Stable Levy Processes In Finance

Risk and expected returns are key concepts in financial investment decisions. Financial theoretical and practical analysis are endogenously affected by the distributional form of financial asset returns. Asset pricing, portfolio analysis, risk management and option pricing theories generally rest on assumptions about returns distribution. Most of the concepts in theoretical and practical finance arose in the last decades lie in the hypothesis that asset returns may be modelled with a normal distribution. Bachelier (1900) and Samuelson (1955) created the foundations to the financial edifice which holds its roots on the “normal distribution” assumption. The hypothesis of normal distribution of asset returns is usually justified by an appeal to the central limit theorem. Whenever a financial variable may be considered as the result of many microscopic effects, it can be described by a normal law, since this is the limit distribution of the sum of independent and identically distributed random variables.