From 7777bddf786dde62927e315b4b2beef5e707e7b5 2011-08-18 20:50:33 From: Brian E. Granger Date: 2011-08-18 20:50:33 Subject: [PATCH] Fixing parallel options pricing example. --- diff --git a/docs/examples/newparallel/options/mcdriver.py b/docs/examples/newparallel/options/mcdriver.py deleted file mode 100644 index c0e1abd..0000000 --- a/docs/examples/newparallel/options/mcdriver.py +++ /dev/null @@ -1,144 +0,0 @@ -#!/usr/bin/env python -"""Run a Monte-Carlo options pricer in parallel.""" - -#----------------------------------------------------------------------------- -# Imports -#----------------------------------------------------------------------------- - -import sys -import time -from IPython.parallel import Client -import numpy as np -from mcpricer import price_options -from matplotlib import pyplot as plt - -#----------------------------------------------------------------------------- -# Setup parameters for the run -#----------------------------------------------------------------------------- - -def ask_question(text, the_type, default): - s = '%s [%r]: ' % (text, the_type(default)) - result = raw_input(s) - if result: - return the_type(result) - else: - return the_type(default) - -cluster_profile = ask_question("Cluster profile", str, "default") -price = ask_question("Initial price", float, 100.0) -rate = ask_question("Interest rate", float, 0.05) -days = ask_question("Days to expiration", int, 260) -paths = ask_question("Number of MC paths", int, 10000) -n_strikes = ask_question("Number of strike values", int, 5) -min_strike = ask_question("Min strike price", float, 90.0) -max_strike = ask_question("Max strike price", float, 110.0) -n_sigmas = ask_question("Number of volatility values", int, 5) -min_sigma = ask_question("Min volatility", float, 0.1) -max_sigma = ask_question("Max volatility", float, 0.4) - -strike_vals = np.linspace(min_strike, max_strike, n_strikes) -sigma_vals = np.linspace(min_sigma, max_sigma, n_sigmas) - -#----------------------------------------------------------------------------- -# Setup for parallel calculation -#----------------------------------------------------------------------------- - -# The Client is used to setup the calculation and works with all -# engines. -c = Client(profile=cluster_profile) - -# 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. -view = c.load_balanced_view() - -# Initialize the common code on the engines. This Python module has the -# price_options function that prices the options. - -#----------------------------------------------------------------------------- -# Perform parallel calculation -#----------------------------------------------------------------------------- - -print "Running parallel calculation over strike prices and volatilities..." -print "Strike prices: ", strike_vals -print "Volatilities: ", sigma_vals -sys.stdout.flush() - -# Submit tasks to the TaskClient for each (strike, sigma) pair as a MapTask. -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) - -print "Submitted tasks: ", len(async_results) -sys.stdout.flush() - -# Block until all tasks are completed. -c.wait(async_results) -t2 = time.time() -t = t2-t1 - -print "Parallel calculation completed, time = %s s" % t -print "Collecting results..." - -# Get the results using TaskClient.get_task_result. -results = [ar.get() for ar in async_results] - -# Assemble the result into a structured NumPy array. -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) - -print "Results are available: strike_mesh, sigma_mesh, prices" -print "To plot results type 'plot_options(sigma_mesh, strike_mesh, prices)'" - -#----------------------------------------------------------------------------- -# Utilities -#----------------------------------------------------------------------------- - -def plot_options(sigma_mesh, strike_mesh, prices): - """ - Make a contour plot of the option price in (sigma, strike) space. - """ - plt.figure(1) - - plt.subplot(221) - plt.contourf(sigma_mesh, strike_mesh, prices['ecall']) - plt.axis('tight') - plt.colorbar() - plt.title('European Call') - plt.ylabel("Strike Price") - - plt.subplot(222) - plt.contourf(sigma_mesh, strike_mesh, prices['acall']) - plt.axis('tight') - plt.colorbar() - plt.title("Asian Call") - - plt.subplot(223) - plt.contourf(sigma_mesh, strike_mesh, prices['eput']) - plt.axis('tight') - plt.colorbar() - plt.title("European Put") - plt.xlabel("Volatility") - plt.ylabel("Strike Price") - - plt.subplot(224) - plt.contourf(sigma_mesh, strike_mesh, prices['aput']) - plt.axis('tight') - plt.colorbar() - plt.title("Asian Put") - plt.xlabel("Volatility") - - - - - - diff --git a/docs/examples/newparallel/options/mckernel.py b/docs/examples/newparallel/options/mckernel.py new file mode 100644 index 0000000..db57904 --- /dev/null +++ b/docs/examples/newparallel/options/mckernel.py @@ -0,0 +1,44 @@ +def price_options(S=100.0, K=100.0, sigma=0.25, r=0.05, days=260, paths=10000): + """ + Price European and Asian options using a Monte Carlo method. + + Parameters + ---------- + S : float + The initial price of the stock. + K : float + The strike price of the option. + sigma : float + The volatility of the stock. + r : float + The risk free interest rate. + days : int + The number of days until the option expires. + paths : int + The number of Monte Carlo paths used to price the option. + + Returns + ------- + A tuple of (E. call, E. put, A. call, A. put) option prices. + """ + import numpy as np + from math import exp,sqrt + + h = 1.0/days + const1 = exp((r-0.5*sigma**2)*h) + const2 = sigma*sqrt(h) + stock_price = S*np.ones(paths, dtype='float64') + stock_price_sum = np.zeros(paths, dtype='float64') + for j in range(days): + growth_factor = const1*np.exp(const2*np.random.standard_normal(paths)) + stock_price = stock_price*growth_factor + stock_price_sum = stock_price_sum + stock_price + stock_price_avg = stock_price_sum/days + zeros = np.zeros(paths, dtype='float64') + r_factor = exp(-r*h*days) + euro_put = r_factor*np.mean(np.maximum(zeros, K-stock_price)) + asian_put = r_factor*np.mean(np.maximum(zeros, K-stock_price_avg)) + euro_call = r_factor*np.mean(np.maximum(zeros, stock_price-K)) + asian_call = r_factor*np.mean(np.maximum(zeros, stock_price_avg-K)) + return (euro_call, euro_put, asian_call, asian_put) + diff --git a/docs/examples/newparallel/options/mcpricer.ipynb b/docs/examples/newparallel/options/mcpricer.ipynb index a0e1b3c..7a68887 100644 --- a/docs/examples/newparallel/options/mcpricer.ipynb +++ b/docs/examples/newparallel/options/mcpricer.ipynb @@ -16,10 +16,10 @@ import time from IPython.parallel import Client import numpy as np -from mcpricer import price_options +from mckernel import price_options from matplotlib import pyplot as plt python - 27 + 1 1 @@ -36,7 +36,7 @@ n_sigmas = 5 # Number of volatility values min_sigma = 0.1 # Min volatility max_sigma = 0.4 # Max volatility python - 28 + 2 1 @@ -44,7 +44,7 @@ max_sigma = 0.4 # Max volatility strike_vals = np.linspace(min_strike, max_strike, n_strikes) sigma_vals = np.linspace(min_sigma, max_sigma, n_sigmas) python - 29 + 3 1 @@ -57,7 +57,7 @@ sigma_vals = np.linspace(min_sigma, max_sigma, n_sigmas) c = Client(profile=cluster_profile) python - 30 + 4 1 @@ -68,7 +68,7 @@ balancing at the expense of not knowing which engine will execute the code. view = c.load_balanced_view() python - 31 + 5 1 @@ -76,7 +76,7 @@ balancing at the expense of not knowing which engine will execute the code.print "Strike prices: ", strike_vals print "Volatilities: ", sigma_vals python - 32 + 6 0 @@ -97,14 +97,14 @@ for strike in strike_vals: ar = view.apply_async(price_options, price, strike, sigma, rate, days, paths) async_results.append(ar) python - 33 + 7 1 print "Submitted tasks: ", len(async_results) python - 34 + 8 0 @@ -123,12 +123,12 @@ t = t2-t1 print "Parallel calculation completed, time = %s s" % t python - 35 + 9 0 stream - Parallel calculation completed, time = 1.8046438694 s + Parallel calculation completed, time = 2.57819604874 s @@ -142,7 +142,7 @@ print "Parallel calculation completed, time = %s s" % t results = [ar.get() for ar in async_results] python - 36 + 10 1 @@ -160,7 +160,7 @@ for i, price in enumerate(results): prices.shape = (n_strikes, n_sigmas) strike_mesh, sigma_mesh = np.meshgrid(strike_vals, sigma_vals) python - 37 + 11 1 @@ -175,436 +175,443 @@ plt.title('European Call') plt.xlabel("Volatility") plt.ylabel("Strike Price") python - 38 + 12 0 pyout - <matplotlib.text.Text at 0x3f7ed90> - 38 + <matplotlib.text.Text at 0x2c54750> + 12 display_data aVZCT1J3MEtHZ29BQUFBTlNVaEVVZ0FBQVdjQUFBRWFDQVlBQUFETkJKYVNBQUFBQkhOQ1NWUUlD -QWdJZkFoa2lBQUFBQWx3U0ZsegpBQUFMRWdBQUN4SUIwdDErL0FBQUlBQkpSRUZVZUp6dDNYbFlW -UGVoLy9IM21Sa1lWdGxsWjFCUlVRUUJaWEZoZGRlNFJWUEZHOU9vCmJSTk5qZGx2bjZiM1Y4MXRr -NXFtTjRuV3hDVXhOclhHYkRVYWpUYlJDQzRvcU9DT083Z1NFWlZOUUxieis4T0dhbVFiR09iTThu -MDkKRDg4anM1ejVNT0xITStkOHovY3J5YklzSXdpQ0lKZ1VsZElCQkVFUWhJZUpjaFlFUVRCQm9w -d0ZRUkJNa0NoblFSQUVFeVRLV1JBRQp3UVNKY2hZRVFUQkJvcHdGd1lDQ2c0UDUvdnZ2QVZpNGND 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