Дисертації з теми "Commodity price dynamics"

Fluctuation in commodity prices is a significant and timely issue to be studied. My first chapter examines the impact of monetary policy and other macroeconomic shocks on the dynamics of agricultural commodity prices. The major contributions of this study are twofold. First, unlike other studies that use indexes, this study analyzes the commodities individually, affording the inclusion of commodity-specific fundamentals such as the level of inventory -- an important determinant of commodity price -- in a structural VAR framework. Second, it exploits a rich dataset of agricultural commodity prices which includes commodities that are usually overlooked in the literature, and extracts a common factor using the dynamic factor model to understand the extent of co-movement of the prices and to gauge the extent to which macroeconomic shocks drive the ‘co-movement’ in a factor-augmented VAR (FAVAR) framework. The findings show that monetary policy, global economic conditions and the US dollar exchange rates play an important role in the dynamics of agricultural commodity prices. My second chapter examines the role played by Wal-Mart in price convergence among US cities. Despite the fact that market structure is an important determinant of price convergence and that US retail architecture has been changed over the past two decades by the expansion of big box stores and supercenters, the role played by such rapidly-expanding ‘big-box’ chain-stores like Wal-Mart in price convergence is completely over-looked in the literature. The possible symmetry in costs and mark-up among Wal-Mart stores, and their influence over the city level prices motivate us to test if their presence helps price convergence among US cities. After controlling for distance, local costs such as wage and rent, and city and time specific fixed effects this study finds that prices are significantly closer in two cities if they have Wal-Mart than if none or only one of them has Wal-Mart. Though the results are mostly robust to the analysis using disaggregate price data and sub-samples, they are more pronounced for grocery items than non-grocery items, within high income cities than low income cities. Moreover, our regional analysis uncovers the regional variations in the effect of Wal-Mart on price convergence, and Wal-Mart’s more prominent role in inter-region rather than intra-region price convergence. Since the presence of Wal-Mart accelerates the rate of price convergence and thus reduces the potential for misallocation of resources, our results suggest that the existence of a positive welfare impact of Wal-Mart cannot be overruled. My third chapter uses county level data to see the effect of Wal-Mart on local economic activities and revenue in Florida. The OLS estimation shows that the presence of Wal-Mart significantly increases total retail sales and decreases sales tax rate, but have no significant effect on total taxable retail sales and total revenue from sales tax. The instrumental variable (IV) estimation shows that presence of Wal-Mart significantly decreases sales tax rate but has no significant effect on total retail sales, total taxable retail sales and total revenue from sales tax. Thus, according to our analysis, Wal-Mart does not necessarily increase local economic activities and tax revenue. However, interestingly, Wal-Mart is found to play an important role in decreasing local sales-tax rate.

This study first shows that a transactions costs band may exist in commodity spot and futures markets and spatially separated markets as a result of the arbitrage process. Then, by using a bivariate vector error correction model (VECM), this thesis shows that the null hypothesis of linearity can be rejected against the alternative of nonlinearity for both lumber spot and futures prices in U.S. and oriented strand board (OSB) prices across regions in North America. The nonlinearity is identified by a transition variable that governs switching between two regimes: one within the transactions cost band and one outside of the band. In the empirical analysis, a bivariate smooth transition vector error correction model (STVECM) is used to test market efficiency for lumber spot and futures prices and for the law of one price (LOP) as pertains to OSB prices across six regions in North America. Results support the market eficiency hypothesis and the LOP in the forest commdity markets. Furthermore, the empirical analysis suggests that when price differences surpass transactions costs by a large margin or are far away from the transactions band, a faster adjustment to the long run equilibrium is observed in part due to adjustment costs. When price differences are within the transactions band, they follow a random walk as no trade takes place. The in-sample analysis indicates that the STVECM model performs better than the linear VECM. Results from generalized impulse response functions (GIs) analysis show that system shocks may, in fact, change the time paths of prices permanently.

Questa tesi analizza prezzi di diverse tipologie di commodities, con lo scopo di capire se esiste un movimento comune tra le varie serie, e se questo è il risultato di determinanti comuni di breve periodo o deriva da delle dinamiche condivise di lungo periodo. Il lavoro è organizzato in tre capitoli. Il primo introduce l’argomento del movimento comune, focalizzandosi anche in una rassegna della letteratura sulle dinamiche dei prezzi delle commodities e proponendo un’analisi univariata di 38 serie storiche mensili di prezzi spot del database dell’IMF. Il secondo capitolo propone un modello in tre equazioni strutturali (consumo, produzione e stoccaggio), con l’aggiunta della condizione di equilibrio, in cui due fattori latenti responsabili per il co-movimento sono incorporati. L’equazione di prezzo in forma ridotta è poi stimata per 10 prezzi sfruttando la metodologia proposta nel terzo capitolo. Quest’ultimo sviluppa una nuova tecnica di stima per Dynamic Factor Models non stazionari e cointegrati con una decomposizione trend-ciclo; inoltre, la procedura è applicata alle 38 serie storiche presentate nel primo capitolo. Dai risultati emerge che mentre la componente ciclica è quasi irrilevante, la parte non stazionaria del co-movimento catturata dalla componente trend ha più peso. Dai fattori estratti è impossibile concludere con chiarezza se l’ipotesi di Prebish e Singer del trend decrescente dei prezzi delle commodities nel lungo periodo è stata surclassata da un’epoca di prezi crescenti dovuta alla maggiore scarsità delle risorse, con conseguente pressione della domanda sull’offerta.
This thesis concerns an analysis of commodity prices belonging to different categories, with the aim of understanding if there is room for a common movement among different price series, and if this co-movement is the result of short-run common drivers or it implies a long-run shared dynamic. The analysis is developed in three Chapters. Chapter 1 introduces the topic of co-movement, also focusing in reviewing other studies on commodity prices general dynamics and providing some univariate results by exploiting a set of 38 commodity spot monthly prices available from the IMF primary commodity database. Chapter 2 proposes a first attempt of modelling commodity markets by including latent factors responsible for co-movement. The model consists in three structural equations determining consumption, production and storage on a multi-commodity framework, plus a market clearing condition which allows to find the equilibrium price. The reduced form model is then estimated for a subset of 10 commodity prices by exploiting the methodology developed in Chapter 3, which contributes both to propose a new estimation procedure for non-stationary and cointegrated Dynamic Factor Models with a Trend Cycle decomposition and further exploits this methodology to empirically assess the co-movement of the 38 commodity prices considered in the firts Chapter. Results assess that whether the short-run common movement of commodity prices is rather marginal, the non-stationary Trend component has more weight. From the extraction of both stationary and non-stationary factors, neither the so called Prebish and Singer Hypothesis of declining commodity prices (with respect to manufactured good prices) nor a paradigm shift due to increasing resource scarcity and consequent higher demand pressure can be fully confirmed.

Supply and demand in the World oil market are balanced through responses to price movement with considerable complexity in the evolution of underlying supply-demand expectation process. In order to be able to understand the price balancing process, it is important to know the economic forces and the behavior of energy commodity spot price processes. The relationship between the different energy sources and its utility together with uncertainty also play a role in many important energy issues. The qualitative and quantitative behavior of energy commodities in which the trend in price of one commodity coincides with the trend in price of other commodities, have always raised the questions regarding their interactions. Moreover, if there is any interaction, then one would like to know the extent of influence on each other. In this work, we undertake the study to shed a light on the above highlighted processes and issues. The presented study systematically deals with the development of stochastic dynamic models and mathematical, statistical and computational analysis of energy commodity spot price and interaction processes. Below we list the main components of the research carried out in this dissertation. (1) Employing basic economic principles, interconnected deterministic and stochastic models of linear log-spot and expected log-spot price processes coupled with non-linear volatility process are initiated. (2) Closed form solutions of the models are analyzed. (3) Introducing a change of probability measure, a risk-neutral interconnected stochastic model is derived. (4) Furthermore, under the risk-neutral measure, expectation of the square of volatility is reduced to a continuous-time deterministic delay differential equation. (5) The by-product of this exhibits the hereditary effects on the mean-square volatility process. (6) Using a numerical scheme, a time-series model is developed and utilized to estimate the state and parameters of the dynamic model. In fact, the developed time-series model includes the extended GARCH model as special case. (7) Using the Henry Hub natural gas data set, the usefulness of the linear interconnected stochastic models is outlined. (8) Using natural and basic economic ideas, interconnected deterministic and stochastic models in (1) are extended to non-linear log-spot price, expected log-spot price and volatility processes. (9) The presented extended models are validated. (10) Closed form solution and risk-neutral models of (8) are outlined. (11) To exhibit the usefulness of the non-linear interconnected stochastic model, to increase the efficiency and to reduce the magnitude of error, it was essential to develop a modified version of extended Kalman filtering approach. The modified approach exhibits the reduction of magnitude of error. Furthermore, Henry Hub natural gas data set is used to show the advantages of the non-linear interconnected stochastic model. (12) Parameter and state estimation problems of continuous time non-linear stochastic dynamic process is motivated to initiate an alternative innovative approach. This led to introduce the concept of statistic processes, namely, local sample mean and sample variance. (13) Then it led to the development of an interconnected discrete-time dynamic system of local statistic processes and (14) its mathematical model. (15) This paved the way for developing an innovative approach referred as Local Lagged adapted Generalized Method of Moments (LLGMM). This approach exhibits the balance between model specification and model prescription of continuous time dynamic processes. (16) In addition, it motivated to initiate conceptual computational state and parameter estimation and simulation schemes that generates a mean square sub-optimal procedure. (17) The usefulness of this approach is illustrated by applying this technique to four energy commodity data sets, the U. S. Treasury Bill Yield Interest Rate and the U.S. Eurocurrency Exchange Rate data sets for state and parameter estimation problems. (18) Moreover, the forecasting and confidence-interval problems are also investigated. (19) The non-linear interconnected stochastic model (8) was further extended to multivariate interconnected energy commodities and sources with and without external random intervention processes. (20) Moreover, it was essential to extend the interconnected discrete-time dynamic system of local sample mean and variance processes to multivariate discrete-time dynamic system. (21) Extending the LLGMM approach in (15) to a multivariate interconnected stochastic dynamic model under intervention process, the parameters in the multivariate interconnected stochastic model are estimated. These estimated parameters help in analyzing the short term and long term relationship between the energy commodities. These developed results are applied to the Henry Hub natural gas, crude oil and coal data sets.

In the present analysis a nonlinear model is discussed in order to capture the presence of several forces acting in commodity markets and the difficulty to disentangle their relative price impacts. Global commodity markets have experienced significant price swings in recent years. Analysts offer two explanations: market forces and speculative expectations, not mutually exclusive. Commodity prices seem to indicate that various factors are acting in a very complex way. We start from one specific feature: price clustering phenomenon, which is the tendency to concentrate in a number of attraction regions, preferring some values over others. Commodities are in the process of becoming mainstream. The mean-reverting class of diffusion models are not able to model the phenomenon of multiple attraction regions. In the potential function approach the price is modelled as a diffusion process governed by a potential function. A fundamental step is to fit the multimodal density of the invariant distribution. We postulate a parametric form of the distribution in the framework of finite mixture models and Expectation-Maximization algorithm. The procedure for identifying and estimating potential function and diffusion parameter is provided. Applications to crude oil and soybean prices capture the essential characteristics of the data remarkably well. An underlying assumption is that potential function and long-term volatility do not change with time. New market conditions and new attraction regions can form, changing the shape of the potential and the magnitude of long-term volatility. We investigate changes in shape of the potential, which reflects new price equilibrium levels (attraction regions) and hence new market conditions. The model allows to generate copies of the observed price series with the same invariant distribution, useful for applications requiring a large number of independent price trajectories. A goodness-of-fit test for the SDE model is provided. A numerical implementation of the analysis is provided.

Energy markets feature a wide range of unusual price behaviour along with a complicated dependence structure between electricity, natural gas, coal and carbon, as well as other variables. We approach this broad modelling challenge by firstly developing a structural framework to modelling spot electricity prices, through an analysis of the underlying supply and demand factors which drive power prices, and the relationship between them. We propose a stochastic model for fuel prices, power demand and generation capacity availability, as well as a parametric form for the bid stack function which maps these price drivers to the spot electricity price. Based on the intuition of cost-related bids from generators, the model describes mathematically how different fuel prices drive different portions of the bid stack (i.e., the merit order) and hence influence power prices at varying levels of demand. Using actual bid data, we find high correlations between the movements of bids and the corresponding fuel prices (coal and gas). We fit the model to the PJM and New England markets in the US, and assess the performance of the model, in terms of capturing key properties of simulated price trajectories, as well as comparing the model’s forward prices with observed data. We then discuss various mathematical techniques (explicit solutions, approximations, simulations and other numerical techniques) for calibrating to observed fuel and electricity forward curves, as well as for pricing of various single and multi-commodity options. The model reveals that natural gas prices are historically the primary driver of power prices over long horizons in both markets, with shorter term dynamics driven also by fluctuations in demand and reserve margin. However, the framework developed in this thesis is very flexible and able to adapt to different markets or changing conditions, as well as capturing automatically the possibility of changes in the merit order of fuels. In particular, it allows us to begin to understand price movements in the recently-formed carbon emissions markets, which add a new level of complexity to energy price modelling. Thus, the bid stack model can be viewed as more than just an original and elegant new approach to spot electricity prices, but also a convenient and intuitive tool for understanding risks and pricing contracts in the global energy markets, an important, rapidly-growing and fascinating area of research.

Le secteur automobile est de plus en plus dépendant aux matières plastiques dont le niveau et la volatilité des prix ont fortement augmenté au cours des dix dernières années, sous l’effet supposé des variations du prix du pétrole qui est le principal input nécessaire à leur fabrication. La thèse vise à fournir des outils économétriques permettant d’analyser et gérer le risque de variations des prix des principales matières plastiques utilisées dans l’industrie automobile. À l’aide des méthodologies de cointégration, nous montrons que les relations d’équilibre de long terme et les dynamiques de court terme mettent en évidence un mécanisme de transmission des variations des coûts de production sur le prix des plastiques situés en aval du processus productif. L’existence de relations de cointégration significatives entre les prix pétrochimiques et pétroliers justifie l’élaboration de stratégies de couverture contre les variations des coûts de production et l’estimation de modèles à correction d’erreur qui permettent d’affiner les prévisions des prix
The automotive industry is increasingly dependent on plastic materials whose price level and volatility have risen sharply over the past decade due to the assumed effect of fluctuations in crude oil prices, which is the key feedstock in the production of final products such as plastics. This thesis aims to provide econometric tools to analyze, understand, and manage the risk of price volatility of major plastics materials consumed in the automotive industry. Using the cointegration methodology, we show that long-term equilibrium relationship and short-term dynamics reveal the transmission mechanism of input prices changes from the upstream market to the prices of plastics materials on the downstream market. The significant cointegration relationships between petrochemical and crude oil prices justify the development of hedging strategies against inputs prices fluctuation and the estimation of error correction models that should produce better prices forecast

In this study, we examine the dynamic link between returns and volatility of commodities and currency markets. Based on weekly data over the period from January 6, 1987 to July 22, 2014, we find the following empirical regularities. First, our results suggest that the information contents of gold, silver, platinum, and the CHF/USD and GBP/USD exchange rates can help improve forecast accuracy of returns and volatilities of palladium, crude oil and the EUR/CHF and GBP/USD exchange rates. Second, gold (CHF/USD) is the dominant commodity (currency) transmitter of return and volatility spillovers to the remaining assets in our model. Third, the analysis of dynamic spillovers shows time{ and event{specific patterns. For instance, the dynamic spillover effects originating in gold and silver (platinum) returns and volatility intensified (degraded) in the period marked by the global financial crisis. After the global financial crisis, the net transmitting role of gold and silver (platinum) returns shocks weakened (strengthened), while the net transmitting role of gold, silver and platinum volatility shocks remained relatively high. Overall, our findings reveal that, while the static analysis clearly classifies the aforementioned variables into net transmitters and net receivers, the dynamic analysis denotes episodes wherein the role of transmitters and receivers of return (volatility) spillovers can be interrupted or even reversed. Hence, even if certain commonalities prevail in each identified category of commodities, such commonalities are time - and event - dependent. (authors' abstract)

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Este trabalho analisa a importância dos fatores comuns na evolução recente dos preços dos metais no período entre 1995 e 2013. Para isso, estimam-se modelos cointegrados de VAR e também um modelo de fator dinâmico bayesiano. Dado o efeito da financeirização das commodities, DFM pode capturar efeitos dinâmicos comuns a todas as commodities. Além disso, os dados em painel são aplicados para usar toda a heterogeneidade entre as commodities durante o período de análise. Nossos resultados mostram que a taxa de juros, taxa efetiva do dólar americano e também os dados de consumo têm efeito permanente nos preços das commodities. Observa-se ainda a existência de um fator dinâmico comum significativo para a maioria dos preços das commodities metálicas, que tornou-se recentemente mais importante na evolução dos preços das commodities.
This study analyses the importance of common factors in metal prices movements for the period 1995-2013. For this purpose, cointegrated VAR models and also a Bayesian dynamic factor model are estimated. Given the effect of the financialization of commodities, DFM can capture dynamic effects common to all commodities. Furthermore, panel data is applied in order to use all heterogeneity between commodities over the period. Our estimation results show that interest rate, US dollar effective rate and also consumption data have permanent effect in the commodity prices. Also, there exists one common significant dynamic factor for most metal commodity prices and that this common factor has recently become increasingly important in driving commodity prices.

Introduction Commodity markets are distinct from other product markets due to the existence of forward sales and futures contracts. Forward selling and the trading of a commodity derivative implies prices are subject to the influence of economic agents who are not directly engaged in consumption or production of the commodity. As a result, even when the forces of supply and demand are in equilibrium, prices may still move and vary purely due to activities of agents operating in the futures markets. Inspired by this observation, the dissertation provides a new analysis of the role of futures markets trading on the dynamics of commodity prices over different time scales. Throughout the dissertation, the underlying economy can be conceived of as populated by a commodity producing firm with access to a stochastic production technology that yields new output of the commodity every time period. The firm also has access to a storage technology which it can use to hold inventory. The firm’s sales are made either in a spot market for cash or can be sold ahead of production for future delivery using a forward contract specifying the price and date of delivery to the holder or buyer. When such forward contracts are traded or exchanged in a centralized market, they become futures contracts. Stochastic production and consumption of the commodity implies that the firm faces a risk of losses from volatile prices. The firm would therefore like to sell forward as much of its output as it can. Those who buy the firm’s contract take on the risk of changing prices (are subject to loss) and demand a risk–premium as compensation for taking over the firm’s risk. In commodity markets, this risk premium is measured either as the basis, the contemporaneous difference between the current spot price and the forward price or the expected return, the difference between the expected future spot price and the forward price (Yang, 2013). These risk premiums depend on transaction costs incurred when trading futures in a commodity exchange (Hasbrouck, 2009) and will have an effect on the firms investments in physical production of the commodity – as it reflects the cost of hedging. Given that the risk premiums are a function of the transaction costs, quantifying the size of these costs has become an important endeavor in understanding of price dynamics. The first paper takes on this task by developing parametric models that can be used to measure liquidity costs using exchange traded futures transactions prices only. Simple dynamic linear regressions with switching are used in this task. The models treat underlying price processes and liquidity costs as unobserved components in state space systems with trade direction indicators of buyer and seller initiated transactions being the outcomes of hidden Markov processes. Simulation studies show that the model provides accurate effective transaction cost estimates and beats the tick-rule method of signing trades using prices. 1 Having developed a way to accurately measure the liquidity costs, focus turns to what is driving price changes observed at a high frequency tick-by-tick level. The second paper presents a new theory of history dependent price setting in limit order book market for commodity futures. In traditional financial markets theory, the price discovery process is a form of tâtonnement; informed agents trading against liquidity providers or market markers slowly reveals private information which is incorporated into prices. The marketmarkers adjust their quotations to reflect the information revealed by the informed agents transactions until a new equilibrium is attained. However, when trading contracts of physically delivered commodities, the transactions are directly informative of expected future supply and demand since they reflect production and consumption intentions. Transactions therefore have price impact: a buyer initiated trade tends to push prices upwards with the opposite effect following a seller initiated trade. The history dependent framework takes this hypothesis to the data and shows that agents trading in a limit order book market for commodity futures adjust their prices in response to order flow – the sequence of trade originator signs. Over long time periods, commodity price time series exhibit boom–bust cycles that may be accompanied by periods of either high or low volatility. One way to model time series subject to such boom and bust cycles is the hidden Markov or regime switching model popularized in economics by Hamilton (1990). The standard regime switching model assumes that the growth and volatility phases of a time series coincide and that autoregressive lag lengths are similar across regimes. This assumption results into biases in estimates of unconditional variances across different regimes. To overcome these problems, the third paper presents a new “Double Mixture Autoregressive” model for time series subject to potentially independent changes in level and volatility. This model allows for the autocorrelation structure of the data generating process to vary across variance regimes. By accounting for the change in the lag length of time series across the different volatility periods, more precise estimates of the unconditional moments are obtained. The model is applied to set of industrial commodity prices and is shown to accurately represent the boom–bust cycles and volatility switches that characterize the time series. The dissertation is divided into three related chapters/papers. The first chapter/paper, “New Open to Old Close: Signs and Spreads in Daily Prices” presents state space models that can be used to obtain accurate measures of transaction costs using daily summaries of trading activity: open, close, max and min prices. The second chapter/paper, “Price impact as reaction to order flow imbalance”, develops and successfully tests a theory of history dependent price formation in a limit order book market of commodity futures. Finally, the third chapter/paper, “A Double Mixture Autoregressive Model of Commodity Prices”, presents a new type of non-linear econometric model that captures the boom– bust cycles and volatility switches that characterize the long term behavior of commodity price time series. I now give compact overviews of each chapter, followed by a brief conclusion of how the works are all related. (I) New Open to Old Close: Signs and Spreads in Daily Prices This chapter shows how to estimate bid-ask spreads using observed transactions prices only. The main contribution of this chapter is to provide a method that almost always guarantees positive estimates of the transaction costs. Concretely, let pt = logPt be the log price of a commodity futures contract. The price follows: pt = mt + sqt , where mt is the unobserved efficient or fundamental price process, s ≥ 0 is the bid-ask spread and qt = ±1 is a trade initiator indicator: qt = +1 if a transaction is buyer initiated, −1 if seller initiated. The fundamental price follows the process mt = mt−1 +u m t where u m t is a zero-mean disturbance uncorrelated with qt . Bid and ask prices are: p Bid t = mt−1 + s and p Ask t = mt−1 − s which imply the pre-trade mid–prices are given by midt = 1 2 (p Bid t + p Ask t ) = mt−1 and bid–ask spreads are p Bid t − p Ask t = 2s. Log returns can be written as: ∆pt = s∆qt +u m t . If qt is observed, we have: sbMLE = Cov(∆pt ,∆qt) Var(∆qt) = s. But qt may not be observed or recorded in some datasets, e.g. open outcry markets. Assuming Prob(qt = +1) = Prob(qt = −1) = 1 2 , Roll (1984) estimated s by: sbRoll = p −Cov(∆pt ,∆pt−1). One major shortcoming of this estimator is that if the sample autocovariance is positive, then sbRoll is undefined. This had led to an active research area with alternatives to Roll’s estimator: Gibbs sampling approach of Hasbrouck (2002), a time consuming and difficult to implement method; Non-parametric estimators of Abdi and Ranaldo (2017), similar to Roll’s estimator: gives +ve autocovariances; and the empirical characteristic function of Chen, Linton and Yi (2017) which is useful but incomplete. We propose an alternative parametric estimator that is: easy and fast to implement, more informative: estimates mt , s and qt , and based on transaction prices only. We make the following assumptions: (i). transaction prices are generated by pt = mt + st qt , mt = mt−1 +u m t , qt = ±1, u m t ∼ N(0,σ 2 m) where {u m t ,qt } ∞ t=1 is a strictly stationary process; (ii). st is a random variable defined by st = s +u s t , where u s t ∼ N ¡ 0,σ 2 s ¢ with u s t ⊥ u m t ; (iii.) the trade initiator indicator is the outcome of a first order Markov process defined by the transition matrix: P = h pj k i where pj k = Prob(qt = k|qt−1 = j), for j,k = 1, 2 and qt = ±1 are transition probabilities. The price process pt = mt + st qt can be written in state space form as: yt ≡ ∆pt = mt − mt−1 + st qt − st−1qt−1 = At xt where xt = ³ mt ,mt−1,st ,st−1 ´0 is an unobserved state VAR(1) process: xt = φxt−1 + γs + ut , and At = h 1,−1,qt ,−qt−1 i is a measurement/observation matrix taking on 4 distinct values. At is a first order Markov process, inheriting properties of qt . The error vector ut = ¡ u m t , 0,u s t , 0¢0 is i.i.d N(0,Σu) where Σu is a (4×4) variance–covariance matrix with off–diagonal elements equal to zero and diagonal (σ 2 m, 0,σ 2 s , 0). To test the model’s ability to give reliable estimates of bid-ask spread and mid–prices, we generate artificial data following Hasbrouck (2004). We assume that: (i) log-prices generated by the equation pt = mt + st qt , with m0 = 100, σ 2 m = 0.012 , st = s = 0.01 each day, (ii) trades per day are drawn from the set {15, 16,..., 25} for 100 days giving 1, 981 observations with a median of 20 trades per day. The model is able to reproduce these vales in after maximum likelihood estimation, providing estimates as precise as the Gibbs sampling estimator of Hasbrouck (2002). Using qt = +1 if Prob[qt = +1|ψt−1] > 1 2 labels 76% of 3 trades correctly which beats the “tick rule” method used for signing trades in the absence of quotes. (II) Price Impact as Reaction Order Flow Imbalance Most modern financial markets are organized around a limit order book (LOB): when a buy(sell) order is submitted, it is matched against still unmatched sell(buy) orders, in which case a transaction occurs. If not immediately matched, remains active in the book until a match against a future incoming order or canceled. We postulate a theory of price dynamics in the LOB market of commodity futures. We begin by assuming: (i) the buyer–seller initiator indicators qt = ±1 are Markovian with transition matrix P as in chapter 1; (ii) the spread st is time varying and, (iii) the LOB’s mid-price/fundamental value mt is updated in a history dependent manner. Our hypothesis is that agents submitting orders to the LOB adjust their prices such that the mid–price evolves according to the price update rule: mt+1 = mt + st+1(qt − qbt+1)+u m t+1 where qbt+1 = E £ qt+1|qt ¤ is the prediction of the next trade sign given the sign of the last observed transaction and u m t+1 ∼ N ¡ 0,σ 2 m ¢ is an innovation to the mid price reflecting public information unrelated to the sequence {qt } ∞ t=1 . Markovian trade signs imply the best linear one-step forecast: qbt+1 = E £ qt+1|qt ¤ = qt ×Prob(qt+1 = qt)− qt ×Prob(qt+1 6= qt) = (1−2π)qt , where π = Prob(qt+1 6= qt) = 1−(π1p11+π2p22), is the probability of a sign reversal. The expected price change is therefore: Et∆mt+1 = 2πsqt . The three assumptions lead to the following properties. (i) Martingale Prices: the transaction price process is a martingale, i.e.: E(pt+1) = pt . (ii) Bid-Ask Spread: regret free price quotations require that the ask and bid prices are respectively set such that: p Ask t = Et £ pt+1|qt+1 = +1 ¤ = mt +(1+2πqt)s and p Bid t = Et £ pt+1|qt+1 = −1 ¤ = mt −(1−2πqt)s, which implies the bid–ask spread given by: p Ask t − p Bid t = 2s. (iii) No Quasi-Arbitrage: the transaction price process pt does not admit quasi-arbitrage or price-manipulation of Huberman and Stanzl (2004). The three assumptions also lead to testable predictions: lag-1 unconditional impact of Bouchaud, Kockelkoren and Potters (2006), defined as : R(1) := ­ (mt+1 −mt)· qt ® t , where the empirical average 〈·〉t is taken over all transactions of any volume. For any k > 0, we can define the lag-k response function: R(k) = E £ (mt+k −mt)· qt ¤ ≡ 〈(mt+k −mt)· qt〉 t , which measures the information content of the current trade on the mid-price k trades into the future. Defining the symbols a = (π1 − π2) 2 , b = 4π1π2 and λ = 1 − p12 − p21 where π1 = p21 p12+p21 and the lag-k anti-correlation function: C(k) = a(k − 1) − b ³ 1 − 1−λ k 1−λ ´ , for k > 0, with C(1) = 0, we find the following one-to-one relationships between lag-1 and lag-k response functions: R(1) = 1 1+C(k) · R(k) for k = 1, 2,.... Stochastic volatility over k trades is the average: 1 k Pk `=1 £ ∆pt+` ¤2 . The price difference between any two trades is ∆pt+1 ≈ ∆mt+1 u 2πst+1qt and we can approximate volatility over k trades by the empirical average: 1 k Pk `=1 E £ ∆pt+` ¤2 ≈ ­ 4π 2 × ¡ s 2 t+1 +σ 2 s ¢® k . We use data from the Tokyo Commodity Exchange (TOCOM) for two of the most liquid commodity futures contracts: Gold Standard (TOCOM Product Code: 11, Bloomberg: JGA ) and Platinum Standard (TOCOM Product Code: 13, Bloomberg: JAA), with the delivery month of February 2020, over the day-time trading session, from 8:45 a.m. to 3:15 p.m. Japanese Standard Time on the 24th April 2019. Each contract has a minimum price increment of JPY 1 per gram. We estimate the model described in Chapter 1 and compute the response functions: R(1) to R(k) and run the regressions R(1) = α + β 1 1+C(k) · R(k) for k = 2, 3, 4, 5 and find that statistically α = 0 and β = 1 with R 2 ≥ 60% in all cases. For stochastic volatility that at least 85% is explained by the update rule. (III) A Double Mixture Autoregressive Model of Commodity Price Many commodity prices exhibit boom–bust type behavior: sustained periods of price increases are followed by sudden sharp collapses. Since around the year 2000, booms have become longer while busts have tended to be short but steep, suggesting a structural change in growth and persistence. We model these features of the data using a novel double mixture autoregression with two independent hidden Markov chains. One chain models shifts in mean growth rates that accounts for rising and falling prices, while a second chain tracks changes in volatility and lag-structure. While the two chains are independent, the persistence of price growth depends on the volatility state, which allows the lag-structure to vary across variance regimes. Let yt = ∆log(Pt) represent a time series of the change in the log price of a commodity. Let S m t and S υ t represent, respectively, indicators of a mean and variance regime. Here S υ t = {0, 1} captures volatility changes characterizing many commodity price series while S m t = {0, 1} represents shifts in the growth rate related to price boom–bust cycles. The regimes S m t and S υ t are each the outcome of an independent first order Markov chain with transition matrices: P m = £ p m j|i ¤ and P υ = £ p υ j|i ¤ ,i, j = {0, 1}, respectively. The two components correspond to a restricted four regime model, with state St = S m t ×S υ t and transition matrix: P m ⊗P υ . The state St defines a dynamic linear model: yt = µS m t + P`S υ t ) l=1 φS υ t ,l ³ yt−l −µS m t−l ´ + σS υ t et , et ∼ i.i.d N(0, 1), with time varying intercepts µS m t and volatilities σS υ t . The lag length `(S υ t ) is potentially changing across variance regimes. This is the first novelty in the paper. In the original model of Hamilton (1989), there are no volatility changes and the state σ can be thought of as a nuisance parameter, in the sense of Sartori (2003) or Elliott, Müller and Watson (2015), which we are not interested in. In the present context, we are interested in modeling the boom–bust related shifts in mean growth rates while treating the change in volatility as incidental shift parameters in the sense of Neyman and Scott (1948, Example 1). This conceptual approach allows us to form a profile likelihood and filtering technique that can be used to estimate the model in two stages. Initially, location related parameters are estimated while suppressing the underlying autoregressive structure. These parameters are then held fixed while the optimal lag-structure across variance regimes is determined. We apply the model to three industrial commodities price time series: Crude Oil, Aluminium and Rubber. We find that in each case, the model captures boom and bust cycles, with data from more recent periods exhibiting higher volatility, longer price rallies 5 and steeper collapses. In order to show the models relevance for other applications in macroeconomics such the identification by heteroskedasticity method of Lütkepohl and Velinov (2016), we aggregate monthly frequency data to quarterly. This temporal aggregation allows us to show that the methods can be used for instance in a structural vector autoregression that includes data only available at the quarterly frequency such as GDP. This avoids using the more complex mixed frequency type models such as those advanced by Christensen, Posch and Van Der Wel (2016). Conclusion The analysis covers a variety of commodities at different observation frequencies or time scales. The first uses commodity price series at a daily frequency for periods of up to one year, approximately 252 days of market open to close futures prices from a commodity exchange. The second paper uses high-frequency trade-by-trade or tick-level data from a continuous trading session in a single day. Finally the third paper uses long time series spanning decades. It is important to look at data from the microscopic(ticklevel) to the macroscopic(decades) time scale in order to obtain a holistic view of the behavior of prices. Over very short time periods, the tick size is the smallest movement over any two prices and price changes can be viewed as random walks over a grid, with jumps occurring at arbitrary times (Curato and Lillo, 2014). This calls for the modeling of the microstructural features of the data such as the bid–ask spread; usually equal to half a tick for highly liquid assets, and the sequence of buy–sell orders which may predict the direction of short term price movements. At a coarser time-scale of months, quarters or years, the microstructural issues can be dispensed with and a more traditional time series approach used to describe price dynamics. While I separate the analysis based on the observation time scales, multi frequency models of price dynamics are possible, albeit with a more complex structure to capture the volatility components at play over every time scale (Calvet and Fisher, 2001, 2004).

This thesis makes new observations of market phenomena for various commodities and trading strategies centered around these observations. In particular, our results imply that many aspects of the commodities markets, from delivery markets to producers and consumer derivative based ETFs can be modeled eectively using nancial engineering techniques. Chapter 2 examines what drives the returns of gold miner stocks and ETFs. Inspired by our real options model, we construct a method to dynamically replicate gold miner stocks using two factors: a spot gold ETF and a market equity portfolio. We find that our real options approach can explain a significant portion of the drivers of firm implied gold leverage. Chapter 3 studies commodity exchange-traded funds (ETFs). From empirical data, we find that many commodity leveraged ETFs underperform significantly against our constructed dynamic benchmark, and we quantify such a discrepancy via the novel idea of realized effective fee. Finally, we consider a number of trading strategies and examine their performance by backtesting with historical price data. Chapter 4 studies the phenomenon of non-convergence between futures and spot prices in the grains market. In our proposed approach, we incorporate stochastic spot price and storage cost, and solve an optimal double stopping problem to understand shipping certificate prices. Our new models for stochastic storage rates explain the spot-futures premium.

by Robert S. Pindyck.
"March 1990."
Includes bibliographical references (p. 26-30).
Supported by M.I.T.'s Center for Energy Policy Research. Supported by the National Science Foundation. SES-8618502

碩士
國立高雄應用科技大學
金融系金融資訊碩士班
103
The aim of this paper is to examine the dynamic linkages among oil price, US dollar exchange rate index and commodity prices, using recursive cointegration analysis over the period from January 1980 to May 2014. The empirical evidence is as the following: First, the empirical results of recursive cointegration confirm there are cointegration relationships among the three precious metals and oil price, US dollar exchange rate. Second, the recursive cointegration' result of the multi-variable model for precious metal shows that there is a cointegration vector over all period, and there are two cointegration vector after 2005. Third, the recursive cointegration' result of the single-variable model for agricultural commodity cofirms that there is a cointegration vector for three agricultural markets,namely maize, wheat and soybeans. From 1987 to 1991, there is no cointegration for the sugar market. Finally, the recursive cointegration's result of the multi-variable model for agricultural commodity comfirms that there is a cointegration vector in the long run, and there are two cointegration vectors after 2006, which implies the integrated trend is more close after 2006.

碩士
輔仁大學
應用統計學研究所
98
DRAM industry in Taiwan has big scale of capacity. It benefits greatly with high profit from scale economy when economic climate is boomy, but it pays relative high costs for its considerable capacity when encountering economic recession. That makes DRAM makers suffer from high pressure of loss. Under attached by global financial tsunami of 2009, they asked for stimulate package from government. When looking back the DRAM industrial development of Taiwan, you can find it comes along with similar difficulties when facing recession. This industry in Taiwan pursues scale economy but relies on overseas’ technical support of its core R&D. Advanced manufacturing process requires enormous capital expenditure while the industry development is limited by great loss. The special industrial phenomenon points out the importance of DRAM price trend control to acquire more gross margin and to accumulate CAPEX for the need of long-term industry development. The past related researches on DRAM price forecast showed inaccuracy in the next period and capacity adjustment presents the interaction of all variables. This research makes use of CHAID to review the interaction of all variables and uses logistic regression to forecast the up and down of DRAM price. The total correct classification rates of this model (CHAID-logistic regression) are greater, which can provide a good reference for DRAM industry related procurement, capacity planning, quotation, etc.

Price swings of commodities affect the economies of commodity exporting nations worldwide and these fluctuations are a major concern for Australian policy makers. Australia is one of the major commodity exporting countries in the global market; therefore, the main focus of this thesis was to shed light on the influence of various fundamental macroeconomic variables on Australian commodity prices. First, emphasis was placed on what magnitude changes in real interest rates and fluctuations of the real exchange rate account for volatility in commodity prices and whether commodity prices tend to show overshooting phenomena (J. Frankel, 1986; J. Frankel, 2006) in reaction to interest rate changes. The possible contribution of global real economic activity to Australian commodities prices was then assessed, which can lead to both higher interest rates and volatile commodity prices (Akram, 2009; Svensson, 2008) within Australia. Similarly, the current slowdown in world economic growth after several years of high growth might clarify the sharp drop in real interest rates and commodity prices. In addition, the present study explored whether Australian resources stock prices had significant predictive ability for the future global commodity price index as suggested by Rossi (2012). Johansen’s (1988, 1991) cointegration technique was utilised to attain the above research objectives and to examine the long-run relationship of the considered variables. This thesis utilised seasonally adjusted monthly time series for real interest rate, real exchange rate, industrial production and resources stock price from January 2000 to December 2015 after considering an appropriate structural break. The study found significant long-run relationships among the variables; therefore, the vector error correction model was applied to judge the short-run dynamic relationship among variables. Then, the forecast ability of all variables was assessed by employing vector error correction Granger causality or block exogeneity tests. Single equation models do not allow the examination of dynamic relations between commodity prices and other macroeconomic variables over different time horizons (Akram, 2009); therefore, the study applied the impulse response technique as well as forecast error variance decomposition to assess the comparative influences of diverse shocks to the variations in key variables of the proposed commodity price model. The research found significant negative relationships between real interest rates and commodity prices. However, the impulse response results did not show any immediate responses of commodity prices because of an impulse in the real interest rate. This showed a significant negative response of commodity prices after six months of the initial shock and the importance of interest rate information to predict the commodity prices in the long run. In two years’ time, approximately one third of the commodity price changes will be explained by the shocks in real interest rate. The shocks from opposite directions showed a significant negative response for real interest rate after having shocks from Australian commodity prices in the medium term. The results of the present study also suggested an immediate fall in Australian commodity prices and thereafter increases at a higher rate significantly in response to the real exchange rate shock, consistent with Frankel’s (1986) overshooting model of commodity prices. This finding raised the question as to whether real exchange rate shocks are a significant factor of Australian macroeconomic instability as commodity export plays an important role in its economy. Results of the present study revealed the response to this query as being in the negative, especially in the long run. The interaction of these two variables from opposite directions showed interesting results. Separate commodity-related drivers of exchange rates results showed that Australian real exchange rate movements were not purely random. Vector error correction-based Granger causality tests indicated a strong support of causality from commodity prices to real exchange rate in the short run. The impulse response results showed the most noteworthy results. The shocks from Australian commodity prices showed immediate significant depreciation in real exchange rates and the index remained depreciated significantly in all horizons, which shows the complete opposite results to many studies (Connolly & Orsmond, 2011; Minifie, Cherastidtham, Mullerworth, & Savage, 2013; Plumb, Kent, & Bishop, 2013; Sheehan & Gregory, 2013). However, this finding is consistent with the theoretical explanation provided by Dumrongrittikul (2012) to explain the puzzle of the Chinese real exchange rate, which is supported by the theoretical explanation of S. Edwards’ (1989) real exchange rate model. The results of the present study also showed that the shock to industrial production had a negative effect on Australian commodity prices and the effect remained significant during all time horizons. It also showed that the commodity price fluctuation had predictive ability of the Australian resources stock prices. After considering these above findings, several policy recommendations for relevant Australian authorities are suggested and limitations are discussed including the pathway for future research.

碩士
銘傳大學
經濟學系碩士在職專班
98
Observing certain research leading indicators is to facilitate investors in making decision on judging behaviors. Meanwhile, it is aimed to provide professional institutes unique perspectives, based on the practical analytical results, toward the influences among VIX, DXY, ADXY, crude price, gold price, and BRIC stock markets. At last, the major purpose is to assist investors to avoid from tumbling, which it might cost them a fortune again. This paper investigates the relation among commodity price, crude price or gold price, and VIX with BRIC stock price respectively. In the meantime, it discusses VIX and DXY or ADXY toward BRIC stock price and commodity price, crude price or gold price, during Sep, 1995 to May, 2010. There are some examines practiced, such as ADF Unit Root Test and Cointegration Test, and models testified, such as VECM and GJR-GARCH. Due to those demonstrations, the evidences are attributed as followings, 1. The empirical results of Johansen cointegration indicates that there is a long term stability between BRIC stock price and VIX ,crude price, or gold price respectively. 2. The empirical results of Johansen cointegration claims that there is a long term stability between BRIC stock price and crude price respectively. 3. The empirical results of Johansen cointegration shows that there is a long term stability between India stock price and gold price. 4. The empirical results of Johansen cointegration claims that there is a long term stability between a pair of BRIC stock price and crude price respectively. 5. The empirical results of Johansen cointegration shows that there is a long term stability only between gold price and a pair of India and Brazil or a pair of India and Russia stock price. 6. VIX and DXY fluctuate while Brazil or Russia Stock fluctuates. 7. VIX and ADXY fluctuate while India or China Stock fluctuates.

This thesis consists of three essays on commodity-linked investment decisions under uncertainty. Specifically, the first essay investigates whether a regime switching model of stochastic lumber prices is a better model for the analysis of optimal harvesting problems in forestry than a more traditional single regime model. Prices of lumber derivatives are used to calibrate a regime switching model, with each of two regimes characterized by a different mean reverting process. A single regime, mean reverting process is also calibrated. The value of a representative stand of trees and optimal harvesting prices are determined by specifying a Hamilton-Jacobi-Bellman Variational Inequality, which is solved for both pricing models using a fully implicit finite difference approach. The regime switching model is found to more closely match the behavior of futures prices than the single regime model. In addition, the optimal harvesting model indicates significant differences in terms of land value and optimal harvest thresholds between the regime switching and single regime models. The second essay investigates whether convenience yield is an important factor in determining optimal decisions for a forestry investment. The Kalman filter method is used to estimate three different models of lumber prices: a mean reverting model, a simple geometric Brownian motion and the two-factor price model due to Schwartz (1997). In the latter model there are two correlated stochastic factors: spot price and convenience yield. The two-factor model is shown to provide a reasonable fit of the term structure of lumber futures prices. The impact of convenience yield on a forestry investment decision is examined using the Schwartz (1997) long-term model which transforms the two-factor price model into a single factor model with a composite price. Using the long-term model an optimal harvesting problem is analyzed, which requires the numerical solution of a Hamilton-Jacobi-Bellman equation. I compare the results for the long-term model to those from single-factor mean reverting and geometric Brownian motion models. The inclusion of convenience yield through the long-term model is found to have a significant impact on land value and optimal harvesting decisions. The third essay investigates the dynamics of recent crude oil prices by comparing and contrasting three different stochastic price models, which are a two-state regime switching model, a two-factor model analyzed in Schwartz (1997) and a two-factor model examined in Schwartz and Smith (2000). Prices of long-term crude oil futures contracts are used to calibrate and estimate the model parameters. The performances of the two-factor models are comparable in terms of fitting the market prices of the long-term oil futures contracts and more closely match the behavior of oil futures prices than the regime switching model.

碩士
國立中興大學
應用經濟學系所
95
Abstract The main concern of this study is to analyze the price dynamic correlation degree among Indexes of CRB and major Commodity Futures contracts. The data period was based on daily records from July 31st, 2003 to August 1st, 2006. Several approaches were applied which included the Johansen Co-integration method, the vector error correction (VEC) model, the Granger causality test, the decomposition of the predictive error variance, and impulse response function to explore the temporal relationship of the CRB index with respect to the energy and the metals futures contracts. Four major results were summarized as follows: (1) Regarding the test of co-integration, CRB futures index existed a long-term balance with various indices except NICKEL index; However, in the VEC model, the COPPER and the GOLD indices were influenced by the ALUMINUM and the LEAD indices each other in terms of laggard effects. Namely, there existed a two-way feedback causality. In particular, the laggard of LEAD index influenced the current COPPER index most. (2) In the part of Granger causality test, the CRB and COPPER indices possessed the feedback causality. Moreover, the CRB index had no causality effect neither on the GOLD index, the NICKEL index, nor the LEAD index. (3) In the part of the decomposition of the predictive error variance, the CRB index had the strongest exogenity effect among various variables, therefore it won’t be influenced by other factor apparently; However, the GOLD index was more easily affected by the variety of an external factor. Furthermore, the CRB and the COPPER indices had the most influence by the CRB index under the long-term fluctuation. (4) The CRB index had the most effect by the OIL index, and the GOLD index was secondary in the impulse response function analysis results. In other words, the tendency of the short-term CRB index was still influenced by two important original materials indices mentioned above. Further, we observed the impulse response among the CRB index and various variables, the two indices, the OIL and COPPER, were affected obviously. Making a comprehensive survey of the inter-attack among the CRB index and other indices, we detected that the impulse directions were almost the same and without convergence as well. Key words： CRB index, commodity futures index, time-series analysis

碩士
東海大學
經濟系
102
This paper constructs a open economy general equilibrium macroeconomic model is characterized by the Dornbusch (1976) exchange rate dynamic adjustment model and Eaton and Turnovsky (1982‚1984)‚Lai (2006) open economy forward foreign exchange market model. We use the “implicit function technique” of first generation regime collapsing‚ which is offered by Chang and Lai (1990) to analyze if the monetary authority tend to curb the rising price level through the tight monetary policy which the economy is facing a beneficial shock on the demand side of the commodity market. Under the former economic circumstances‚ what will be the dynamic effect of the relevant macroeconomic variables if the monetary authority executes the policy? The major findings are (i) not only the price ceiling threshold level is the key factor of price regime collapsing‚ but also is the important determinant of the price regime collapsing whether or not? (ii) if the price ceiling threshold level is between the initial price level and the new long run equilibrium price level‚ then (a) the relative amplitude of “real exchange rate of trade balance reaction coefficient” and “the tight money effect”(b) the relative amplitude of“ the speculation degree of speculator” are the two key factors to decide the dynamic path of the forward exchange rate.