# <nbformat>2</nbformat> # <markdowncell> # # Parallel Monto-Carlo options pricing # <markdowncell> # ## Problem setup # <codecell> import sys import time from IPython.parallel import Client import numpy as np from mcpricer 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 = 5 # 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) strike_mesh, sigma_mesh = np.meshgrid(strike_vals, sigma_vals) # <markdowncell> # Plot the value of the European call in (volatility, strike) space. # <codecell> plt.contourf(sigma_mesh, strike_mesh, 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.contourf(sigma_mesh, strike_mesh, 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.contourf(sigma_mesh, strike_mesh, 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.contourf(sigma_mesh, strike_mesh, prices['aput']) plt.axis('tight') plt.colorbar() plt.title("Asian Put") plt.xlabel("Volatility") plt.ylabel("Strike Price")