On Term Structure Models of Commodity Futures Prices and the Kaldor-Working Hypothesis

Both prices and the volatility of storable agricultural commodity futures contracts have been rising since 2005 and particularly since 2007. This paper aims to answer two principal questions: (i) How has the behavior of these futures prices over time and across maturities changed with the rise of biofuels and their demand-side pres- sure on corn and related crops?, and (ii) Is there now stronger or weaker evidence of the Kaldor-Working convenience yield-storage hypothesis, whereby futures price backwardation can be explained by the high value of remaining inventory stocks when these are near stockouts? The empirical application is to Chicago Board of Trade corn, wheat and soybeans futures. To make use of all available futures data rather than only the nearby, this paper adopts a recently developed affine term structure model approach and conducts estimation in state-space form using the Kalman filter. A novel aspect of the research is that it allows an arbitrary number N of state vari- ables, where more variables provide further precision and curvature but at a higher computational cost. It is found that a three-state variable model containing both ran- dom walk and mean reversion components provides the most parsimonious fit during 1988-2004, but that a simple one-state variable model is optimal for the period 2005- 2007. The main implication is that futures prices since 2005 behave much more like a \random walk" than before. Also, the model allows us to estimate the term struc- ture of volatility and it is found that distant maturity futures should be expected to be much more volatile than historically normal. Two practical but only tentative implications are: (a) hedgers should use significantly lower hedge ratios than before, and (b) for traders, the classic Black-Scholes option pricing solution should perform better now than it has historically. Lastly, the paper finds partial empirical support for the convenience yield relationship with relative inventory stocks, especially for soybeans and wheat.Agricultural Finance, C52, C53, G12, G13, Q13, Q14,

The Confidence Limits of a Geometric Brownian Motion

This paper investigates whether the assumption of Brownian motion often used to describe commodity price movements is satisfied. Using historical data from 17 commodity futures contracts specific tests of fractional and ordinary Brownian motion are conducted. The analyses are conducted under the null hypothesis of ordinary Brownian motion against the alternative of persistent or ergodic fractional Brownian motion. Tests for fractional Brownian motion are based on a variance ratio test. However, standard errors based on Monte Carlo simulations are quite high, meaning that the acceptance region for the null hypothesis is large. The results indicate that for the most part, the null hypothesis of ordinary Brownian motion cannot be rejected for 14 of 17 series. The three series that did not satisfy the tests were rejected because they violated the stationarity property of the random walk hypothesis.Marketing,

Spurious Long Memory in Commodity Futures: Implications for Agribusiness Option Pricing

Long memory, and more precisely fractionally integration, has been put forward as an explanation for the persistence of shocks in a number of economic time series data as well as to reconcile misleading findings of unit roots in data that should be stationary. Recent evidence suggests that long memory characterizes not commodity futures prices but rather price volatility (generally defined as $L_p$ norms of price logreturns). One implication of long memory in volatility is the mispricing of options written on commodity futures, the consequence of which is that fractional Brownian motion should replace geometric Brownian motion as the building block for option pricing solutions. This paper asks whether findings of long memory in volatility might be spurious and caused either by fragile and inaccurate estimation methods and standard errors, by correlated short memory dynamics, or by alternative data generating processes proven to generate the illusion of long memory. We find that for nine out of eleven agricultural commodities for which futures contracts are traded, long memory is spurious but is not caused by the effect of short memory. Alternative explanations are addressed and implications for option pricing are highlighted.Q13, Q14, Marketing, C52, C53, G12, G13,

Investigation of parabolic computational techniques for internal high-speed viscous flows

A feasibility study was conducted to assess the applicability of an existing parabolic analysis (ADD-Axisymmetric Diffuser Duct), developed previously for subsonic viscous internal flows, to mixed supersonic/subsonic flows with heat addition simulating a SCRAMJET combustor. A study was conducted with the ADD code modified to include additional convection effects in the normal momentum equation when supersonic expansion and compression waves were present. It is concluded from the present study that for the class of problems where strong viscous/inviscid interactions are present a global iteration procedure is required

Salmon Investigations on the Whale River, Ungava in 1960 and the Development of an Eskimo Fishery for Salmon in Ungava Bay

A study of the Atlantic salmon populations breeding in the Ungava Bay watershed, which commenced in 1956 on the George River and in 1957 on the Koksoak River, was continued during the summer of 1960 on the Whale River. The two principal collecting stations were at the site of the old Hudson's Bay Company's post, in tidal waters, and in a rapid section of the river 15 miles above the post, in non-tidal waters. In spite of a very wet summer, which resulted in high water levels all season, a good sample of salmon was obtained. Almost 900 specimens were examined, of which 185 were adults that had entered the river to spawn, 32 were spent fish from the run of the previous year, and the rest were juvenile smolts and parr. Most of the large fish were captured in gill nets of 4-, 6-, and 8-inch mesh, about one-half of the juveniles were taken in 1.5-inch-mesh gill nets, and the remainder by angling. The spawning run in Whale River began about August 6 and continued until the end of the month, when catches at the post fell to almost nothing. The 1960 run in the Koksoak River followed a similar pattern. Whale River salmon were the same size as those examined from other Ungava rivers. The majority are between 9 and 13 lbs. in weight and have spent 2 years or longer feeding at sea. The grilse, after 1 or more years at sea, are between 3.5 and 6 lbs. in weight. Analysis of the data on the juveniles is not yet complete, but indicates a growth and age range similar to that found previously in the George and Koksoak rivers, that is, they migrate to the sea when they are 3 to 7 years old and between 18 and 26 cms. long. ... The information that has been accumulated during this series of investigations on Ungava salmon is now proving to be of practical importance. During the summer of 1961 the Department of Northern Affairs and National Resources plans to initiate an experimental Eskimo fishery for salmon on the Koksoak River and possibly also on the Whale River. Fresh salmon are to be flown from Chimo to Montreal for sale. It has been possible to provide the Department with information on desirable mesh sizes for the nets and on the probable weight distribution of the catch. By continuing to collect data during the course of the fishing and following closely any changes in the composition of the catch it will be possible to find out whether the expected fishing pressure (removal of 10,000 lbs. of fish per river per year) is having any effect on the population. In this way it can be discovered whether the salmon inhabiting these northern waters can maintain themselves against both the physical handicap of their environment and the stress of fishing. The scanty and probably unreliable evidence from the records of the Hudson's Bay Company fishery started in the 1880's and abandoned in the 1930's indicates that catches may decline after a period of fishing. It is hoped that by employing university students to assist with the project accurate records can be obtained of the size and age composition of the catches and that a careful watch can be maintained on any effects of the planned fishery. ..

Salmon Investigations on the Koksoak River, 1957

Continuing the investigations that were begun at the George River in 1956, the salmon population of the Koksoak River was examined during the summer of 1957. Sampling was by the use of nylon gill nets placed at various stations along the river and its two major tributaries, the Kaniapiskau and the Larch. A fairly large sample of juvenile salmon was obtained by angling. It was found that probably the majority of the Koksoak salmon travel up the Larch River to spawn. How far they can ascend is not known, but they do so for a minimum of 60 miles and probably can go much farther. Only the lower 20 miles of the Kaniapiskau River are accessible to salmon, beyond this they are stopped by the 60-foot Limestone Falls. On the basis of catches of adult salmon twenty times as many ascend the Larch than the Kaniapiskau; however, since only one salmon was taken in the Kaniapiskau in 30 net nights, this estimate is probably not reliable. The Eskimo salmon fishery at Fort Chimo was observed when it was in full swing and a good sample of the catch was examined. This fishery can hardly be described as intensive and undoubtedly the Eskimo could obtain far more salmon. The major obstacles are (1) the high cost of gear; (2) the difficulties of fishing the Koksoak River at Fort Chimo due to the large size of the stream and the strong tidal currents; (3) the coincidence of the fishing season and the time of seasonal employment in loading and unloading the ships. This occupation is very attractive because the Eskimo can earn $1.40 per hour, whereas fishing does not bring in cash, only a supply of dog food for the winter. ... In addition to collecting, physiological studies on the speckled trout [brook trout] and the Atlantic salmon were continued. These involved measurements of the basal oxygen consumption of these fish under different temperature regimes at different seasons. Results obtained for the speckled trout in previous years suggested that diurnal temperature fluctuations at low temperatures had an exaggerated effect on the oxygen consumption of the fish. To complement the hourly measurements of temperatures made in conjunction with the physiological experiments, a number of continuous recordings were obtained using a thermograph .... The results of these investigations, which were supported by a Banting Fund grant from the Arctic Institute of North America and a grant from the Department of Fisheries, Quebec, will be published in detail later

Breeding Success of the Common Tern on the North Shore of the Gulf of St. Lawrence in 1961 and 1962

Colonies of the common tern, Sterna hirundo, occur on many of the small islands off the north shore of the Gulf of St. Lawrence. In 1961 and 1962 the author had the opportunity to observe a number of colonies near the mouth of the Nabisipi River, 50°14'N, 62°13'W. It was evident that breeding success in the colonies can change greatly from year to year. The breeding in 1962 was an almost complete failure and contrasted sharply with that in 1961. Annual recruitment in the tern colonies is very much influenced by weather and perhaps also by egg collecting. ..