Searching for scaling laws in distributional properties of price variations : a review over 40 years

摘要: Due to the increasing importance of long-term risk management issues (mutual funds, pension corporates), it is now necessary extend generally used short-term models implemented in financial industry (for example, VaR) a longer term context. Longhorizon forecasts lead consider concept scaling study statistical properties price changes markets. I provide first survey and review major works devoted search for laws fluctuations, over last 40 years. Following Mandelbrot’s intuition, this academic current began by looking scale invariances before switching other forms laws. two (1963, 1965) paved way an active research, but no totally conclusive results have emerged. For return process, tests were unclear, certain anomalies revealed, which seems contradict stable (fractal) hypothesis. However invariance (relative extremes) detected, thus partially confirming volatility though common knowledge that process exhibits long range dependence structure.