Parallel Monto-Carlo options pricing¶

Problem setup¶

In [1]:
import sys
import time
from IPython.parallel import Client
import numpy as np
from mckernel import price_options
from matplotlib import pyplot as plt

In [2]:
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

In [3]:
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.

In [4]:
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.

In [5]:
view = c.load_balanced_view()

In [6]:
print "Strike prices: ", strike_vals
print "Volatilities: ", sigma_vals

Strike prices:  [  90.   94.   98.  102.  106.  110.]
Volatilities:  [ 0.1    0.175  0.25   0.325  0.4  ]

Submit tasks for each (strike, sigma) pair.

In [7]:
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)

In [8]:
print "Submitted tasks: ", len(async_results)

Submitted tasks:  30

Block until all tasks are completed.

In [9]:
c.wait(async_results)
t2 = time.time()
t = t2-t1

print "Parallel calculation completed, time = %s s" % t

Parallel calculation completed, time = 4.46057891846 s

Process and visualize results¶

Get the results using the get method:

In [10]:
results = [ar.get() for ar in async_results]


Assemble the result into a structured NumPy array.

In [11]:
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.

In [12]:
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")

Out[12]:
&lt;matplotlib.text.Text at 0x106b618d0&gt;

Plot the value of the Asian call in (volatility, strike) space.

In [13]:
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")

Out[13]:
&lt;matplotlib.text.Text at 0x106bd90d0&gt;

Plot the value of the European put in (volatility, strike) space.

In [14]:
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")

Out[14]:
&lt;matplotlib.text.Text at 0x106d34150&gt;

Plot the value of the Asian put in (volatility, strike) space.

In [15]:
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")

In [16]:
plt.show()