </codecell>
149 <markdowncell>
149 <markdowncell>
150 <source>Assemble the result into a structured NumPy array.</source>
150 <source>Assemble the result into a structured NumPy array.</source>
151 </markdowncell>
151 </markdowncell>
152 <codecell>
152 <codecell>
153 <input>prices = np.empty(n_strikes*n_sigmas,
153 <input>prices = np.empty(n_strikes*n_sigmas,
154 dtype=[('ecall',float),('eput',float),('acall',float),('aput',float)]
154 dtype=[('ecall',float),('eput',float),('acall',float),('aput',float)]
155 )
155 )
156
156
157 for i, price in enumerate(results):
157 for i, price in enumerate(results):
158 prices[i] = tuple(price)
158 prices[i] = tuple(price)
159
159
160 prices.shape = (n_strikes, n_sigmas)
160 prices.shape = (n_strikes, n_sigmas)
161 strike_mesh, sigma_mesh = np.meshgrid(strike_vals, sigma_vals)</input>
161 strike_mesh, sigma_mesh = np.meshgrid(strike_vals, sigma_vals)</input>
162 <language>python</language>
162 <language>python</language>
163 <prompt_number>37</prompt_number>
163 <prompt_number>11</prompt_number>
164 <collapsed>1</collapsed>
164 <collapsed>1</collapsed>
165 <outputs />
165 <outputs />
166 </codecell>
166 </codecell>
167 <markdowncell>
167 <markdowncell>
168 <source>Plot the value of the European call in (volatility, strike) space.</source>
168 <source>Plot the value of the European call in (volatility, strike) space.</source>
169 </markdowncell>
169 </markdowncell>
170 <codecell>
170 <codecell>
171 <input>plt.contourf(sigma_mesh, strike_mesh, prices['ecall'])
171 <input>plt.contourf(sigma_mesh, strike_mesh, prices['ecall'])
172 plt.axis('tight')
172 plt.axis('tight')
173 plt.colorbar()
173 plt.colorbar()
174 plt.title('European Call')
174 plt.title('European Call')
175 plt.xlabel("Volatility")
175 plt.xlabel("Volatility")
176 plt.ylabel("Strike Price")</input>
176 plt.ylabel("Strike Price")</input>
177 <language>python</language>
177 <language>python</language>
178 <prompt_number>38</prompt_number>
178 <prompt_number>12</prompt_number>
179 <collapsed>0</collapsed>
179 <collapsed>0</collapsed>
180 <outputs>
180 <outputs>
181 <output>
181 <output>
182 <output_type>pyout</output_type>
182 <output_type>pyout</output_type>
183 <text>&amp;lt;matplotlib.text.Text at 0x3f7ed90&amp;gt;</text>
183 <text>&amp;lt;matplotlib.text.Text at 0x2c54750&amp;gt;</text>
184 <prompt_number>38</prompt_number>
184 <prompt_number>12</prompt_number>
185 </output>
185 </output>
186 <output>
186 <output>
187 <output_type>display_data</output_type>
187 <output_type>display_data</output_type>
188 <png>aVZCT1J3MEtHZ29BQUFBTlNVaEVVZ0FBQVdjQUFBRWFDQVlBQUFETkJKYVNBQUFBQkhOQ1NWUUlD
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608 </png>
615 </png>
609 </output>
616 </output>
610 </outputs>
617 </outputs>
611 </codecell>
618 </codecell>
612 <markdowncell>
619 <markdowncell>
613 <source>Plot the value of the Asian call in (volatility, strike) space.</source>
620 <source>Plot the value of the Asian call in (volatility, strike) space.</source>
614 </markdowncell>
621 </markdowncell>
615 <codecell>
622 <codecell>
616 <input>plt.contourf(sigma_mesh, strike_mesh, prices['acall'])
623 <input>plt.contourf(sigma_mesh, strike_mesh, prices['acall'])
617 plt.axis('tight')
624 plt.axis('tight')
618 plt.colorbar()
625 plt.colorbar()
619 plt.title("Asian Call")
626 plt.title("Asian Call")
620 plt.xlabel("Volatility")
627 plt.xlabel("Volatility")
621 plt.ylabel("Strike Price")</input>
628 plt.ylabel("Strike Price")</input>
622 <language>python</language>
629 <language>python</language>
623 <prompt_number>39</prompt_number>
630 <prompt_number>13</prompt_number>
624 <collapsed>0</collapsed>
631 <collapsed>0</collapsed>
625 <outputs>
632 <outputs>
626 <output>
633 <output>
627 <output_type>pyout</output_type>
634 <output_type>pyout</output_type>
628 <text>&amp;lt;matplotlib.text.Text at 0x7fda543977d0&amp;gt;</text>
635 <text>&amp;lt;matplotlib.text.Text at 0x2e14610&amp;gt;</text>
629 <prompt_number>39</prompt_number>
636 <prompt_number>13</prompt_number>
630 </output>
637 </output>
631 <output>
638 <output>
632 <output_type>display_data</output_type>
639 <output_type>display_data</output_type>
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1084 </png>
1087 </png>
1085 </output>
1088 </output>
1086 </outputs>
1089 </outputs>
1087 </codecell>
1090 </codecell>
1088 <markdowncell>
1091 <markdowncell>
1089 <source>Plot the value of the European put in (volatility, strike) space.</source>
1092 <source>Plot the value of the European put in (volatility, strike) space.</source>
1090 </markdowncell>
1093 </markdowncell>
1091 <codecell>
1094 <codecell>
1092 <input>plt.contourf(sigma_mesh, strike_mesh, prices['eput'])
1095 <input>plt.contourf(sigma_mesh, strike_mesh, prices['eput'])
1093 plt.axis('tight')
1096 plt.axis('tight')
1094 plt.colorbar()
1097 plt.colorbar()
1095 plt.title("European Put")
1098 plt.title("European Put")
1096 plt.xlabel("Volatility")
1099 plt.xlabel("Volatility")
1097 plt.ylabel("Strike Price")</input>
1100 plt.ylabel("Strike Price")</input>
1098 <language>python</language>
1101 <language>python</language>
1099 <prompt_number>40</prompt_number>
1102 <prompt_number>14</prompt_number>
1100 <collapsed>0</collapsed>
1103 <collapsed>0</collapsed>
1101 <outputs>
1104 <outputs>
1102 <output>
1105 <output>
1103 <output_type>pyout</output_type>
1106 <output_type>pyout</output_type>
1104 <text>&amp;lt;matplotlib.text.Text at 0x7fda5453d350&amp;gt;</text>
1107 <text>&amp;lt;matplotlib.text.Text at 0x32ee190&amp;gt;</text>
1105 <prompt_number>40</prompt_number>
1108 <prompt_number>14</prompt_number>
1106 </output>
1109 </output>
1107 <output>
1110 <output>
1108 <output_type>display_data</output_type>
1111 <output_type>display_data</output_type>
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1582 </png>
1585 </png>
1583 </output>
1586 </output>
1584 </outputs>
1587 </outputs>
1585 </codecell>
1588 </codecell>
1586 <markdowncell>
1589 <markdowncell>
1587 <source>Plot the value of the Asian put in (volatility, strike) space.</source>
1590 <source>Plot the value of the Asian put in (volatility, strike) space.</source>
1588 </markdowncell>
1591 </markdowncell>
1589 <codecell>
1592 <codecell>
1590 <input>plt.contourf(sigma_mesh, strike_mesh, prices['aput'])
1593 <input>plt.contourf(sigma_mesh, strike_mesh, prices['aput'])
1591 plt.axis('tight')
1594 plt.axis('tight')
1592 plt.colorbar()
1595 plt.colorbar()
1593 plt.title("Asian Put")
1596 plt.title("Asian Put")
1594 plt.xlabel("Volatility")
1597 plt.xlabel("Volatility")
1595 plt.ylabel("Strike Price")
1598 plt.ylabel("Strike Price")
1596 </input>
1599 </input>
1597 <language>python</language>
1600 <language>python</language>
1598 <prompt_number>25</prompt_number>
1601 <prompt_number>15</prompt_number>
1599 <collapsed>0</collapsed>
1602 <collapsed>0</collapsed>
1600 <outputs>
1603 <outputs>
1601 <output>
1604 <output>
1602 <output_type>pyout</output_type>
1605 <output_type>pyout</output_type>
1603 <text>&amp;lt;matplotlib.text.Text at 0x3bd67d0&amp;gt;</text>
1606 <text>&amp;lt;matplotlib.text.Text at 0x3487c50&amp;gt;</text>
1604 <prompt_number>25</prompt_number>
1607 <prompt_number>15</prompt_number>
1605 </output>
1608 </output>
1606 <output>
1609 <output>
1607 <output_type>display_data</output_type>
1610 <output_type>display_data</output_type>
1608 <png>aVZCT1J3MEtHZ29BQUFBTlNVaEVVZ0FBQVdjQUFBRVhDQVlBQUFCeG1vVk1BQUFBQkhOQ1NWUUlD
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2046 </png>
2047 </png>
2047 </output>
2048 </output>
2048 </outputs>
2049 </outputs>
2049 </codecell>
2050 </codecell>
2050 </cells>
2051 </cells>
2051 </worksheet>
2052 </worksheet>
2052 </worksheets>
2053 </worksheets>
2053 </notebook>
2054 </notebook>
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