The Distributional Characteristics of a Selection of Contracts Traded on the London International Financial Futures Exchange

Abstract

This study examines the distributional properties of futures prices for contracts traded on LIFFE. A filtering process is employed to remove day of the week and holiday effects, a maturity effect, moving average effects and the influence of an asset's conditional variance from the raw returns series. Alternative distributional models from the stable paretian and ARCH families are examined for their applicability to futures data using a stability under additions. The results conclusively reject the hypothesis that futures returns are normally distributed with findings in favour of two related hypotheses -the mixtures of stable distribution and the ordinary stable distribution.

Modelling catastrophic risk in international equity markets: an extreme value approach

“…The shape parameter is the key to using EVT as it separates three types of extreme value distributions according to different shapes, the Gumbel (ξ = 0), Weibull (ξ < 0) and Fréchet (ξ > 0) distributions. The latter extreme value distribution is supported in the finance literature as it exhibits a fat-tails property, also found for market returns (Cotter and McKillop, 2000).…”

Margin Exceedences for European Stock Index Futures Using Extreme Value Theory

“…This important classification of distributions for extreme futures price movements has tail values that decay by a power function. A vast literature on financial returns (Longin, 1999b;Cotter, 1998;Danielsson and DeVries, 1997a, 1997b, 1997cKearns and Pagan, 1997;Venkataraman, 1997;Lux, 1996;and Koedijk et al, 1992) and on derivative first differences (Cotter and McKillop, 2000;Longin, 1999a;Hull and White, 1998;and Duffie and Pan, 1997) has recognised the existence of fat-tailed characteristics. For this reason the rest of the theory section deals with this Frechet type of extreme value distribution.…”

“…Given, the true distribution of futures price changes being non-nor mal and in fact, unknown (Cotter and McKillop, 2000;Yang and Brorsen, 1993;and Hall et al, 1989), it is appropriate to examine the theoretical underpinnings of the asymptotic behaviour of a range of possible distributions. Leadbetter et al (1983) and Embrechts et al (1997) document a family of distributions that are separated into three distinguishing types, the assumption is that a sequence of values display asymptotic behaviour belonging either to a Gumbell, Frechet or Weibull distribution.…”

Extreme risk in futures contracts

“…The key addition that EVT makes to extreme risk estimation is that it removes the need to make exact distributional assumptions for futures tail returns. Furthermore, futures tail returns may follow any of the three types of distributions, but asymptotically they converge to the Fre´chet extreme value distribution as they exhibit fat tails (Dewachter and Gielens, 1999;Cotter and McKillop, 2000). Formally, taking a sequence of identical and independently distributed (iid) returns {R 1 , R 2 , .…”