# 2
#
# # Parallel Monto-Carlo options pricing
#
# ## Problem setup
#
from __future__ import print_function
import sys
import time
from IPython.parallel import Client
import numpy as np
from mckernel import price_options
from matplotlib import pyplot as plt
#
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 = 6 # 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
#
strike_vals = np.linspace(min_strike, max_strike, n_strikes)
sigma_vals = np.linspace(min_sigma, max_sigma, n_sigmas)
#
# ## Parallel computation across strike prices and volatilities
#
# 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()
#
print("Strike prices: ", strike_vals)
print("Volatilities: ", sigma_vals)
#
# Submit tasks for each (strike, sigma) pair.
#
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))
#
# Block until all tasks are completed.
#
c.wait(async_results)
t2 = time.time()
t = t2-t1
print("Parallel calculation completed, time = %s s" % t)
#
# ## Process and visualize results
#
# Get the results using the `get` method:
#
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)
#
# Plot the value of the European call in (volatility, strike) space.
#
plt.figure()
plt.contourf(sigma_vals, strike_vals, prices['ecall'])
plt.axis('tight')
plt.colorbar()
plt.title('European Call')
plt.xlabel("Volatility")
plt.ylabel("Strike Price")
#
# Plot the value of the Asian call in (volatility, strike) space.
#
plt.figure()
plt.contourf(sigma_vals, strike_vals, prices['acall'])
plt.axis('tight')
plt.colorbar()
plt.title("Asian Call")
plt.xlabel("Volatility")
plt.ylabel("Strike Price")
#
# Plot the value of the European put in (volatility, strike) space.
#
plt.figure()
plt.contourf(sigma_vals, strike_vals, prices['eput'])
plt.axis('tight')
plt.colorbar()
plt.title("European Put")
plt.xlabel("Volatility")
plt.ylabel("Strike Price")
#
# Plot the value of the Asian put in (volatility, strike) space.
#
plt.figure()
plt.contourf(sigma_vals, strike_vals, prices['aput'])
plt.axis('tight')
plt.colorbar()
plt.title("Asian Put")
plt.xlabel("Volatility")
plt.ylabel("Strike Price")
#
plt.show()