rationality of preliminary money stock estimates earlier studies have presented mixed evidence on the rationality of the federal reserve s preliminary money stock estimates the authors investigate the rationality of m1a m1 m2 and m3 for both seasonally and not seasonally adjusted data they find preliminary growth rates of these aggregates to be rational for not seasonally adjusted data but irrational when data are seasonally adjusted using monte carlo studies the authors conclude that irrationality in seasonally adjusted data arises from the specific seasonal adjustment procedure used by the federal reserve as a result researchers conducting similar tests may want to focus exclusively on not seasonally adjusted data copyright 1995 by mit press

an analysis of revisions to the industrial production index revisions to percentage changes in the total index of industrial production ip contain systematic components and are correlated with other information available at the time the provisional estimates are prepared indicating that the preliminary estimates are inefficient in particular revisions to percentage changes in ip i tend to be upward ii contain substantial seasonality iii generally increasse during periods in which ip is accelerating and iv revisions to the same month tend to be in the same direction filters for the provisional estimates that exploit these inefficiencies are estimated and the estimates generated from these filters pass the efficiencies are estimated and the estimates generated from these filters pass the efficiency test

option pricing when the variance changes randomly theory estimation and an application in this paper we examine the pricing of european call options on stocks that have vari ance rates that change randomly we study continuous time diffusion processes for the stock return and the standard deviation parameter and we find that one must use the stock and two options to form a riskless hedge the riskless hedge does not lead to a unique option pricing function because the random standard deviation is not a traded security one must appeal to an equilibrium asset pricing model to derive a unique option pricing function in general the option price depends on the risk premium associated with the random standard deviation we find that the problem can be simplified by assuming that volatility risk can be diversified away and that changes in volatility are uncorrelated with the stock return the resulting solution is an integral ofthe black scholes formula and the distribution function for the variance of the stock price we show that accurate option prices can be computed via monte carlo simulations and we apply the model to a set of actual prices

technical efficiency and scope economies in hospitals the main purposes are to develop a method for measuring the economies of scope which involves the use of non parametric production frontiers and does not require information on input prices and to apply this method to individual hospital data drawn from a sample of spanish hospitals the results confirm the presence of technical inefficiencies and also of potential and non exploited economies of scope the combination that produces most economies of scope is that of gynaecology and paediatrics

the pricing of options on assets with stochastic volatilities one option pricing problem that has hitherto been unsolved is the pricing of a european call on an asset that has a stochastic volatility this paper examines this problem the option price is determined in series form for the case in which the stochastic volatility is independent of the stock price numerical solutions are also produced for the case in which the volatility is correlated with the stock price it is found that the black scholes price frequently overprices options and that the degree of overpricing increases with the time to maturity one option pricing problem that has hitherto remained unsolved is the pricing of a european call on a stock that has a stochastic volatility from the work of merton 12 garman 6 and cox ingersoll and ross 3 the differential equation that the option must satisfy is known the solution of this differential equation is independent of risk preferences if a the volatility is a traded asset or b the volatility is uncorrelated with aggregate consumption if either of these conditions holds the risk neutral valuation arguments of cox and ross 4 can be used in a straightfoward way this paper produces a solution in series form for the situation in which the stock price is instantaneously uncorrelated with the volatility we do not assume that the volatility is a traded asset also a constant correlation between the instantaneous rate of change of the volatility and the rate of change of aggregate consumption can be accommodated the option price is lower than the blackscholes b s 1 price when the option is close to being at the money and higher when it is deep in or deep out of the money the exercise prices for which overpricing by b s takes place are within about ten percent of the security price this is the range of exercise prices over which most option trading takes place so we may in general expect the b s price to overprice options this effect is exaggerated as the time to maturity increases one of the most surprising implications of this is that if the b s equation is used to determine the implied volatility of a near the money option the longer the time to maturity the lower the implied volatility numerical solutions for the case in which the volatility is correlated with the stock price are also examined the stochastic volatility problem has been examined by merton 13 geske 7 johnson 10 johnson and shanno 11 eisenberg 5 wiggins 16 and

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

do government agencies use public data the case of gnp in 1991 the u s council of economic advisers undertook an initiative to increase the quality of economic statistics one specific objective was to reduce the size of revisions in gnp estimates we present evidence that one straightforward and inexpensive way of forwarding this objective is for the department of commerce to utilize better publicly available information released by other governmental agencies an important caveat however applies the relationship appears to be non linear specifically the inefficient use of information is concentrated in those quarters where the change in the preliminary gnp estimate is large in absolute value

what do market calibrated stochastic processes indicate about the long term price of crude oil abstract stochastic process models of commodity prices are important inputs in energy investment evaluation and planning problems in this paper we focus on modeling and forecasting the long term price level since it is the dominant factor in many such applications to provide a foundation for our modeling approach we first evaluate the empirical characteristics of crude oil price data from 1990 to 2013 using unit root and variance ratio tests statistical evidence from these tests shows only weak support for the applicability of stationary mean reverting type processes up through 2004 with non stationary brownian motion type processes becoming more plausible when the data from 2005 to 2013 is added we then apply a kalman filtering method with maximum likelihood approach to estimate the model parameters for both a single factor geometric brownian motion gbm process as well as the two factor schwartz and smith 2000 process the latter process decomposes the spot price into unobservable factors for the long term equilibrium level and short term deviation and it accommodates aspects of both a gbm process and a mean reverting process both empirical and simulated data are analyzed with these models and we quantify the increases in both the drift rate and volatility of these processes that result from developments in the crude oil markets since the middle of the last decade we conclude by comparing and contrasting both historical accuracy and forecasts from the parameterized models and show that when the emphasis is on the long term expectations a single factor gbm forecast may be sufficient

bond pricing and the term structure of interest rates a new methodology for contingent claims valuation this paper presents a unifying theory for valuing contingent claims under a stochastic term structure of interest rates the methodology based on the equivalent martingale measure technique takes as given an initial forward rate curve and a family of potential stochastic processee for its subsequent movements a no arbitrage condition restricts this family of processes yielding valuation formulae for interest rate sensitive contingent claims which do not explicitly depend on the market prices of risk examples are provided to illustrate the key results in relation to the term structure of interest rates arbitrage pricing theory has two purposes the first is to price all zero coupon default free bonds of varying maturities from a finite number of economic fundamentals called state variables the second is to price all interest rate sensitive contingent claims taking as given the prices of the zero coupon bonds this paper presents a general theory and a unifying framework for understanding arbitrage pricing theory in this context of which all existing arbitrage pricing models are special cases in particular vasicek 1977 brennan and schwartz 1979 langetieg 1980 ball and torous 1983 ho and lee 1986 schaefer and schwartz 1987 and artzner and delbaen 1988 the primary contribution of this paper however is a new methodology for solving the second problem i e the pricing of interest rate sensitive contingent claims given the prices of all zero coupon bonds the methodology is new because i it imposes its stochastic structure directly on the evolution of the forward rate curve ii it does not require an inversion of the term structure to eliminate the market prices of risk from contingent claim values and iii it has a stochastic spot rate process with multiple stochastic factors influencing the term structure the model can be used to consistently price and hedge all contingent claims american or european on the term structure and it is derived from necessary and more importantly sufficient conditions for the absence of arbitrage the arbitrage pricing models of vasicek 1977 brennan and schwartz 1979 langetieg 1980 and artzner and delbaen 1988 all require an iformerly titled bond pricing and the term structure of interest rates a new methodology

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

risk premia and seasonality in commodity futures we develop and estimate a multifactor a ne model of commodity futures that allows for stochastic variations in seasonality we show conditions under which the yield curve and the cost of carry curve adopt augmented nelson and siegel functional forms this restricted version of the model is parsimonious does not suer from identi cation problems and matches well the yield curve and futures curve over time we estimate the model using heating oil futures prices over the period 1984 2012 we nd strong evidence of stochastic seasonality in the data we analyze risk premia in futures markets and discuss two traditional theories of commodity futures the theory of storage and the theory of normal backwardation the data strongly support the theory of storage

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

geometric brownian motion and structural breaks in oil prices a quantitative analysis the purpose of this paper is to present a quantitative analyses of oil price s path we try to argue that despite its parsimony and simplicity geometric brownian motion can perform well as a proxy for the movement of oil prices and for a state variable to evaluate oil deposits we base our argument on evidences of very low speed of mean reverting or long half life since unit root tests only can reject its null hypothesis in a sample longer than 100 years on the other hand we reject the null hypothesis of unit root with two endogenous breaks showing that the usual rejection can be attributed to omitted structural breaks we conclude that the average half life of oil price between 4 and 8 years depending on the model chosen is long enough to allow a good approximation as a geometric brownian motion

economies of diversification a generalization and decomposition of economies of scope abstract the paper investigates the benefits of diversification for a multi product firm it examines economies of diversification reflecting the cost reduction associated with producing outputs in an integrated firm compared to specialized firms the analysis applies under complete specialization as well as partial specialization when firms are not fully specialized and or when the specialization scheme does not cover all outputs it decomposes economies of diversification into four additive parts a part measuring complementarity among outputs a part reflecting economies of scale a part reflecting convexity and a part reflecting the role of fixed cost this new decomposition appears useful in investigating how scale effects complementarity effects and convexity effects can contribute to economies of scope in a multiproduct firm and helps generate valuable insights into the economics of specialization for multiproduct firms

value of an option to purchase electric power the case of uncertain consumption abstract large manufacturers and corporations often purchase options on power to protect themselves against unanticipated price increases this paper analyzes the impact of uncertainty in power consumption by a corporation on the value of an option to purchase electric power because there is no economically viable method to store power these options are exercised to satisfy immediate consumption needs only the amount exercised may differ from the maximum amount contracted which in turn alters the payoffs that accrue to the option contract we apply a monte carlo methodology to show that consumption uncertainty may substantively lower the price of an option contract under different conditions

an intertemporal general equilibrium model of asset prices this paper develops a continuous time general equilibrium model of a simple but complete economy and uses it to examine the behavior of asset prices in this model asset prices and their stochastic properties are determined endogenously one principal result is a partial differential equation which asset prices must satisfy the solution of this equation gives the equilibrium price of any asset in terms of the underlying real variables in the economy in this paper we develop a general equilibrium asset pricing model for use in applied research an important feature of the model is its integration of real and financial markets among other things the model endogenously determines the stochastic process followed by the equilibrium price of any financial asset and shows how this process depends on the underlying real variables the model is fully consistent with rational expectations and maximizing behavior on the part of all agents our framework is general enough to include many of the fundamental forces affecting asset markets yet it is tractable enough to be specialized easily to produce specific testable results furthermore the model can be extended in a number of straightforward ways consequently it is well suited to a wide variety of applications for example in a companion paper cox ingersoll and ross 7 we use the model to develop a theory of the term structure of interest rates many studies have been concerned with various aspects of asset pricing under uncertainty the most relevant to our work are the important papers on intertemporal asset pricing by merton 19 and lucas 16 working in a continuous time framework merton derives a relationship among the equilibrium expected rates of return on assets he shows that when investment opportunities are changing randomly over time this relationship will include effects which have no analogue in a static one period model lucas considers an economy with homogeneous individuals and a single consumption good which is produced by a number of processes the random output of these processes is exogenously determined and perishable assets are defined as claims to all or a part of the output of a process and the equilibrium determines the asset prices our theory draws on some elements of both of these papers like merton we formulate our model in continuous time and make full use of the analytical tractability that this affords the economic structure of our model is somewhat similar to that of lucas however we include both endogenous production and

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

the effect of uncertainty on investment evidence from texas oil drilling this paper estimates the response of investment to changes in uncertainty using data on oil drilling in texas and the expected volatility of the future price of oil using a dynamic model of firms investment problem i find that i the response of drilling activity to changes in price volatility has a magnitude consistent with the optimal response prescribed by theory ii the cost of failing to respond to volatility shocks is economically significant and iii implied volatility data derived from futures options prices yields a better fit to firms investment behavior than backward looking volatility measures such as garch jel c58 d92 g13 g31 l71 q31 the real options literature beginning with marschak 1949 and arrow 1968 and developed in bernanke 1983 pindyck 1991 and dixit and pindyck 1994 explains how firms should make decisions about investments that involve sunk costs real options theory views such investments as options in that at any point in time a firm may choose to either invest immediately or delay and observe the evolution of the investment s payoff a key insight is that the option to delay has value when future states of the world with positive returns to investing and states with negative returns are both possible even holding the expected future return constant at its present level thus in the presence of irreversibility and uncertainty a naive investment timing rule proceed with an investment if its expected benefit even slightly exceeds its cost is suboptimal because it does not account for the value of continuing to hold the option instead firms should delay irreversible investments until a significant gap develops between the investments expected benefits and costs moreover as uncertainty increases real options theory tells us that the incentive to delay should grow stronger and the gap between the expected benefit and cost necessary to trigger investment should widen while real options theory therefore prescribes how firms should carry out irreversible investments in uncertain environments it is not empirically well known

a continuous time equilibrium model of forward prices and futures prices in a multigood economy abstract this paper is a theoretical investigation of equilibrium forward and futures prices we construct a rational expectations model in continuous time of a multigood identical consumer economy with constant stochastic returns to scale production using this model we find three main results first we find formulas for equilibrium forward futures discount bond commodity bond and commodity option prices second we show that a futures price is actually a forward price for the delivery of a random number of units of a good the random number is the return earned from continuous reinvestment in instantaneously riskless bonds until maturity of the futures contract third we find and interpret conditions under which normal backwardation or contango is found in forward or futures prices these conditions reflect the usefulness of forward and futures contracts as consumption hedges

on the stochastic properties of carbon futures prices pricing carbon is a central concern in environmental economics due to the worldwide importance of emissions trading schemes to regulate pollution this paper documents the presence of small and large jumps in the stochastic process of the co 2 futures price the large jumps have a discrete origin i e they can arise from various demand factors or institutional decisions on the tradable permits market contrary to the existing literature we show that the stochastic process of carbon futures prices does not contain a continuous component brownian motion the results are derived by using high frequency data in the activity signature function framework todorov and tauchen in j econom 154 125 138 2010 todorov and tauchen in j bus econ stat 29 356 371 2011 the implication is that the carbon futures price should be modeled as an appropriately sampled centered levy or poisson process the pure jump behavior of the carbon price might be explained by the lower volume of trades on this allowance market compared to other highly liquid financial markets

international money and stock market contingent claims abstract we develop a unified approach with closed form solutions for pricing bonds stocks currencies and their derivatives the specification assumes a fundamental risk factor represented by a stochastic positive definite matrix following a wishart autoregressive war process by assuming a volatility in mean specification for the domestic stock returns and the relative changes of exchange rates and a domestic stochastic discount factor exponential affine with respect to the fundamental risk it is possible to derive closed form solutions for the term structures of interest rates and for the risk neutral probabilities while keeping the flexibility of the model in particular i the domestic and foreign term structures are jointly affine and correspond to wishart quadratic term structures which can ensure the positivity of interest rates ii in this framework where the stock price follows a model with stochastic volatility we obtain explicit or quasi explicit formulas for futures and forward contracts swaps and options this extends results by heston 1993 and ball and roma 1994

modeling co2 emission allowance prices and derivatives evidence from the european trading scheme this paper studies the three main markets for emission allowances within the european union emissions trading scheme eu ets powernext nord pool and european climate exchange ecx the analysis suggests that the prohibition of banking of emission allowances between distinct phases of the eu ets has significant implications in terms of futures pricing motivated by these findings we develop an empirically and theoretically valid framework for the pricing and hedging of intra phase and inter phase futures and options on futures respectively

the crash of ʼ87 was it expected the evidence from options markets transactions prices of s p 500 futures options over 1985 1987 are examined for evidence of expectations prior to october 1987 of an impending stock market crash first it is shown that out of the money puts became unusually expensive during the year preceding the crash second a model is derived for pricing american options on jump diffusion processes with systematic jump risk the jump diffusion parameters implicit in options prices indicate that a crash was expected and that implicit distributions were negatively skewed during october 1986 to august 1987 both approaches indicate no strong crash fears during the 2 months immediately preceding the crash attempts to explain what caused the stock market crashes around the world in october 1987 have suffered from the paucity of major economic developments occurring around that time that could have triggered the crashes shifting expectations regarding monetary policy foreign investors fears of a dollar decline increasing riskiness of assets none of these appeared major enough if present at all to explain the magnitude of the crashes and although portfolio insurance strategies could conceivably magnify the effects of a jump in fundamentals the initiating jump in fundamentals appears to be lacking

nonconvex costs and the behavior of inventories this paper explores one possible explanation for the apparent excess volatility of production relative to sales nonconvexities in the technology facing firms it is shown that if firms operate in a region of declining marginal costs then small shifts in demand can cause production to jump substantially estimates for six production to stock industries as well as the automobile industry suggest that all these industries behave as if they were operating in the region of nonconvex costs the results have important implications not only for inventory investment but also for the cyclical behavior of productivity and prices

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

how informative are preliminary announcements of the money stock in canada the authors examine hypotheses about the relation between provisional estimates and final values of m1 m2 and m3 and their growth rates in canada using monthly data and multiple revisions preliminary values cannot be viewed as final values plus an error revision uncorrelated with these but they are approximately unbiased forecasts of final values the second difference in short term interest rates is a leading indicator of revisions in m1 growth rates and revisions exhibit significant seasonality hence preliminary values are not completely rational forecasts

humps in the volatility structure of the crude oil futures market new evidence abstract this paper analyses the volatility structure of commodity derivatives markets the model encompasses hump shaped unspanned stochastic volatility which entails a finite dimensional affine model for the commodity futures curve and quasi analytical prices for options on commodity futures using an extensive database of crude oil futures and futures options spanning 21 years we find the presence of hump shaped partially spanned stochastic volatility in the crude oil market the hump shaped feature is more pronounced when the market is more volatile and delivers better pricing as well as hedging performance under various dynamic factor hedging schemes

measuring and decomposing economies of diversification an application to biogas fuelled cogeneration plants in austria abstract this paper investigates the existence and the degree of economies of diversification for small scaled renewable fuelled cogeneration systems using 2014 cross sectional data from 67 austrian biogas plants it is the first study applying the recently introduced concept of economies of diversification proposed by chavas and kim 2010 which is a generalization and decomposition of economies of scope economies of diversification are decomposed into three additive parts a part measuring complementarity among outputs a part reflecting economies of scale a part reflecting convexity in addition this paper extends the decomposition introduced by chavas and kim 2010 in such a way that the contribution of each input to economies of diversification and its components can be investigated the results indicate substantial cost savings from diversification for very small scaled plants 100 kwel most of the cost savings come from scale economies for larger plants 250 kwel positive complementarity and convexity effects are the main source of economies of diversification and outweigh the negative effect from scale diseconomies in addition to substantial fuel feedstock cost reductions significant costs saving effects from the jointness in labour and other inputs positively contribute to the complementarity effect while on average capital and labour costs positively contribute to economies of scale feedstock costs work in the direction of diseconomies of scale

petroleum spreads and the term structure of futures prices we employ the term structure of gasoline and heating oil prices proxied by convenience yields to explain the variation in the spread between the prices of gasoline and crude oil and the prices of heating oil and crude oil we demonstrate that the marginal convenience yields in the gasoline and heating oil markets explained much of the variation in the spreads between 1986 and 1999 the evidence indicates the importance of a disaggregated treatment of the term structure of prices the convenience yield is found to explain a substantially higher amount of the variation in the spread when it is decomposed by maturity even after controls for seasonality and inventory levels are implemented these findings support the notion that the futures term structure contains information beyond what can be garnered via obvious or easily available proxies of current supply and demand the findings are also supported in an alternate specification that tests for the origins of information spillover leadership between t

time irreversibility and business cycle asymmetry the problem of business cycle symmetry is addressed within the context of time reversibility to this effect the authors introduce a time domain test of time reversibility the tr test in an application they show that time irreversibility is the rule rather than the exception for two well known representative macroeconomic data sets this shows that many components of the business cycle have asymmetric fluctuations the characterization of asymmetry provided by the tr test shows that many series exhibit steepness asymmetry a few series appear to be either deep or sharp copyright 1996 by ohio state university press

measurement of hospital efficiency using a latent class stochastic frontier model this article analyses the technical efficiency of portuguese hospitals from 1997 to 2008 with the latent class frontier model enabling the identification of different segments in the cost frontier it is found that there are three statistically significant segments in the sample leading to the conclusion that no common health policy can be applicable to all the hospitals analysed calling rather for policies conceived for each hospital segment identified the health policy based in the identified segments enables a more accurate and cost effective management of resources

money prices interest rates and the business cycle the mechanisms governing the relationship of money prices and interest rates to the business cycle are the most studied and most disputed topics in macroeconomics in this paper we first document key empirical aspects of this relationship we then ask how well three benchmark rational expectations macroeconomic models a real business cycle model a sticky price model and a liquidity effect model account for these central facts while the models have diverse successses and failures none can account for the fact that real and nom inal interest rates are inverted leading indicators of real economic activity that is none of the models captures the post war u s business cycle fact that a high real or nominal interest rate in the current quarter predicts a low level of real economic activity two to four quarters in the future i introduction the positive correlation of monetary aggregates and real economic activity over the course of many business cycles is a key empirical fact about the u s economy indeed the dynamic dimension of this covariation is so strong and stable that a monetary variable has long been included in the commerce department s index of leading economic indica tors while this pattern of cyclical comovement is widely agreed upon its interpretation is not some macroeconomists view money as purely passive with a positive response to varying levels of economic activity producing the positive correlation others view changes in the quantity of money as an important perhaps dominant source of economic fluctua tions frequently the real effects of monetary changes are suggested to arise from frictions in commodity labor or financial markets in economic theories that describe the influence of these frictions the transmission mechanism from monetary changes to real activity is typically viewed as involving interest rates and the price level the primary goal of this paper is to evaluate three models that explain the link between money prices interest rates and the business cycle we do this in three steps first we docu ment the cyclical behavior of these variables in the united states over the postwar period second we construct three quantitative rational expectations models of macroeconomic activity i a real business cycle model with endogenous money ii a model of commodity market frictions with mon etary non neutralities arising from gradual adjustment of goods prices and iii a model of financial market frictions with monetary non neutralities arising from gradual adjust ments of portfolios finally we compare the models predic tion for the business cycle behavior of money prices and interest rates with the data in exploring the predictions of these models we take the stock of money to be one of several exogenous variables in the system all of our models are capable of generating a forecasting role for money relative to real economic activity similar to that found in the u s data in the real business model monetary changes can forecast real activity because productivity is related to many underlying sources of shocks and because these real shocks also affect the money stock in the models with sticky prices and liquidity effects short hand names for the models with frictions in the com modity and financial markets monetary changes have an additional direct positive effect on aggregate output the outline of the paper is as follows section ii describes the data and documents its business cycle characteristics section iii outlines the three macroeconomic models and develops the particular quantitative versions of the models used in our analysis our main empirical results are pre sented in section iv and section v summarizes our results and concludes

dynamic speculation and hedging in commodity futures markets with a stochastic convenience yield the main objective of this paper is to address in an a continuous time framework the issue of using storable commodity futures as vehicles for hedging purposes when in particular the convenience yield as well as the market prices of risk evolve randomly over time following the martingale route and by operating a suitable constant relative risk aversion utility function crra specific change of numeraire we solve the investor s dynamic optimization program to obtain quasi analytical solutions for optimal demands which can be expressed in terms of two discount bonds traded and synthetic contrary to the existing literature we explicitly derive the individual optimal proportions invested in the spot commodity in a discount bond and in the futures contracts which can be computed in a simple recursive way we suggest various decompositions allowing an investor to assess the sensitivity of the optimal demands to the state variables and to specify the role played by each risky asset empirical evidence shows that the convenience yield has a strong impact on the speculation and hedging positions and the interaction among time varying risk premia determines the magnitude and the sign of these positions

exotic options for interruptible electricity supply contracts this paper presents the design and pricing of financial contracts for the supply and procurement of interruptible electricity service while the contract forms and pricing methodology have broader applications the focus of this work is on electricity market applications which motivate the contract structures and price process assumptions in particular we propose a new contract form that bundles simple forwards with exotic call options that have two exercise points with different strike prices such options allow hedging and valuation of supply curtailment risk while explicitly accounting for the notification lead time before curtailment the proposed instruments are priced under the traditional gbm price process assumption and under the more realistic assumption for electricity markets of a mean reverting price process with jumps the latter results employ state of the art fourier transforms techniques

no arbitrage conditions for storable commodities and the modeling of futures term structures abstract one distinguishable feature of storable commodities is that they relate to two markets cash market and storage market this paper proves that if no arbitrage exists in the storage cash dual markets the commodity convenience yield has to be non negative however classical reduced form models for futures term structures could allow serious arbitrages due to the high volatility of the convenience yield to avoid negative convenience yield this paper proposes a semi affine arbitrage free model which prices futures analytically and fits futures term structures reasonably well importantly our model prices commodity related contingent claims such as calendar spread options quite differently with classical models

are statistical reporting agencies getting it right data rationality and business cycle asymmetry this article provides new evidence on the rationality of early releases of industrial production ip and producer price index ppi data rather than following the usual practice of examining only first available and fully revised data we examine the entire revision history for each variable thus we are able to assess for example whether earlier releases of data are in any sense less rational than later releases and when data become rational our findings suggest that seasonally unadjusted ip and ppi become rational after approximately 3 4 months whereas seasonally adjusted versions of these series remain irrational for at least 6 12 months after initial release for all variables examined we find evidence that the remaining revision is predictable from its own past or from publicly available information in other economic and financial variables in addition we find a clear increase in the volatility of revisions during recessions suggesting that early data releases are less reliable in toughe

pricing of options on commodity futures with stochastic term structures of convenience yields and interest rates we develop a model to value options on commodity futures in the presence of stochastic interest rates as well as stochastic convenience yields in the development of the model we distinguish between forward and future convenience yields a distinction that has not been recognized in the literature assuming normality of continuously compounded forward interest rates and convenience yields and log normality of the spot price of the underlying commodity we obtain closed form solutions generalizing the black scholes merton s formulas we provide numerical examples with realistic parameter values showing that both the effect of introducing stochastic convenience yields into the model and the effect of having a short time lag between the maturity of a european call option and the underlying futures contract have significant impact on the option prices

the stochastic seasonal behavior of energy commodity convenience yields abstract this paper contributes to the commodity pricing literature by consistently modeling the convenience yield with its empirically observed properties specifically in this paper we show how a four factor model for the stochastic behavior of commodity prices with two long and short term factors and two additional seasonal factors may accommodate some of the most important empirically observed characteristics of commodity convenience yields such as the mean reversion and stochastic seasonality based on this evidence a theoretical model is presented and estimated to characterize the commodity convenience yield dynamics that are consistent with previous findings we also show that commodity price seasonality is better estimated through convenience yields than through futures prices

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

a multifactor stochastic volatility model of commodity prices we propose a novel representation of commodity spot prices in which the cost of carry and the spot price volatility are both driven by an arbitrary number of risk factors nesting many existing specifications the model exhibits unspanned stochastic volatility provides simple closed form expressions of commodity futures and yields analytic formulas of european options on futures we estimate the model using oil futures and options data and find that the pricing of traded contracts is accurate for a wide range of maturities and strike prices the results suggest that at least three risk factors in the spot price volatility are needed to accurately fit the volatility surface of options on oil futures highlighting the importance of using general multifactor models in pricing commodity contingent claims

price mean reversion seasonality and options markets options on agricultural commodities with maturities exceeding one year seldom trade one possible reason to explain this lack of trading is that we do not have an accurate option pricing model for products where mean reversion in spot price levels can be expected standard option pricing models assume proportionality between price variance and time to maturity this proportionality is not a valid assumption for commodities whose supply response brings prices back to production costs the model proposed here incorporates mean reversion in spot price levels and includes a correction for seasonality mean reversion and seasonality are both observed in the soybean market the empirical analysis lends strong support to the model

estimating economies of scope and scale under price risk and risk aversion this study uses duality to examine the effects of excluding output price risk and risk aversion on cost structures using data for kansas wheat and beef cow operations a dual risk model was used to determine multi product and product specific scale economies and economies of scope estimates for these measures were compared with those obtained from a deterministic model the results show that product specific scale economies are over estimated and economies of scope and multi product scale economies are under estimated for the deterministic model compared to the risk model

testing the rationality of price forecasts new evidence from panel data this paper tests the rationality of individual price forecasts in a panel of professional forecasters here unlike in most previous studies rationality is not rejected the results here differ because 1 using individual forecasts avoids aggregation bias 2 comparison of forecasts to initial data avoids bias due to data revision 3 the professional forecasters have economic incentives to state their expectations accurately and 4 a new covariance matrix estimator consistent when forecast errors are correlated across individuals is used copyright 1990 by american economic association

pricing of long dated commodity derivatives do stochastic interest rates matter abstract does modelling stochastic interest rates beyond stochastic volatility improve pricing performance on long dated commodity derivatives to answer this question we consider futures price models for commodity derivatives that allow for stochastic volatility and stochastic interest rates and a correlation structure between the underlying variables we examine the empirical pricing performance of these models on pricing long dated crude oil derivatives estimating the model parameters from historical crude oil futures prices and option prices we find that stochastic interest rate models improve pricing performance on long dated crude oil derivatives when the interest rate volatility is relatively high furthermore increasing the model dimensionality does not tend to improve the pricing performance on long dated crude oil option prices but it matters for long dated futures prices we also find empirical evidence for a negative correlation between crude oil futures prices and interest rates that contributes to improving fit to long dated crude oil option prices

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

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

evaluating the oecd s forecasts for economic growth the size and nature of the errors in gdp forecasts in the g 7 countries from 1968 to 1995 are examined these gdp estimates are published by the organization for economic cooperation and development in oecd economic outlook two alternative hypotheses are tested concerning why revisions arise the first hypothesis is that preliminary announcement is simply the true variable measured with error in this case the preliminary announcement is an unconditionally unbiased but irrational forecast of the true value that is the revision is correlated with known variables in particular it is correlated with the preliminary announcement itself the second hypothesis is that revisions arise because the early gdp estimates are a rational forecast of the true variable in this case the error is a rational forecast error and is therefore uncorrelated with known information

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

a jump diffusion model for pricing and hedging with margined options an application to brent crude oil contracts abstract we develop a jump diffusion model for pricing and hedging with margined options on futures unlike a standard equity option margined options require no up front payment an attractive feature of margined options is that there is no early exercise premiums under general assumptions model parameter estimates and out of sample pricing errors are calculated using data on brent crude contracts using the same pricing technology we also hedge equity style options with margined options hedging coefficients are derived by matching an extended set of greeks we find that a target equity option can be effectively hedged using a portfolio of two margined options and the underlying as has been reported elsewhere a delta hedge is inappropriate when the underlying is a jump diffusion

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

pricing rainfall futures at the cme abstract many business people such as farmers and financial investors are affected by indirect losses caused by scarce or abundant rainfall because of the high potential of insuring rainfall risk the chicago mercantile exchange cme began trading rainfall derivatives in 2011 compared to temperature derivatives however pricing rainfall derivatives is more difficult in this article we propose to model rainfall indices via a flexible type of distribution namely the normal inverse gaussian distribution which captures asymmetries and heavy tail behaviour the prices of rainfall futures are computed by employing the esscher transform a well known tool in actuarial science this approach is flexible enough to price any rainfall contract and to adjust theoretical prices to market prices by using the calibrated market price of risk the empirical analysis is conducted with us precipitation data and cme futures data providing first results on the market price of risk for rainfall derivatives

news and noise in g 7 gdp announcements revisions to gdp announcements are known to be quite large in all g 7 countries quarterly growth rate revisions are regularly more than a full percentage point at an annualized rate we examine the predictability of these revisions using standard statistical tests of whether the preliminary announcement is a rational forecast of the subsequently revised data previous work suggests that u s gdp revisions are largely unpredictable as would be the case if the revisions reflect news not available at the time that the preliminary number is produced we find that the degree of predictability varies throughout the g 7 although we find little predictability in u s revisions the data revisions for several foreign countries are highly predictable we also perform a simple real time forecasting exercise showing that for several countries the predictability of data revision could be used to generate improved preliminary data

the valuation of options on futures contracts rational restrictions are derived for the values of american options on futures contracts for these options the optimal policy in general involves premature exercise a model is developed for valuing options on futures contracts in a constant interest rate setting despite the fact that premature exercise may be optimal the value of this american feature appears to be small and a european formula due to black serves as a useful approximation finally a model is developed to value these options in a world with stochastic interest rates it is shown that the pricing errors caused by ignoring the location of the interest rate relative to its long run mean range from 5 to 7 when the current rate is 200 basis points from its long run value the role of interest rate expectations is therefore crucial to the valuation optimal exercise policies are found from numerical methods for both models in recent years there has been a steady growth in the number of financial assets which one might properly call derivative assets that are available for trading on the organized exchanges among these the most recent and notable are options contracts written on available futures contracts options are now traded on the futures contracts on stock market indexes on the futures contracts on treasury instruments on the futures contracts on foreign exchange rates and on the futures contracts on some metals in design these options contracts do not differ substantially from the well known options contracts on common stock except that the underlying asset is a futures contract the received theory of the valuation of these options suggests that such contracts provide a direct vehicle for investors to alter the terminal payoffs on their portfolios to a desired distribution in the absence of these contracts investors would be forced to pursue a dynamic portfolio policy at the expense of considerable transactions in order to achieve a similar distribution indeed the availability of put options on the futures contracts on stock market indexes now enables well diversified investors to purchase portfolio insurance in his seminal work black 1 provided a complete description of forward and futures contracts as well as the description and valuation of european options on forward contracts and on spot commodities breeden 3 has examined the use of commodity options in a theoretical framework and courtadon 6 has studied the valuation of options on treasury bond futures french 13 cox