Futures prices are not stable‐paretian distributed

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

“…Within the stable paretian family, many alternative distributional models are suggested for their applicability in correctly describing the leptokurtosis in futures series'. Those that attract strong attention include Mandelbrot's stable model (Hudson et al, 1987), the mixtures of stables (Gribbin et al, 1992) and the mixtures of normals (Hall et al, 1989). These hypotheses are tested using a stability under additions test, relying on an attribute of the stable paretian family (McCulloch, 1986).…”

“…The changing of a particular characteristic has led to suggestions that futures price series may involve mixtures of specific distributions (Gribbin et al, 1992). Also, favourable evidence is presented for spot markets (Anderson and Bollerslev, 1997).…”

“…In this context many alternative distributional models have been suggested for their applicability in correctly describing properties of futures price series. Those that have attracted strong attention include the stable paretian (Hudson et al, 1987;and So, 1987), the mixtures of normals (Hall et al, 1989), the mixtures of stables (Gribbin et al, 1992), ARCH (Fujihara and Park, 1990) and GARCH-M (McCurdy and Morgan, 1988). To examine the applicability of the above noted distributional forms the stability under additions procedure, as developed by McCulloch (1986), is employed.…”

The systematic risk of futures contracts

“…These briefly summarized conclusions are characteristic of a literature that is becoming voluminous. The following studies all agree that futures returns are not distributed normally: Stevenson and Bear (1970); Dusak (1 973); Clark ( 1973); Mann and Heifner ( 1976); Tauchen and Pitts ( 1983);Cornew, Town, and Crowson (1984); Helms and Martell (1985);Gordon (1985); Hudson, Leuthold, and Sarassoro (1987); So (1987);Hall Brorsen, and Irwin (1989);and Gribbin, Harris, and Lau (1992). In addition to the non-normality of futures returns, there may also be a problem with serial correlation in daily futures returns.…”

Correlations and cross-correlations in the Brazilian agrarian commodities and stocks

“…Unlike stock and currency markets, the commodity price data are not as easily accessible and have attracted less attention [27][28][29][30][31]. Although there is a significant difference between stocks and commodities from the point of view that stocks have an abstract character, while commodities represent physical products that require storage and transportation and consequently may exhibit a slower response to change in demand, recently it was found by Matia at al.…”