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The choice of the distribution of asset returns: How extreme value theory can help?
Affiliation:1. Surrey Business School, University of Surrey, GU2 7XH, UK;2. Canterbury Christ Church University Business School, Canterbury, Kent CT1 1QU, UK;1. Dipartimento di Energia, Ingegneria dell’Informazione e Modelli Matematici, Scuola Politecnica Ingegneria, Università di Palermo, I-90128 Palermo, Italy;2. I.N.F.N., Sezione di Torino, Italy;3. School of Management, Institute of Finance and IQSCS, University of Leicester, LE1 7RH Leicester, UK;1. School of Physics, Trinity College Dublin, Ireland;2. Capital Fund Management, Paris, France;1. School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China;2. School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241003, China
Abstract:One of the issues of risk management is the choice of the distribution of asset returns. Academics and practitioners have assumed for a long time (for more than three decades) that the distribution of asset returns is a Gaussian distribution. Such an assumption has been used in many fields of finance: building optimal portfolio, pricing and hedging derivatives and managing risks. However, real financial data tend to exhibit extreme price changes such as stock market crashes that seem incompatible with the assumption of normality. This article shows how extreme value theory can be useful to know more precisely the characteristics of the distribution of asset returns and finally help to chose a better model by focusing on the tails of the distribution. An empirical analysis using equity data of the US market is provided to illustrate this point.
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