essays on duopoly competition with asymmetric firms is profit maximization always an evolutionary stable strategy abstract we propose both a well mixed and spatially structured evolutionary game to analyze the competitive behavior of retail firms in duopolistic markets firms from two different populations high low efficiency compete and the available strategies are i profit or ii revenue maximization under bounded rationality assumptions firms can update their behavior through dynamic learning mechanisms in addition to a replicator dynamics approach we develop an agent based model to increase realism and to capture possible spatial effects on firms strategic behavior a convergence between the methods is observed and given specific conditions revenue maximization may corresponds to an evolutionary stable strategy ess

stochastic convenience yield and the pricing of oil contingent claims this paper develops and empirically tests a two factor model for pricing financial and real assets contingent on the price of oil the factors are the spot price of oil and the instantaneous convenience yield the parameters of the model are estimated using weekly oil futures contract prices from january 1984 to november 1988 and the model s performance is assessed out of sample by valuing futures contracts over the period november 1988 to may 1989 finally the model is applied to determine the present values of one barrel of oil deliverable in one to ten years time

electricity derivatives pricing with forward looking information in order to increase overall transparency on key operational information power transmission system operators publish an increasing amount of fundamental data including forecasts of electricity demand and available capacity we employ a fundamental model for electricity prices which lends itself well to integrating such forecasts while retaining ease of implementation and tractability to allow for analytic derivatives pricing formulae in an extensive futures pricing study the pricing performance of our model is shown to further improve based on the inclusion of electricity demand and capacity forecasts thus confirming the general importance of forward looking information for electricity derivatives pricing however we also find that the usefulness of integrating forecast data into the pricing approach is primarily limited to those periods during which electricity prices are highly sensitive to demand or available capacity whereas the impact is less visible when fuel prices are the primary underlying driver to prices instead

pre emptive mergers and downstream cost asymmetry abstract with sufficient downstream cost asymmetry a horizontal merger will be chosen over a vertical merger this results because the technology transfer is large and the incentive to vertically merge shrinks as the horizontal merger eliminates a cost asymmetry induced bottleneck

long term spread option valuation and hedging this paper investigates the valuation and hedging of spread options on two commodity prices which in the long run are in dynamic equilibrium i e cointegrated the spread exhibits properties different from its two underlying commodity prices and should therefore be modelled directly this approach offers significant advantages relative to the traditional two price methods since the correlation between two asset returns is notoriously hard to model in this paper we propose a two factor model for the spot spread and develop pricing and hedging formulae for options on spot and futures spreads two examples of spreads in energy markets the crack spread between heating oil and wti crude oil and the location spread between brent blend and wti crude oil are analyzed to illustrate the results

bilateralism and free trade we study a setting with many countries in each country there are firms that can sell in the domestic as well as foreign markets countries can sign bilateral free trade agreements that lower import tariffs and thereby facilitate trade we allow a country to sign any number of bilateral free trade agreements a profile of free trade agreements defines the trading regime our principal finding is that in symmetric settings bilateralism is consistent with global free trade we also explore the effects of asymmetries across countries and political economy considerations on the incentives to form trade agreements

sourcing by design product complexity and the supply chain this paper focuses on the connection between product complexity and vertical integration using original empirical evidence from the auto industry a rich literature has addressed the choice between internal production and external sourcing of components in the auto industry more recent literature has developed the concept of product architecture as another choice variable that may be one of the important contributors to product complexity in this paper we connect these two important decisions and study them jointly we use the property rights approach to argue that complexity in product design and vertical integration of production are complements that in house production is more attractive when product complexity is high as firms seek to capture the benefits of their investment in the skills needed to coordinate development of complex designs we test this hypothesis with a simultaneous equations model applied to data from the luxury performance segment of the auto industry we find a significant and positive relationship between product complexity and vertical integration this has implications for optimal incentive structures within firms as well as for interpreting firm performance

product differentiation in successive vertical oligopolies this is a successive oligopoly model with two varieties of a final product downstream firms choose one variety to sell on a final market upstream firms specialize in the production of one input specifically designed for one variety but they also produce the input for the other variety at an extra cost we show that as more downstream firms choose one particular variety more upstream firms specialize in the input specific to that variety and vice versa multiple equilibria may result and the softening effect of product differentiation on competition might not be strong enough to induce maximal differentiation jel classification l11 l13 l23

forward curves scarcity and price volatility in oil and natural gas markets the role of inventory in explaining the shape of the forward curve and spot price volatility in commodity markets is central in the theory of storage developed by kaldor kaldor n 1939 speculation and economic stability the review of economic studies 7 1 27 and working working h 1949 the theory of the price of storage american economic review 39 1254 1262 and has since been documented in a vast body of financial literature including the reference paper by fama and french fama e f and k r french 1987 commodity futures prices some evidence on forecast power premiums and the theory of storage journal of business 60 55 73 on metals the goal of this paper is twofold i validate in the case of oil and natural gas the use of the slope of the forward curve as a proxy for inventory the slope being defined in a way that filters out seasonality ii analyze directly for these two major commodities the relationship between inventory and price volatility in agreement with the theory of storage we find that i the negative correlation between price volatility and inventory is globally significant for crude oil ii this negative correlation prevails only during those periods of scarcity when the inventory is below the historical average and increases importantly during the winter periods for natural gas our results are illustrated by the analysis of a 15 year database of us oil and natural gas prices and inventory

renegotiation design with unverifiable information this paper considers a buyer seller relationship with observable but unverifiable investments and or random utility parameters in such situations it is known that contract renegotiation may prevent the implementation of first best outcomes in this paper we show however that efficient investments and optimal risk sharing can typically be achieved provided the initial contract is able to monitor the ex post renegotiation process specifically we focus on the following two features of renegotiation design first default options in case renegotiation breaks down second the allocation of all bargaining power to either contracting party moreover we show that these two features can be obtained in standard rubinstein bargaining games through contractual provisions such as specific performance clauses and penalties for delay or equivalently financial hostages refundable without interest

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

vertical governance change and product differentiation under decreasing component costs in deciding on whether and when to outsource component production firms should consider the trade off between total production costs and the ability to horizontally differentiate products we study the outsourcing decision in a duopoly under decreasing but uncertain market rates for components given that outsourcing increases the substitutability of the final products we find that there is at least one firm that eventually outsources component production because it cannot differentiate its product enough by in house production to justify the eventually higher costs the follower outsources at a lower market rate or may even remain vertically integrated the follower thus incurs the eventually much higher in house component costs longer while the low substitutability is enjoyed by both firms under endogenous roles firms thus engage in a preemption game to be the first to outsource we also find that firms generally outsource at lower market rates if uncertainty is higher but seek to preempt at remarkably higher market rates if substitutability remains low

long term swings and seasonality in energy markets abstract this paper introduces a two factor continuous time model for commodity pricing under the assumption that prices revert to a stochastic mean level which shows smooth periodic fluctuations over long periods of time we represent the mean reversion price by a fourier series with a stochastic component we also consider a seasonal component in the price level an essential characteristic of many commodity prices which we represent again by a fourier series we obtain analytical pricing expressions for futures contracts using futures price data on natural gas we provide evidence on the presence of long term fluctuations and show how to estimate the long term component simultaneously with a seasonal component using the kalman filter we analyse the in sample and out of sample empirical performance of our pricing model with and without a seasonal component and compare it with schwartz and smith 2000 model our findings show the in sample and out of sample superiority of our model with seasonal fluctuations thereby providing a simple and powerful tool for portfolio management risk management and derivative pricing

seasonal stochastic volatility implications for the pricing of commodity options many commodity markets contain a strong seasonal component not only at the price level but also in volatility in this paper the importance of seasonal behavior in the volatility for the pricing of commodity options is analyzed we propose a seasonally varying long run mean variance process that is capable of capturing empirically observed patterns semi closed form option valuation formulas are derived we then empirically study the impact of the proposed seasonal stochastic volatility model on the pricing accuracy of natural gas futures options traded at the new york mercantile exchange nymex and corn futures options traded at the chicago board of trade cbot our results demonstrate that allowing stochastic volatility to fluctuate seasonally significantly reduces pricing errors for these contracts

vertical foreclosure with the choice of input specifications we develop an equilibrium model of vertical foreclosure with the choice of input specifications vertical foreclosure occurs as the upstream division of the integrated firm makes a specialized input for its sister downstream division while it would as an independent firm provide a generalized input the changes in incentives with vertical integration can be explained by the externalities the choice of a specialized input entails vertical integration allows the upstream firm to internalize the benefit of raising the rival firm s costs at the downstream level we derive conditions for equilibrium vertical foreclosure to occur and discuss its welfare consequences

competition of firms discriminatory pricing and location1 two costlessly mobile firms are to be located in a market region a subset of the plane the firms compete by setting locations and delivered price schedules to study this competitive stiuation an appropriate extensive form game is defined along with an appropri ate noncooperative solution concept existence and general properties of the equilibrium are demonstrated among the results are each firm increases its profit by locating so as to decrease total cost to both firms of serving the market firms will never locate coinciden tally if they have identical production costs and transport cost rates or if these are different and the firms are located in a circular market region having a uniform demand distribution this paper studies competition between two profit maximizing firms in space who are costlessly mobile and may discriminate in price we will allow the firms to set locations and delivered price schedules and we will be concerned with the existence and properties of equilibria in location and price starting with hotelling 9 the spatial competition literature has focused on location on bounded linear markets by two or more firms hotelling assumed identical firms that produced a single good with constant cost of production and considered consumers to be uniformly distributed and to have inelastic demand he also assumed that the consumers pay transport cost and purchase the good from the cheapest source hotelling claimed that a nash equilibrium in locations for the two firm market existed and yielded back to back locations at the center of the market many authors most recently d aspremont gabszewicz and thisse 2 have noted that an equilbrium in prices and location does not exist for hotelling s model however if the firms employ identical exogeneously specified prices hotelling s conclusions hold subsequent work by smithies 14 hartwick and hartwick 7 and eaton 3 claimed to show that a nash equi librium in f o b prices and locations can exist in markets with a uniform distribu tion of consumers each of whom have identical elastic demand functions for the two and three firm problems the work of d aspremont et al casts doubt on these conclusions without the adoption of restrictive conditions our work contrasts with these works and related research which has dealt with linear markets with uniform distributions of customers and with identical firms our work will involve markets that are subsets of the plane having nonuniform distributions of customers our firms will be allowed to be different that is have differences in production and transport costs however the fundamental difference in our approach is that our firms will set discriminatory prices and not price f o b in many ways our work will represent the discriminatory pricing

cooperative investments and the value of contracting recent articles have shown that contracts can support the efficient outcome for bilateral trade even in the face of specific investments and incomplete contracting these studies typically considered selfish investments that benefit the investor e g the seller s investment reduces her production costs the authors find very different results for cooperative investments that directly benefit the investor s partner e g the seller s investment improves the buyer s value of the good most importantly if committing not to renegotiate the contract is impossible then contracting has no value i e the parties cannot do better than to abandon contracting altogether in favor of ex post negotiation

computing the market price of volatility risk in the energy commodity markets abstract in this paper we demonstrate the need for a negative market price of volatility risk to recover the difference between black scholes black f scholes m 1973 the pricing of options and corporate liabilities journal of political economy 81 637 654 black black f 1976 studies of stock price volatility changes in proceedings of the 1976 meetings of the business and economics statistics section american statistical association pp 177 181 implied volatility and realized term volatility initially using quasi monte carlo simulation we demonstrate numerically that a negative market price of volatility risk is the key risk premium in explaining the disparity between risk neutral and statistical volatility in both equity and commodity energy markets this is robust to multiple specifications that also incorporate jumps next using futures and options data from natural gas heating oil and crude oil contracts over a 10 year period we estimate the volatility risk premium and demonstrate that the premium is negative and significant for all three commodities additionally there appear distinct seasonality patterns for natural gas and heating oil where winter withdrawal months have higher volatility risk premiums computing such a negative market price of volatility risk highlights the importance of volatility risk in understanding priced volatility in these financial markets

spot and derivative pricing in the eex power market using spot and futures price data from the german eex power market we test the adequacy of various one factor and two factor models for electricity spot prices the models are compared along two different dimensions 1 we assess their ability to explain the major data characteristics and 2 the forecasting accuracy for expected future spot prices is analyzed we find that the regime switching models clearly outperform its competitors in almost all respects the best results are obtained using a two regime model with a gaussian distribution in the spike regime furthermore for short and medium term periods our results underpin the frequently stated hypothesis that electricity futures quotes are consistently greater than the expected future spot a situation which is denoted as contango

short term variations and long term dynamics in commodity prices in this article we develop a two factor model of commodity prices that allows meanreversion in short term prices and uncertainty in the equilibrium level to which prices revert although these two factors are not directly observable they may be estimated from spot and futures prices intuitively movements in prices for long maturity futures contracts provide information about the equilibrium price level and differences between the prices for the short and long term contracts provide information about short term variations in prices we show that although this model does not explicitly consider changes in convenience yields over time this short term long term model is equivalent to the stochastic convenience yield model developed in gibson and schwartz 1990 we estimate the parameters of the model using prices for oil futures contracts and apply the model to some hypothetical oil linked assets to demonstrate its use and some of its advantages over the gibson schwartz model

a theory of buyer seller networks this paper introduces a new model of exchange networks rather than markets of buyers and sellers it begins with the empirically motivated premise that a buyer and seller must have a relationship a link to exchange goods networks buyers sellers and the pattern of links connecting them are common exchange environments this paper develops a methodology to study network structures and explains why agents may form networks in a model that captures characteristics of a variety of industries the paper shows that buyers and sellers acting strategically in their own self interests can form the network structures that maximize overall welfare

cost raising strategies advantage rivals by raising their costs in this paper we show that strategies designed to raise rivals costs have a number of advantages over predatory pricing they are credible do not necessarily require the victim to exit and do not necessarily require the existence of classical market power the paper sets up a general model proves a number of general results and then applies the model to specific strategies involving overbuying inputs and vertical integration

vertical mergers and product differentiation this paper presents an equilibrium theory of vertical mergers that incorporates strategic behaviors in the hotelling type location model this enables one to consider the relationship between downstream firms strategies for product differentiation and vertical integration i show that vertical integration enhances the degree of product differentiation of the integrated firm under some conditions partial integration arises in equilibrium which may increase the profit of the nonintegrated downstream firm the paper also discusses the welfare implications of vertical integration

procurement and renegotiation parties bound by an incomplete contract have an incentive to renegotiate after acquiring new information the issue of the parties investment in the relationship before renegotiation is analyzed in a simple two period procurement model the firm invests in the first period it then learns its production cost and the sponsor learns its value for the project williamson s underinvestment presumption is shown to hold under very general assumptions about bargaining and about the ex post asymmetry of information as long as the firm s investment is not observable by the sponsor the introduction of a cancellation fee may well lead to even less investment contrary to what is sometimes argued the role of ex ante price fixing as an alternative way to reintroduce some form of commitment and the problem of cost overruns are discussed last it is shown that if investment is observable by the sponsor andthus may become a joint decision variable the two parties may choose to under or overinvest

valuation of commodity futures and options under stochastic convenience yields interest rates and jump diffusions in the spot this paper investigates the effects of stochastic convenience yields stochastic interest rates and jumps in the spot price on the pricing of commodity futures forwards and futures options numerical examples show that one factor prices differ materially from the stochastic convenience yield two factor prices when convenience yield is considerably above its long term average the extension to a three factor model with stochastic interest rates leads to a different futures price but the forward price is unchanged the extension ofthe three factor model to include jumps in the spot price process does not affect forward or futures prices but it can have an impact on options prices the model is applied to price the present value of future cash flows from a real asset

complexity and renegotiation a foundation for incomplete contracts the paper considers a hold up model where only one of n future trading opportunities will prove to be efficient and where ex post renegotiation of the ex ante contract cannot be prevented as the environment becomes more complex n the outcome under any message contingent long term contract converges to that of the incomplete contracting model where trade is contractible ex post but not ex ante when trades are costly to describe both ex ante and ex post the incomplete contracting result is extended to a broader class of environments

cross sectional versus time series estimation of term structure models empirical results for the dutch bond market abstract we compare time series and cross section estimates of the well known vasicek and cir term structure models for a dataset of daily bond prices and short term interest rates for the netherlands the main finding is the great similarity between the two models with respect to the cross sectional term structure parameter estimates and implied bond option values from a time series perspective we find that for some maturities the data reject the constant volatility vasicek model and indicate the presence of the cir volatility effects

when to initiate an international vertical merger the impact of negative demand shock this paper develops an extended hotelling type product and technology differentiated model with two upstream and two downstream firms the us upstream respectively downstream firm is technologically more advanced than the chinese upstream respectively downstream firm the locations of the upstream firms and the us downstream firm are fixed and the chinese downstream firm chooses its product location the downstream firms compete with each other in us market we aim to explore the conditions under which an international vertical merger between the chinese downstream firm and the us upstream firm occurs and its welfare implications we show that the incentive for the chinese downstream firm to initiate a technology acquiring international vertical merger crucially depends on the market conditions of the united states as compared to exporting or domestic vertical merger international vertical merger is by no means an optimal choice for the chinese downstream firm when there is no negative demand shocks to us market this result remains to hold when the us downstream firm also has the option of initiating a merger with the us upstream firm nevertheless in the case of a negative demand shock a profitable international vertical merger may occur however such mergers worsen the social welfare of the united states

non cooperative networks in oligopolies in an oligopoly prior to competing in the market firms have an opportunity to pick up externalities from other firms by setting links the links formation defines an industrial network we study the incentives for firms to form links and the effect of this links formation on the architecture of the resulting networks our analysis shows that equilibrium networks differ dramatically depending on the nature of market competition cournot or bertrand more precisely in the case of cournot oligopoly we should expect to see networks in which each firm obtains access to externalities of either all firms or no firm in the case of bertrand oligopoly we should expect to see networks in which one firm derives benefits from externalities of all other firms while the latter get no externality we also present some results on the architecture of socially efficient networks

unspanned stochastic volatility and the pricing of commodity derivatives commodity derivatives are becoming an increasingly important part of the global derivatives market here we develop a tractable stochastic volatility model for pricing commodity derivatives the model features unspanned stochastic volatility quasi analytical prices of options on futures contracts and dynamics of the futures curve in terms of a low dimensional affine state vector we estimate the model on nymex crude oil derivatives using an extensive panel data set of 45 517 futures prices and 233 104 option prices spanning 4082 business days we find strong evidence for two predominantly unspanned volatility factors jel g13

vertical mergers and market foreclosure ythe model in this paper illustrates three effects of vertical mergers when both stages are oligopolistic and vertically integrated and unintegrated producers coexist first the merging firm increases its final good output second the resulting backward shift in the residual demand curve facing unintegrated final good producers ylowers their demand for the intermediate good third the merged firm withdraws from the intermediate good market the increased concentration pushes the intermediate good price upward which effect dominates depends on market structure under some conditions a vertical merger causes the price of the final good to increase

criminal deterrence revisiting the issue with a birth cohort we estimate the general deterrent effect of criminal justice resources on criminal behavior using panel data for a sample representative of young men in u s urban areas our data which combine individual level information on arrests and personal characteristics with aggregate information on criminal justice resources allow us to obtain deterrence measures that reflect theoretical concepts and are of potential policy relevance we find robust evidence of a general deterrent effect flowing from criminal justice particularly police resources the nature of our data also allows us to conduct extensive exogeneity tests and to explore a number of possible third causes for the deterrent effect we find strong evidence that our deterrence variables are exogenous and no evidence that our deterrence result stems from commonly hypothesized third causes copyright 1994 by mit press

a strategic model of social and economic networks we study the stability and efficiency of social and economic networks when self interested individuals can form or sever links first for two stylized models we characterize the stable and efficient networks there does not always exist a stable network that is efficient next we show that this tension persists generally to assure that there exists a stable network that is efficient one is forced to allocate resources to nodes that are not responsible for any of the production we characterize one such allocation rule the equal split rule and another rule that arises naturally from bargaining of the players

networks versus vertical integration we construct a theory to compare vertically integrated firms to networks of manufacturers and suppliers vertically integrated firms make their own specialized inputs in networks manufacturers procure specialized inputs from suppliers that in turn sell to several manufacturers the analysis shows that networks can yield greater social welfare when manufacturers experience large idiosyncratic demand shocks individual firms may also have the incentive to form networks despite the lack of long term contracts the analysis is supported by existing evidence and provides predictions as to the shape of different industries

seasonality and the valuation of commodity options price movements in many commodity markets exhibit significant seasonal patterns however given an observed futures price a deterministic seasonal component at the price level is not relevant for the pricing of commodity options in contrast this is not true for the seasonal pattern observed in the volatility of the commodity price analyzing an extensive sample of soybean corn heating oil and natural gas options we find that seasonality in volatility is an important aspect to consider when valuing these contracts the inclusion of an appropriate seasonality adjustment significantly reduces pricing errors in these markets and yields more improvement in valuation accuracy than increasing the number of stochastic factors

price discrimination and equilibrium in monopolistic competition modern theories of monopolistic competition have borrowed extensively from techniques developed in location theory and the theory of spatial pricing the monopolistically competitive firm is assumed to choose a location and price for its product a subject that has been of increasing concern in this corpus of theory is that there exists no free entry price location equilibrium in this paper we demonstrate that free entry price location equilibrium exists provided only that producers are allowed to price discriminate among customers in a reasonable manner equilibrium is modelled as a two stage game using the selten concept of subgame perfect nash equilibrium it is shown that the equilibrium discriminatory price system is one initially identified by hoover in addition we show that equilibrium is not unique the precise nature of equilibrium in a particular market will be dependent upon the history of that market

volatility and price jumps in agricultural futures prices evidence from wheat options revised version published in american journal of agricultural economics vol 86 number 4 november 2004 1018 1031

the relation between forward prices and futures prices abstract this paper consolidates the results of some recent work on the relation between forward prices and futures prices it develops a number of propositions characterizing the two prices these propositions contain several testable implications about the difference between forward and futures prices many of the propositions show that equilibrium forward and futures prices are equal to the values of particular assets even though they are not in themselves asset prices the paper then illustrates these results in the context of two valuation models and discusses the effects of taxes and other institutional factors

incomplete contracts specific investments and risk sharing an optimal contract design problem is considered contracts which are incomplete and simple are used to investigate the extent to which constrained revisions can mitigate inefficiencies resulting from contractual incompleteness an optimal contract is characterized in two cases first when a contract is being used to facilitate trade between two risk neutral parties who must make relationship specific investments it is possible to implement the first best by a simple contract second when a contract is being used to share risk it is generally not possible to implement the first best when one party is risk neutral however it is possible to implement the first best by assigning all the ex post decision rights to that party

filtering and forecasting commodity futures prices under an hmm framework abstract we propose a model for the evolution of arbitrage free futures prices under a regime switching framework the estimation of model parameters is carried out using the hidden markov filtering algorithms comprehensive numerical experiments on real financial market data are provided to illustrate the effectiveness of our algorithm in particular the model is calibrated with data from heating oil futures and its forecasting performance as well as statistical validity is investigated the proposed model is parsimonious self calibrating and can be very useful in predicting futures prices

free trade networks abstract the paper examines the formation of free trade agreements ftas as a network formation game we consider an n country model in which possibly asymmetric countries trade differentiated industrial commodities we show that if all countries are symmetric the complete fta network is pairwise stable and it is the unique stable network if industrial commodities are not highly substitutable we also compare ftas and customs unions cus as to which of these two regimes facilitates global trade liberalization noticing that unlike cus each signatory of an fta can have another fta without consent of other member countries

the dynamics of convenience and the brazilian soybean boom u s and brazilian soybeans are harvested on an alternating semiannual cycle that generates predictable dynamic behavior in the soybean futures market because corn and soybeans are storage substitutes their physical storage costs move together and can be isolated separately from crop specific marginal convenience yields along the futures price profile the kaldor working convenience yield hypothesis is tested for the international soybean market and storage risk is measured

anticompetitive vertical integration by a dominant firm backward vertical integration by a dominant firm into an upstream competitive industry causes both input and output prices to rise the dominant firm s advantage may or may not offset the negative effect of higher prices on social welfare whether it does depends on a simple indicator derived from input and output market shares and the degree of prior vertical integration a vertical merger is similar to a hypothetical horizontal merger suggesting that vertical merger policy for this industry should be similar to horizontal merger policy the dominant firm model yields an observable sufficient indicator of welfare improving vertical mergers copyright 1998 by american economic association

a two factor cointegrated commodity price model with an application to spread option pricing in this paper we propose an easy to use yet comprehensive model for a system of cointegrated commodity prices while retaining the exponential affine structure of previous approaches our model allows for an arbitrary number of cointegration relationships we show that the cointegration component allows capturing well known features of commodity prices i e upward sloping contango and downward sloping backwardation term structures smaller volatilities for longer maturities and an upward sloping correlation term structure the model is calibrated to futures price data of ten commodities the results provide compelling evidence of cointegration in the data implications for the prices of futures and options written on common commodity spreads e g spark spread and crack spread are thoroughly investigated