A Mathematical Analysis for Options Outside Europe: the case of Asian

Marco Mele

Abstract


In this paper we want analyze some pricing models for options Asian type and appropriate perturbation methods that allow it to find satisfactory approximations of prices and implied volatility with respect in these models.

The class of models which we will go to fill the gaps in the Monte Carlo methods. In particular, for estimation of the volatility will be necessary that it be a function of time and of the underlying, or that it proves described as (St,t). The model that we have built over to estimate volatility and its rupture, also examine the best price and the constant elasticity of variance model and this will allow us to obtain the areas of the implied volatility. In this way we will approach estimates that most represent those of the market, though not entirely satisfactory.

So, given a fixed maturity, the implied volatility curves resulting from the equations will always decreasing with respect to the strike.

With this model, therefore, you can reproduce a wide range of areas of volatility as it will be possible to act on ni calibration of parameters in order to reproduce  as efficiently as possible a series of market prices of an option  Asian, compared to those that would result from a Monte Carlo models.


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ISSN : 2251-1555