European Exercise

The first case to which we want to specialize the generic valuation class is European

exercise. To this end, consider the following simplified recipe to generate a Monte Carlo

estimator for an option value:

1 . Simulate the relevant underlying risk factor S under the risk-neutral measure I times

to come up with as many simulated values of the underlying at the maturity of the

option T — i.e.,

2 . Calculate the payoff hT of the option at maturity for every simulated value of the

underlying — i.e.,

3 . Derive the Monte Carlo estimator for the option’s present value as

The Valuation Class

Example 17-2 shows the class implementing the present_value method based on this

recipe. In addition, it contains the method generate_payoff to generate the simulated

paths and the payoff of the option given the simulated paths. This, of course, builds the

very basis for the Monte Carlo estimator.

Example 17-2. Valuation class for European exercise

DX Library Valuation

valuation_mcs_european.py

import numpy as np

from valuation_class import valuation_class

class valuation_mcs_european(valuation_class):
”’ Class to value European options with arbitrary payoff
by single-factor Monte Carlo simulation.

            Methods

            =======

            generate_payoff :

                            returns payoffs given   the paths   and the payoff  function

            present_value   :

                            returns present value   (Monte  Carlo   estimator)

            ”’

def generate_payoff(self, fixed_seed=False):
”’
Parameters
==========
fixed_seed : Boolean
use same/fixed seed for valuation
”’
try:

strike defined?

strike = self.strike
except:
pass
paths = self.underlying.get_instrument_values(fixed_seed=fixed_seed)
time_grid = self.underlying.time_grid
try:
time_index = np.where(time_grid == self.maturity)[ 0 ]
time_index = int(time_index)
except:
print “Maturity date not in time grid of underlying.”