Post by Sapphire Capital on Aug 12, 2008 20:23:55 GMT 4
Finiteness of Variance is Irrelevant in the Practice of Quantitative Finance
Nassim Nicholas Taleb
London Business School
June 09, 2008
Abstract:
Outside the Platonic world of financial models, assuming the underlying distribution is a scalable "power law", we are unable to find a consequential difference between finite and infinite variance models - a central distinction emphasized in the econophysics literature and the financial economics tradition. While distributions with power law tail exponents ±>2 are held to be amenable to Gaussian tools, owing to their "finite variance", we fail to understand the difference in the application with other power laws (1<±<2) held to belong to the Pareto-Lévy-Mandelbrot stable regime. The problem invalidates derivatives theory (dynamic hedging arguments) and portfolio construction based on mean-variance. This paper discusses methods to deal with the implications of the point in a real world setting.
papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1142785_code475810.pdf?abstractid=1142785&mirid=3
Nassim Nicholas Taleb
London Business School
June 09, 2008
Abstract:
Outside the Platonic world of financial models, assuming the underlying distribution is a scalable "power law", we are unable to find a consequential difference between finite and infinite variance models - a central distinction emphasized in the econophysics literature and the financial economics tradition. While distributions with power law tail exponents ±>2 are held to be amenable to Gaussian tools, owing to their "finite variance", we fail to understand the difference in the application with other power laws (1<±<2) held to belong to the Pareto-Lévy-Mandelbrot stable regime. The problem invalidates derivatives theory (dynamic hedging arguments) and portfolio construction based on mean-variance. This paper discusses methods to deal with the implications of the point in a real world setting.
papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1142785_code475810.pdf?abstractid=1142785&mirid=3