consumer demand for food diversity evidence for germany abstract whereas a large number of empirical studies have been devoted to analysing consumer demand for specific products much less attention has been paid to the household s demand for product variety the number of different products consumed in a specific time period this paper analyses consumer demand for food variety in germany the econometric analysis of 4632 households suggests that variety significantly increases with income and the number of children aged between 7 and 17 years and is significantly higher if the family lives in larger cities in east germany and the housekeeping person is not additionally working full time a single male household consumes a significantly smaller number of different food products the significant and positive impact of household income on food variety is in line with the hypothesis that consumption evolves along a hierarchical order as income increases

a stochastic production function for machine repair although work by levhari and sheshinski 1970 and syrquin 1972 suggests that general functional forms such as the cobb douglas and ces accurately approximate a machine repair stochastic production process this paper shows that these authors have not adequately captured the stochastic nature of the production process more importantly while general forms are convenient and widely employed this paper argues that there is a more direct method for determining the properties of the production process

leveraged investments and agency conflicts when cash flows are mean reverting we analyse the effect of mean reverting cash flows on the costs of shareholder bondholder conflicts arising from partially debt financed investments in a partial equilibrium setting we find that such agency costs are significantly lower under mean reverting mr dynamics when compared to the ubiquitous geometric brownian motion gbm the difference is attributed to the stationarity of the mr process in addition through the application of a novel agency cost decomposition we show that for a larger speed of mean reversion agency costs are driven mainly by suboptimal timing decisions as opposed to suboptimal financing decisions in contrast under the standard gbm assumption the agency costs are driven mainly by suboptimal financing decisions for large growth rates and by suboptimal timing decisions for smaller or negative growth rates

an equilibrium analysis of hedging with liquidity constraints speculation and government price subsidy in a commodity market we develop a simple commodity model to analyze i the effects of hedgying with liquidity constraints due to producers inability to bear unlimited trading losses ii the role of speculation in the process of risk allocation between consumers and producers and iii the equilibrium implications of government price subsidies to the producers we find that 1 liquidity constraints can cause futures prices to exhibit mean reversion which then makes speculation profitable 2 speculation tends to make futures price volatility an increasing function of futures price and 3 government price subsidy if actively hedged by the producers serves to lower the futures risk premium and reduce futures volatility commodity spot and futures prices are determined by the following types of market participants producers consumers speculators and governments producers have generally taken short futures positions in order to hedge against price declines consumers have generally taken long futures positions in order to hedge against price increases speculators who neither produce nor intend to consume the commodity are present in the spot and futures markets for the purpose of making a profit governments play significant roles in the markets by providing producers with various support programs and in some cases by directly intervening in the markets to affect commodity prices or adjust inventory levels the traditional approach to commodity futures pricing has been based on the theory of storage 1 as fama and french 1987 1988 show this approach to commodity pricing is particularly useful for explaining the basis movement as a function of inventory levels based on the hypothesis that the marginal convenience yield on inventory declines at a decreasing rate as

detecting spot price forecasts in futures prices futures markets are often described as having two important social functions first they facilitate the transfer of commodity price risk and second they provide forecasts of commodity prices the evidence that futures markets transfer price risk is irrefutable however there is some debate about the markets forecasting ability in particular forecasts based on the current spot price are often as good as those based on the futures price some economists cite a failure to detect superior forecast power in futures prices as evidence of market inefficiency see e g leuthold 1974 and martin and garcia 1981 there are at least two other explanations first there may be nothing for the futures market to forecast if the current spot price equals the true expectation of the future spot price the futures market cannot provide a better forecast second a superior futures market forecast may be obscured by the unexpected component of the realized spot price the true expectation of the future spot price is unobservable one must approximate this expectation with the actual future spot price

analytical pricing of discrete arithmetic asian options with mean reversion and jumps abstract empirical evidence indicates that commodity prices are mean reverting and exhibit jumps as some commodity option payoffs involve the arithmetic average of historical commodity prices we derive an analytical solution to arithmetic asian options under a mean reverting jump diffusion process the analytical solution is implemented with the fast fourier transform based on the joint characteristic function of the terminal asset price and the realized average value we also examine the accuracy and computational efficiency of the proposed method through numerical studies

valuing managerial flexibility an application of real option theory to mining investments abstract the value of managerial flexibility is assessed using data on prices costs grades reserves ore extraction and metal output for a panel of canadian copper mines a real option model is estimated and solved for project and option values most empirical researchers i consider the initial investment decision but neglect flexible operation thereafter ii assume that price is stochastic but ignore cost and reserve uncertainty and iii model price as a nonstationary stochastic process the evolution of three state variables price cost and reserves is assessed here differences in assumptions compared to others are found to lead to large differences in estimated project and option values

soybean inventory and forward curve dynamics we present two results concerning soybean prices first we exhibit a simple relationship between stocks and price volatility the observation of an increasing price volatility with decreasing inventory is often mentioned in the literature but has so far been documented using a proxy for inventory see fama and french 1987 1988 litzenberger and rabinowitz 1995 instead we reconstruct a yearly quarterly and monthly database of worldwide soybean inventories using aggregate data from the united states brazil and argentina we show that under all time scales price volatility is an increasing linear function of inverse inventory which we term scarcity second we show how the addition of the factor scarcity in a state variable approach to the dynamics of the term structure of soybean forward prices improves the quality of the fit we document this property on a 25 year database of cbot futures contracts and show that the superior accuracy also affects long maturity futures contracts an important property for the valuation of long term origination contracts between producing countries and the agrifood industry

variance swap with mean reversion multifactor stochastic volatility and jumps abstract this paper examines variance swap pricing using a model that integrates three major features of financial assets namely the mean reversion in asset price multi factor stochastic volatility sv and simultaneous jumps in prices and volatility factors closed form solutions are derived for vanilla variance swaps and gamma swaps while the solutions for corridor variance swaps and conditional variance swaps are expressed in a one dimensional fourier integral the numerical tests confirm that the derived solution is accurate and efficient furthermore empirical studies have shown that multi factor sv models better capture the implied volatility surface from option data the empirical results of this paper also show that the additional volatility factor contributes significantly to the price of variance swaps hence the results favor multi factor sv models for pricing variance swaps consistent with the implied volatility surface

option pricing with mean reversion and stochastic volatility many underlying assets of option contracts such as currencies commodities energy temperature and even some stocks exhibit both mean reversion and stochastic volatility this paper investigates the valuation of options when the underlying asset follows a mean reverting lognormal process with stochastic volatility a closed form solution is derived for european options by means of fourier transform the proposed model allows the option pricing formula to capture both the term structure of futures prices and the market implied volatility smile within a unified framework a bivariate trinomial lattice approach is introduced to value path dependent options with the proposed model numerical examples using european options american options and barrier options demonstrate the use of the model and the quality of the numerical scheme

optimal inventory policies when purchase price and demand are stochastic in this paper we consider the problem of a firm that faces a stochastic poisson demand and must replenish from a market in which prices fluctuate such as a commodity market we describe the price evolution as a continuous stochastic process and we focus on commonly used processes suggested by the financial literature such as the geometric brownian motion and the ornstein uhlenbeck process it is well known that under variable purchase price a price dependent base stock policy is optimal using the single unit decomposition approach we explicitly characterize the optimal base stock level using a series of threshold prices we show that the base stock level is first increasing and then decreasing in the current purchase price we provide a procedure for calculating the thresholds which yields closed form solutions when price follows a geometric brownian motion and implicit solutions under the ornstein uhlenbeck price model in addition our numerical study shows that the optimal policy performs much better than inventory policies that ignore future price evolution because it tends to place larger orders when prices are expected to increase

pricing discrete path dependent options under a double exponential jump diffusion model abstract we provide methodologies to price discretely monitored exotic options when the underlying evolves according to a double exponential jump diffusion process we show that discrete barrier or lookback options can be approximately priced by their continuous counterparts pricing formulae with a simple continuity correction the correction is justified theoretically via extending the corrected diffusion method of siegmund 1985 we also discuss the jump effects on the performance of this continuity correction method numerical results show that this continuity correction performs very well especially when the proportion of jump volatility to total volatility is small therefore our method is sufficiently of use for most of time

the stochastic determinants of hospital bed supply this paper uses a general queuing theoretic model to derive more appropriate measures of hospital quality such as turn away probabilities and patient s expected waiting time than have been used in recent empirical work e g joskow 1980

a complete system of engel curves in the spanish economy the main goal of this article is the estimation of the consumption income relationship along with socio economic factors using cross section data from the spanish household expenditure survey 1991 the data has been grouped according to exogenous criteria to avoid the problem of null expenditure first a non linear system of equation is estimated from which the linear form that best fits the used data is tested finally income elasticities are calculated considering three alternative formulations depending on how an initial income increment is distributed among consumers income elasticities are shown for the whole income distribution

jump processes in commodity futures prices and options pricing empirical evidence shows that log return relatives on commodity futures prices are not normally distributed this departure from normality seems to be caused by large price changes occurring in the commodity markets with the arrival of important new information this suggests that a jump diffusion model may be a plausible choice for modeling the stochastic process underlying commodity option prices merton 1976a develops a jump diffusion option pricing model assuming that jump risk is unsystematic however the jump diffusion model developed by bates 1991 is more appropriate for commodity option pricing since it allows jump risk to be systematic in this article recent transactions data on futures and futures options are used to test out of sample options using american versions of black s diffusion and bates s jump diffusion models the results show that bates s model performs considerably better than black s model jump diffusion asian option prices are also shown to differ considerably from geometric brownian motion asian option prices

the economies of massed reserves the economy of massed reserves first mentioned by e a g robinson 1958 pp 26 27 is now firmly established in the industrial organization literature as an example of a potential plant level scale economy the massing of reserves results in a savings in the proportion of required reserves to expected output as the scale of a facility increases examples of such reserves are bank tellers specialized tools and equipment repairmen inventories spare parts and checkout lines the potential economies from massing reserves are dependent on the underlying stochastic processes governing the supply and or demand of the service provided theoretical justification for the economies of massed reserves has usually been based on an appeal to the law of large numbers for example donald hay and derek morris wrote the law of large numbers makes the number of breakdowns more predictable in a plant using a large number of machines so that the number of stand by maintenance staff need not be increased in proportion to size 1979 p 44 this paper demonstrates that the law of large numbers does not provide a theoretical explanation of massed reserves scale economies instead it is shown that the expected economies of massed reserves can be calculated from the steady state properties of well known queuing models queuing models apply to any case where a servicing input is held in reserve to cope with the stochastic nature of the market or production process in addition a method for quantifying the expected economies of queuing processes is developed the magnitude of these expected economies is shown to be significant and calculable for example the expected economies inherent in a widely applied queuing model are shown to exceed 23 percent in some cases section i establishes the irrelevance of the law of large numbers as a theory of scale economies section ii provides a formal method for determining the scale economies inherent in the most often mentioned massed reserves example machine repair section iii shows that the same method can be used to calculate scale economies for the remaining massed reserves examples specialized repair tools and equipment checkout counter clerks bank tellers and other service personnel capacity and inventories and spare parts in addition it is demonstrated that the same method can be used to calculate scale economies for some multiproduct operations

an fft network for levy option pricing abstract this paper develops a simple network approach to american exotic option valuation under levy processes using the fast fourier transform fft the forward shooting grid fsg technique of the lattice approach is then generalized to expand the fft network to accommodate path dependent variables this network pricing approach is applicable to all levy processes for which the characteristic function is readily available in other words the log value of the underlying asset can follow finite activity or infinite activity levy processes with the powerful computation of fft the proposed network has a negligible additional computational burden compared to the binomial tree approach the early exercise policy and option values in the continuation region are determined in a way very similar to that of the lattice approach numerical examples using american style barrier lookback and asian options demonstrate that the fft network is accurate and efficient

cointegration and detectable linear and nonlinear causality analysis using the london metal exchange lead contract this study applies linear and nonlinear granger causality tests to examine the dynamic relation between london metal exchange lme cash prices and three possible predictors the analysis uses matched quarterly inventory uk treasury bill interest rates futures prices and cash prices for the commodity lead traded on the lme the effects of cointegration on both linear and nonlinear granger causality tests is also examined when cointegration is not modelled evidence is found of both linear and nonlinear causality between cash prices and analysed predictor variables however after controlling for cointegration evidence of significant nonlinear causality is no longer found these results contribute to the empirical literature on commodity price forecasting by highlighting the relationship between cointegration and detectable linear and nonlinear causality the importance of interest rate and inventory as well as futures price in forecasting cash prices is also illustrated failure to detect significant

mean reversion in equilibrium asset prices evidence from the futures term structure we use the term structure of futures prices to test whether investors anticipate mean reversion in spot asset prices the empirical results indicate mean reversion in each market we examine for agricultural commodities and crude oil the magnitude of the estimated mean reversion is large for example point estimates indicate that 44 percent of a typical spot oil price shock is expected to be reversed over the subsequent eight months for metals the degree of mean reversion is substantially less but still statistically significant we detect only weak evidence of mean reversion in financial asset prices in this study we provide evidence of mean reversion in the prices of several real and financial assets rather than examining evidence of ex post reversion using time series of asset prices we use price data from futures contracts with varying delivery horizons to test whether investors expect asset prices to revert this approach offers two advantages first since futures prices are readily available for many markets our procedure can be implemented for many assets including those for which reliable spot price data is elusive second there is little ambiguity as to the source of any mean reversion detected using our method subject only to the maintained assumption that the no arbitrage cost of carry condition holds our test detects mean reversion that is expected to occur in equilibrium but has no power to detect mean reversion resulting from noise or inefficiencies our methodology focuses on relations between price levels and the slope of the futures term structure defined as the change across delivery dates in the futures prices observed on a given trading date an inverse relation between prices and the futures term slope constitutes evidence that investors expect mean reversion in spot prices to illustrate initially assume there are no

commodity derivatives pricing with cointegration and stochastic covariances abstract empirically cointegration and stochastic covariances including stochastic volatilities are statistically significant for commodity prices and energy products to capture such market phenomena we develop a continuous time dynamics of cointegrated assets with a stochastic covariance matrix and derive the joint characteristic function of asset returns in closed form the proposed model offers an endogenous explanation for the stochastic mean reverting convenience yield the time series of spot and futures prices of wti crude oil and gasoline shows cointegration relationship under both physical and risk neutral measures the proposed model also allows us to fit the observed term structure of futures prices and calibrate the market implied cointegration relationship we apply it to value options on a single commodity and on multiple commodities

asian and australian options a common perspective we show that australian options are equivalent to fixed or floating strike asian options and consequently that by studying asian options from the australian perspective and vice versa much can be gained one specific application of this australian approach leads to a natural dimension reduction for the pricing pde of asian options with or without stochastic volatility featuring time independent coefficients another application lies in the improvement of monte carlo schemes where the australian approach results in a path independent method we also show how the milevsky and posner 1998 result on the reciprocal approximation for asian options can be quickly obtained by using the connection to australian options further we present an analytical exact pricing formula for australian options and adapt a result of carr et al 2008 to show that the price of an australian call option is increasing in the volatility and by doing this answering a standing question by moreno and navas 2008

analytical pricing of discretely monitored asian style options theory and application to commodity markets we compute an analytical expression for the moment generating function of the joint random vector consisting of a spot price and its discretely monitored average for a large class of square root price dynamics this result combined with the fourier transform pricing method proposed by carr and madan carr p madan d 1999 option valuation using the fast fourier transform journal of computational finance 2 4 summer 61 73 allows us to derive a closed form formula for the fair value of discretely monitored asian style options our analysis encompasses the case of commodity price dynamics displaying mean reversion and jointly fitting a quoted futures curve and the seasonal structure of spot price volatility four tests are conducted to assess the relative performance of the pricing procedure stemming from our formulae empirical results based on natural gas data from nymex and corn data from cbot show a remarkable improvement over the main alternative techniques developed for pricing asian style options within the market standard framework of geometric brownian motion