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