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Fixing parallel options pricing example.
Brian E. Granger -
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@@ -0,0 +1,44 b''
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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@@ -16,10 +16,10 b''
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>
@@ -36,7 +36,7 b' 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>
@@ -44,7 +44,7 b' max_sigma = 0.4 # Max volatility</input>'
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>
@@ -57,7 +57,7 b' sigma_vals = np.linspace(min_sigma, max_sigma, n_sigmas)</input>'
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>
@@ -68,7 +68,7 b' balancing at the expense of not knowing which engine will execute the code.</sou'
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>
@@ -76,7 +76,7 b' balancing at the expense of not knowing which engine will execute the code.</sou'
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>
@@ -97,14 +97,14 b' for strike in strike_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>
@@ -123,12 +123,12 b' 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>
@@ -142,7 +142,7 b' print "Parallel calculation completed, time = %s s" % t</input>'
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>
@@ -160,7 +160,7 b' for i, price in enumerate(results):'
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>
@@ -175,436 +175,443 b" 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>
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608 </png>
615 </png>
609 </output>
616 </output>
610 </outputs>
617 </outputs>
@@ -620,467 +627,463 b' 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>
@@ -1096,489 +1099,489 b' 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>
@@ -1595,454 +1598,452 b' 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>
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2046 </png>
2047 </png>
2047 </output>
2048 </output>
2048 </outputs>
2049 </outputs>
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