Pricing of Double Barrier Options by Spectral Theory

We propose to discuss the efficiency of the spectral method for computing the value of Double Barrier Options. Using this method, one may write the option price as a Fourier series, with suitable coefficients. We propose a simple approach for its computing. One consider the general case, in which the volatility is time dependent, but it is immediate extend our methodology also in the case of constant volatility. The advantage to write the arbitrage price of the Double Barrier Options as Fourier series, is matter of computation complexity. The methods used to evaluate options of this kind have a high value of computation complexity, furthermore, them have not the capacity to manage it, while using our method, one can define, through an easy analytical report, the computation complexity of the problem, and also one can choice its accuracy. The results obtained are compared with those given from several authors that have used different ways to compute the price, from Monte-Carlo method to that of Laplace transform. Our results are compatible with those obtained from Geman-Yor and Kunitomo-Ikeda, but unlike them we are able to improve the accuracy with little effort of calculus.