Observations on the effectiveness of procedures and some improvement techniques
We will describe in this article a method allowing the simulation of financial models.
This method is often useful in the context of financial mathematics, because it allows
calculating the price of any option as long as we know to express it in the form of
the expectation of a random variable that we simulate. In this case, the Monte Carlo
method described later allows then writing quickly an algorithm to evaluate this option
and it is often very greedy in time calculation. Effective procedure leads to a sufficient
precision at the cost of a limited calculation time. To identify more precisely the
efficiency notation and indicate some techniques to increase it, we assume that we
want to estimate by Monte Carlo simulations, a parameter e of the distribution of
V (T;Y (t)). It can be a quantile of this distribution (that is the case when it comes
to appreciating a VaR), of an expectation (for example if we try to evaluate an
option) or of any time of the distribution V (T;Y (t)). On the other hand, Monte
Carlo simulations, in the standard form is not suitable for the evaluation of american
options. The reason is that the opportunity to exercise at any time requires to calculate
at each date and each trajectory a conditional expectation, thus to remove trajectories
at each step. This is infeasible in practice, even if it is limited to a finite number of
possible exercise dates. Thus, we use the techniques of improving the adaptation of
Monte Carlo method to make it suitable for the evaluation of american options.
Keywords: Monte Carlo, Financial models, Preci- sion, Computation time.
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ABOUT THE AUTHORS
Naima Soukher
Applied Mathematics
Boubker Daafi
Applied Mathematics
Jamal Bouyaghroumn
Applied Mathematics
Abdelwahed Namir
Applied Mathematics
Fouad Lahmidi
Applied Mathematics
Naima Soukher
Applied Mathematics
Boubker Daafi
Applied Mathematics
Jamal Bouyaghroumn
Applied Mathematics
Abdelwahed Namir
Applied Mathematics
Fouad Lahmidi
Applied Mathematics