Monday 25th of September 2017

Observations on the effectiveness of procedures and some improvement techniques

Naima Soukher, Boubker Daafi, Jamal Bouyaghroumn, Abdelwahed Namir and Fouad Lahmidi

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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Naima Soukher
Applied Mathematics

Boubker Daafi
Applied Mathematics

Jamal Bouyaghroumn
Applied Mathematics

Abdelwahed Namir
Applied Mathematics

Fouad Lahmidi
Applied Mathematics

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