Derivatives Models on Models

1

The Discovery of Fat-tails in Price Data

Fat-tails is one of the most important topics in financial economics, in particular for derivatives valuation and hedging, but also for risk management and almost any aspects of the investment process. The early discoveries of fat-tails in price data have in my view received too little attention. Thousands and thousands of papers have been written related to fat-tails; time-varying volatility, stochastic volatility, local volatility, jumps-diffusion, implied distributions, and alternative theoretical fat-tailed distributions are all important tools in derivatives valuation and financial risk management. Few or none of these books and papers refer to the early discoveries on fat-tails in price data,¹ and few traders and quants I have talked with seem to even be aware of that the discovery of fat-tails in price data at the time of writing goes back almost 100 years.²

Wesley C. Mitchell (1874–1948) seems to be the very first to empirically detect and describe both time varying “volatility” and high-peaked/fat-tailed distributions in commodity prices. Mitchell was not the first to point to fat-tailed distributions; Vilfredo Pareto had looked at the fat-tailed distributions of income already in the late 1800s and had even developed a theory for such distributions. Mitchell was however the first to empirically show that we had fat-tailed distributions in price data. All this he published in his work titled “The Making and Using of Index Numbers” ...