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In this paper, a new valuation methodology is tested as an alternative way to value European options by applying Fast Fourier Transform (FFT) on Lévy processes. It is shown how this new approach can be applied to the Variance-Gamma model by Madan, Carr and Chang (1998). This model has a closed form formula, which can be obtained, as in many other models, by partial differential equations or by probabilistic methods, but even these methodologies will not prove to be useful when we encounter ourselves with more complex models. Nevertheless, if we take into account the fact that there is a one-to-one relationship between a characteristic function of an exponential Lévy process and its probability density and that this cash flows are known in closed forms or can be expressed in terms of special mathematic functions, then it is possible to use this new methodology to obtain an alternate and maybe simpler valuation forms for models which do not have a closed form solution. Madan, Carr and Changs model is a particular case of general exponential Lévy processes. If there is a way to develop a new valuation method by using Fourier transform and this method proves to give same results as closed form solutions or by numerical method solutions, then we could be on our way to find simpler ways to price assets than using a traditional approach

The paper estimates the matrix of expectations of the economic factors that defined the local and foreign trade in the Mexican industry. With an application of the Black-Scholes-Merton model, it warns about the financial problems that may face an exporting company

The Credit Default Swap (CDS) is the most popular credit derivative and it is used as insurance against the risk of default by a particular company, known as a reference entity. If a portfolio of debt instruments is created with a complex structure where the cash flows from such portfolio are channeled to different categories of investors, we have a collateralized debt obligation (CDO). If the CDO is formed by a portfolio of CDS it is called a Synthetic CDO. The synthetic CDO transfers to market the credit risk of the portfolio. In this paper I describe the synthetic CDO valuation process and I propose an algorithm for the fair pricing of tranches, which does not require Monte Carlo simulation or Copulas, even with different notional principal values

In this paper we apply random matrix theory (RMT) to the analysis of cross-correlation matrix C constructed from daily returns of 65 stocks traded at the Bolsa Mexicana de Valores during a trading period of eighth years. We find that the statistics of most of the eigenvalues in the spectrum of C agrees with the prediction of RMT, but there are deviations for a few of the larger eigenvalues. We show that C has the universal properties of the Gaussian orthogonal ensemble of random matrices. Furthermore, we analyze the eigenvectors of C through their inverse participation ratio, such analysis allow us to indicate matrix C has a random band structure