maturity_value = paths[time_index]

average value over whole path

mean_value = np.mean(paths[:time_index], axis= 1 )

maximum value over whole path

max_value = np.amax(paths[:time_index], axis= 1 )[- 1 ]

minimum value over whole path

min_value = np.amin(paths[:time_index], axis= 1 )[- 1 ]
try:
payoff = eval(self.payoff_func)
return payoff
except:
print “Error evaluating payoff function.”

def present_value(self, accuracy= 6 , fixed_seed=False, full=False):
”’
Parameters
==========
accuracy : int
number of decimals in returned result
fixed_seed : Boolean
use same/fixed seed for valuation
full : Boolean
return also full 1d array of present values
”’
cash_flow = self.generate_payoff(fixed_seed=fixed_seed)
discount_factor = self.discount_curve.get_discount_factors(
(self.pricing_date, self.maturity))[ 0 , 1 ]
result = discount_factor np.sum(cash_flow) / len(cash_flow)
if full:
return round(result, accuracy), discount_factor cash_flow
else:
return round(result, accuracy)

The generate_payoff method provides some special objects to be used for the definition

of the payoff of the option:

strike is the strike of the option.

maturity_value represents the 1D ndarray object with the simulated values of the

underlying at maturity of the option.

mean_value is the average of the underlying over a whole path from today until

maturity.

max_value is the maximum value of the underlying over a whole path.

min_value gives the minimum value of the underlying over a whole path.

The last three especially allow for the efficient handling of options with Asian (i.e.,

lookback) features.

A Use Case

The application of the valuation class valuation_mcs_european is best illustrated by a

specific use case. However, before a valuation class can be instantiated, we need a

simulation object — i.e., an underlying for the option to be valued. From Chapter 16, we

use the geometric_brownian_motion class to model the underlying. We also use the

example parameterization of the respective use case there:

In  [ 1 ]:  from dx import  *

In  [ 2 ]:  me_gbm  =   market_environment(‘me_gbm’,    dt.datetime( 2015 ,  1 ,     1 ))

In  [ 3 ]:  me_gbm.add_constant(‘initial_value’,    36.)

me_gbm.add_constant(‘volatility’,   0.2)

me_gbm.add_constant(‘final_date’,   dt.datetime( 2015 ,  12 ,    31 ))

me_gbm.add_constant(‘currency’, ‘EUR’)

me_gbm.add_constant(‘frequency’,    ‘M’)

me_gbm.add_constant(‘paths’,     10000 )