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,

Type I and Type II Errors in the Unit Root Determination of a Fractional Brownian Motion

Economists who deal with time-series data usually take the unit root test as the ‘prerequisite’ test for a Brownian motion. It is typical for any researchers to apply a battery of well-known unit root tests to their models to confirm stationarity in the model specification. Nonetheless, often times, we see a conclusion that fail to reject the null in favor of the existence of unit root even though the model specification is such that the lag coefficients of an AR(q) process do not sum up to unity. In this study, we show that having the sum of the lag coefficients equals to unity is indeed a necessary and sufficient condition for the existence of a unit root. Hence, the aforementioned incident will lead to a type II error in the unit root determination. On the other hands, type I error results when we reject the null that there exists a unit root when in fact the null is true. The fractional Brownian motion (fBm) process which has stationary but not necessarily independent increments is used to convey the findings of this study. We use Hurst exponent as a gauge for persistency in the data and show that a fBm process is a legitimate stochastic process with unit root even though it exhibits a degree of persistency in time.Unit root, Hurst exponent, Fractional Brownian Motion, Financial Economics, Risk and Uncertainty,

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,

Guiding of Rydberg atoms in a high-gradient magnetic guide

We study the guiding of $^{87}$Rb 59D$_{5/2}$ Rydberg atoms in a linear, high-gradient, two-wire magnetic guide. Time delayed microwave ionization and ion detection are used to probe the Rydberg atom motion. We observe guiding of Rydberg atoms over a period of 5 ms following excitation. The decay time of the guided atom signal is about five times that of the initial state. We attribute the lifetime increase to an initial phase of $l$-changing collisions and thermally induced Rydberg-Rydberg transitions. Detailed simulations of Rydberg atom guiding reproduce most experimental observations and offer insight into the internal-state evolution

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

Spatial Control of Photoemitted Electron Beams using a Micro-Lens-Array Transverse-Shaping Technique

A common issue encountered in photoemission electron sources used in electron accelerators is the transverse inhomogeneity of the laser distribution resulting from the laser-amplification process and often use of frequency up conversion in nonlinear crystals. A inhomogeneous laser distribution on the photocathode produces charged beams with lower beam quality. In this paper, we explore the possible use of microlens arrays (fly-eye light condensers) to dramatically improve the transverse uniformity of the drive laser pulse on UV photocathodes. We also demonstrate the use of such microlens arrays to generate transversely-modulated electron beams and present a possible application to diagnose the properties of a magnetized beam.Comment: arXiv admin note: text overlap with arXiv:1609.0166