Statistical properties of derivatives: A journey in term structures

Abstract

a b s t r a c tThis article presents an empirical study of 13 derivative markets for commodities and financial assets. The study goes beyond statistical analysis by including the maturity as a variable for the daily returns of futures contracts from 1998 to 2010, and for delivery dates up to 120 months. We observe that the mean and variance of the commodities follow a scaling behavior in the maturity dimension with an exponent characteristic of the Samuelson effect. The comparison between the tails of the probability distribution according to the expiration dates shows that there is a segmentation in the fat tails exponent term structure above the Lévy stable region. Finally, we compute the average tail exponent for each maturity, and we observe two regimes of extreme events for derivative markets, reminiscent of a phase diagram with a sharp transition at the 18th delivery month.

The topology of macro financial flows: An application of stochastic flow diagrams

“…However, we believe that it can be improved in a number of ways. Boginski et al (2003Boginski et al ( , 2005Boginski et al ( , 2006 and Lautier et al (2011aLautier et al ( , 2011bLautier et al ( , 2012aLautier et al ( , 2012b base their analysis on synchronous correlations. Correlations depend on characteristics of the joint distribution between two related markets.…”

“…If such methods were the solution to every estimation problem, there would be no need for theory, which of course would constitute a preposterous position. Lautier et al (2011aLautier et al ( , 2011bLautier et al ( , 2012aLautier et al ( , 2012b) define a distance measure between two elements x,y as…”

“…We feel that those studies mutually complement each other, and that combining their different angles and strengths would be useful. For example, Boginski et al (2003Boginski et al ( , 2005Boginski et al ( , 2006 and Lautier et al (2011aLautier et al ( , 2011bLautier et al ( , 2012aLautier et al ( , 2012b are rich in Graph Theory, however relatively modest in their time series treatment. In contrast, Billio et al (2012) is stronger in time series analysis however relatively limited in terms of Graph Theory.…”

“…They also suggest new data mining techniques for classifying stocks based on this market graph, which provide a deeper insight into the internal structure of the stock market. • Lautier et al (2011a• Lautier et al ( , 2011b• Lautier et al ( , 2012a• Lautier et al ( , 2012b: These authors build graphs in order to investigate integration and systemic risk in derivative markets on multiple asset classes. Like Boginski et al (2003, 2006, they also use synchronous correlation above a given threshold to determine whether an edge exists.…”

Systemic Risk and Complex Systems: A Graph-Theory Analysis

“…Such a scaling is appealing from an empirical as well as a theoretical point of view and suggests a possible universal behavior of the topologies of derivatives networks. Additionally arbitrage operations have also a deep impact on the prices dynamic leading to ubiquitous statistical properties of price returns along the term structure [9].…”