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This thesis presents three applications of Mathematics to Finance, from the empirical to the analytic level. The first part shows how the CBOE's market volatility index (VIX) has seasonal movements, using several statistical and econometrical tools. These tools complement each other. The application is shown in a way that illustrates how dangerous it is to apply only ordinary least squares methods to look for seasonality. The second part shows interesting patterns emerging from empiricaldoi:10.26021/8229 fatcat:itg3rg2tnrd5lc5umlxda5kugi