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Calibration And Model Uncertainty Of A Two Factor Mean Reverting Diffusion Model For Commodity Prices
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Book Synopsis Calibration and Model Uncertainty of a Two-factor Mean-reverting Diffusion Model for Commodity Prices by : Jue Jun Chuah
Download or read book Calibration and Model Uncertainty of a Two-factor Mean-reverting Diffusion Model for Commodity Prices written by Jue Jun Chuah and published by . This book was released on 2013 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the development of various derivative instruments and index products, commodities have become a distinct asset class which can offer enhanced diversification benefits to the traditional asset allocation of stocks and bonds. In this thesis, we begin by discussing some of the key properties of commodity markets which distinguish them from bond and stock markets. Then, we consider the informational role of commodity futures markets. Since commodity prices exhibit mean-reverting behaviour, we will also review several mean-reversion models which are commonly used to capture and describe the dynamics of commodity prices. In Chapter 4, we focus on discussing a two-factor mean-reverting model proposed by Hikspoors and Jaimungal, as a means of providing additional degree of randomness to the long-run mean level. They have also suggested a method to extract the implied market prices of risk, after estimating both the risk-neutral and real-world parameters from the calibration procedure. Given the usefulness of this model, we are motivated to investigate the robustness of this calibration process by applying the methodology to simulated data. The capability to produce stable and accurate parameter estimates will be assessed by selecting various initial guesses for the optimization process. Our results show that the calibration method had a lot of difficulties in estimating the volatility and correlation parameters of the model. Moreover, we demonstrate that multiple solutions obtained from the calibration process would lead to model uncertainty in extracting the implied market prices of risk. Finally, by using historical crude oil data from the same time period, we can compare our calibration results with those obtained by Hikspoors and Jaimungal.
Book Synopsis Modelling the Dynamics of Commodity Prices for Investment Decisions Under Uncertainty by : Shan Chen
Download or read book Modelling the Dynamics of Commodity Prices for Investment Decisions Under Uncertainty written by Shan Chen and published by . This book was released on 2010 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Calibration and Filtering for Multi Factor Commodity Models with Seasonality by : Gareth Peters
Download or read book Calibration and Filtering for Multi Factor Commodity Models with Seasonality written by Gareth Peters and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We construct a general multi-factor model for estimation and calibration of commodity spot prices and futures valuation. This extends the multi-factor long-short model in Schwartz and Smith (2000) and Yan (2002) in two important aspects: firstly we allow for both the long and short term dynamic factors to be mean reverting incorporating stochastic volatility factors and secondly we develop an additive structural seasonality model. In developing this non-linear continuous time stochastic model we maintain desirable model properties such as being arbitrage free and exponentially affine, thereby allowing us to derive closed form futures prices. In addition the models provide an improved capability to capture dynamics of the futures curve calibration in different commodities market conditions such as backwardation and contango. A Milstein scheme is used to provide an accurate discretized representation of the s.d.e.model. This results in a challenging non-linear non-Gaussian state-space model. To carry out inference, we develop an adaptive particle Markov chain Monte Carlo method. This methodology allows us to jointly calibrate and filter the latent processes for the long-short and volatility dynamics. This methodology is general and can be applied to the estimation and calibration of many of the other multi-factor stochastic commodity models proposed in the literature. We demonstrate the performance of our model and algorithm on both synthetic data and real data for futures contracts on crude oil.
Book Synopsis Commodity Price Dynamics by : Craig Pirrong
Download or read book Commodity Price Dynamics written by Craig Pirrong and published by Cambridge University Press. This book was released on 2011-10-31 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Commodities have become an important component of many investors' portfolios and the focus of much political controversy over the past decade. This book utilizes structural models to provide a better understanding of how commodities' prices behave and what drives them. It exploits differences across commodities and examines a variety of predictions of the models to identify where they work and where they fail. The findings of the analysis are useful to scholars, traders and policy makers who want to better understand often puzzling - and extreme - movements in the prices of commodities from aluminium to oil to soybeans to zinc.
Book Synopsis Quantitative Techniques for Spread Trading in Commodity Markets by : Mir Hashem Moosavi Avonleghi
Download or read book Quantitative Techniques for Spread Trading in Commodity Markets written by Mir Hashem Moosavi Avonleghi and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis investigates quantitative techniques for trading strategies on two commodities, the difference of whose prices exhibits a long-term historical relationship known as mean-reversion. A portfolio of two commodity prices with very similar characteristics, the spread may be regarded as a distinct process from the underlying price processes so deserves to be modeled directly. To pave the way for modeling the spread processes, the fundamental concepts, notions, properties of commodity markets such as the forward prices, the futures prices, and convenience yields are described. Some popular commodity pricing models including both one and two factor models are reviewed. A new mean-reverting process to model the commodity spot prices is introduced. Some analytical results for this process are derived and its properties are analyzed. We compare the new one-factor model with a common existing one-factor model by applying these two models to price West Texas Intermediate (WTI) crude oil, and discuss its advantages and disadvantages. We investigate the recent behavioral change in the location spread process between WTI crude oil and Brent oil. The existing three major approaches to price a spread process namely cointegration, one-factor and two-factor models fail to fully capture these behavioral changes. We, therefore, extend the one-factor and two-factor spread models by including a compound Poisson process where jump sizes follow a double exponential distribution. We generalize the existing one-factor mean-reverting dynamics (Vasicek process) by replacing the constant diffusion term with a nonlinear term to price the spread process. Applying the new process to the empirical location spread between WTI and Brent crude oils dataset, it is shown how the generalized dynamics can rigorously capture the most important characteristics of the spread process namely high volatility, skewness and kurtosis. To consider the recent structural breaks in the location spread between WTI and Brent, we incorporate regime switching dynamics in the generalized model and Vasicek process by including two regimes. We also introduce a new mean-reverting random walk, derive its continuous time stochastic differential equation and obtain some analytical results about its solution. This new mean-reverting process is compared with the Vasicek process and its advantages discussed. We showed that this new model for spread dynamics is capable of capturing the possible skewness, kurtosis, and heavy tails in the transition density of the price spread process. Since the analytical transition density is unknown for this nonlinear stochastic process, the local linearization method is deployed to estimate the model parameters. We apply this method to empirical data for modeling the spread between WTI crude oil and West Texas Sour (WTS) crude oil. Finally, we apply the introduced trading strategies to empirical data for the location spread between WTI and Brent crude oils, analyze, and compare the profitability of the strategies. The optimal trading strategies for the spread dynamics in the cointegration approach and the one-factor mean-reverting process are discussed and applied to our considered empirical dataset. We suggest to use the stationary distribution to find optimal thresholds for log-term investment strategies when the spread dynamics is assumed to follow a Vasicek process. To incorporate essential features of a spread process such as skewness and kurtosis into the spread trading strategies, we extend the optimal trading strategies by considering optimal asymmetric thresholds.
Book Synopsis Model Uncertainty in Commodity Markets by : Álvaro Cartea
Download or read book Model Uncertainty in Commodity Markets written by Álvaro Cartea and published by . This book was released on 2015 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: Agents who acknowledge that their models are incorrectly specified are said to be ambiguity averse, and this affects the prices they are willing to trade at. Models for prices of commodities attempt to capture three stylized features: seasonal trend, moderate deviations (a diffusive factor), and large deviations (a jump factor) both of which mean-revert to the seasonal trend. Here we model ambiguity by allowing the agent to consider a class of models absolutely continuous w.r.t. their reference model, but penalize candidate models that are far from it. We show that the buyer (seller) of a forward contract introduces a negative (positive) drift in the dynamics of the spot price, and enhances downward (upward) jumps so the prices they are willing to trade at are lower (higher) than that of the forward price under P. When ambiguity averse buyers and sellers employ the same reference measure they cannot trade because the seller requires more than what the buyer is willing to pay. Finally, we observe that when ambiguity averse agents price options written on the commodity forward, the effect of ambiguity aversion is strongest when the option is at-the-money, and weaker when it is deep in-the-money or deep out-of-the-money.
Book Synopsis A Supply/Demand Commodity Pricing Model by : Ali Bashiri
Download or read book A Supply/Demand Commodity Pricing Model written by Ali Bashiri and published by . This book was released on 2020 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a two-factor mean-reverting stochastic model for forecasting storable commodity prices and valuing commodity derivatives. We define a variable called normalized excess supply based on the observable production rate, consumption rate, and inventory levels of the commodity. Our analysis indicates a strong inverse correlation between normalized excess supply and crude oil spot and futures prices. Our first stochastic factor is normalized excess supply, following a mean-reverting process. The second stochastic factor is the deviation of prices from a mean level determined by normalized excess supply. Moreover, we develop valuation models for futures and options on futures contracts based on the two-factor model. We apply this model to crude oil prices from 1995 to 2017 via a Kalman filter. We perform out-of-sample tests for forecasting spot prices. Additionally, we develop a scenario analysis framework for incorporating variant views of future supply, demand, and inventories in risk management and valuation of commodity related financial products. We show the utility of the model for investment management professionals and risk managers aiming to incorporate macroeconomic conditions in valuation and risk management endeavors.
Book Synopsis Affine Diffusion Modeling of Commodity Futures Price Term Structure by :
Download or read book Affine Diffusion Modeling of Commodity Futures Price Term Structure written by and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Diffusion modeling of commodity price behavior is important for commodity risk management. This research seeks to improve upon the existing commodity diffusion models by incorporating stochastic volatility and seasonality through the affine diffusion framework. In particular, it evaluates affine diffusion models' performance at modeling commodity futures price term structure. Six affine diffusion models are studied in this research. They are one, two, three-factor Gaussian model and one, two, three-factor stochastic volatility model with a single stochastic volatility factor. Seasonality is modeled by allowing the forcing terms of the instantaneous drift and the instantaneous covariance to be seasonal. Model estimation is done through Q-MLE, for which the state variables are filtered through the Kalman Filter. To build the connection between affine diffusion models and known market regularities, affine state variables are interpreted. Factor interpretations used include the log of the spot price, a spot drift factor, and a spot variance factor. Empirical analysis covers models' performance at fitting and predicting futures price term structures; behavior of the interpretable models; and model stability. Empirical studies are applied to the corn and the unleaded gasoline markets. The following conclusions can be drawn from both markets: 1. For the purpose of modeling futures price dynamics alone, stochastic volatility models have no advantage over Gaussian models; 2. At least two factors are needed to adequately model commodity futures price term structures; the advantage of three-factor models, which is better capturing the curvature of the term structures, become evident under extreme market conditions; 3. State independent seasonality modeling is effective under most market conditions, but under extreme market conditions, seasonality can be mis-represented and it is the source of big measurement errors and prediction errors. 4. Two and three-factor affine diffusio.
Book Synopsis Commodities and Commodity Derivatives by : Helyette Geman
Download or read book Commodities and Commodity Derivatives written by Helyette Geman and published by John Wiley & Sons. This book was released on 2009-09-24 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last few years have been a watershed for the commodities, cash and derivatives industry. New regulations and products have led to an explosion in the commodities markets, creating a new asset for investors that includes hedge funds as well as University endowments, and has resulted in a spectacular growth in spot and derivative trading. This book covers hard and soft commodities (energy, agriculture and metals) and analyses: Economic and geopolitical issues in commodities markets Commodity price and volume risk Stochastic modelling of commodity spot prices and forward curves Real options valuation and hedging of physical assets in the energy industry It is required reading for energy companies and utilities practitioners, commodity cash and derivatives traders in investment banks, the Agrifood business, Commodity Trading Advisors (CTAs) and Hedge Funds. In Commodities and Commodity Derivatives, Hélyette Geman shows her powerful command of the subject by combining a rigorous development of its mathematical modelling with a compact institutional presentation of the arcane characteristics of commodities that makes the complex analysis of commodities derivative securities accessible to both the academic and practitioner who wants a deep foundation and a breadth of different market applications. It is destined to be a "must have" on the subject.” —Robert Merton, Professor, Harvard Business School "A marvelously comprehensive book of interest to academics and practitioners alike, by one of the world's foremost experts in the field." —Oldrich Vasicek, founder, KMV
Download or read book Energy Derivatives written by Les Clewlow and published by Twayne Publishers. This book was released on 2000 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Maximal Stochastic Volatility Model for Commodity Prices by : Walker Keener Hughen
Download or read book A Maximal Stochastic Volatility Model for Commodity Prices written by Walker Keener Hughen and published by . This book was released on 2007 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Energy and Power Risk Management by : Alexander Eydeland
Download or read book Energy and Power Risk Management written by Alexander Eydeland and published by John Wiley & Sons. This book was released on 2003-02-03 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for Energy and Power Risk Management "Energy and Power Risk Management identifies and addresses the key issues in the development of the turbulent energy industry and the challenges it poses to market players. An insightful and far-reaching book written by two renowned professionals." -Helyette Geman, Professor of Finance University Paris Dauphine and ESSEC "The most up-to-date and comprehensive book on managing energy price risk in the natural gas and power markets. An absolute imperative for energy traders and energy risk management professionals." -Vincent Kaminski, Managing Director Citadel Investment Group LLC "Eydeland and Wolyniec's work does an excellent job of outlining the methods needed to measure and manage risk in the volatile energy market." -Gerald G. Fleming, Vice President, Head of East Power Trading, TXU Energy Trading "This book combines academic rigor with real-world practicality. It is a must-read for anyone in energy risk management or asset valuation." -Ron Erd, Senior Vice President American Electric Power
Book Synopsis Energy Risk: Valuing and Managing Energy Derivatives by : Dragana Pilipovic
Download or read book Energy Risk: Valuing and Managing Energy Derivatives written by Dragana Pilipovic and published by McGraw Hill Professional. This book was released on 2007-08-13 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Latest Methods and Strategies for Successfully Trading and Managing Risk in Today's Volatile Energy Markets The updated Second Edition of Energy Risk presents an authoritative overview of the contemporary energy trading arena, combining the lesson's from the last decade with proven methods and strategies required for valuing energy derivatives and managing risk in these ever volatile markets. Written by renowned energy risk expert Dragana Pilipovic this revised classic examines market behavior, covering both quantitative analysis and trader-oriented insights. The book shows how to establish a modeling process that involves the key players_managers, traders, quantitative analysts, and engineers_and provides practical answers to energy trading and risk management questions. The Second Edition of Energy Risk features: Detailed coverage of the primary factors that influence energy risk Techniques for building marked-to-market forward price curves, creating volatility matrices, and valuing complex options Specific guidelines and tools for achieving risk goals New to this edition: three new chapters on the emerging energy market and marked-to-market issues; new material on energy-specific models, seasonal effects, and the derivation of the mean-reverting price model; and more
Book Synopsis A Two-Factor Model for Commodity Prices and Futures Valuation by : Diana Ramos Ribeiro
Download or read book A Two-Factor Model for Commodity Prices and Futures Valuation written by Diana Ramos Ribeiro and published by . This book was released on 2004 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper develops a new reduced form two-factor model for commodity spot prices and futures valuation. This models extends Schwartz's (1997) two-factor model by adding two new features. First we replace the Ornstein-Uhlenbeck process for the convenience yield by a Cox-Ingersoll-Ross (CIR) process. This ensures that our model is arbitrage free while Schwartz's model does not rule out arbitrage possibilities. Second, we introduce a time-varying volatility for the spot price process. In particular, we consider the spot price volatility is proportional to the square root of the convenience yield level. This implicitly implies that the spot price volatility depends on inventory levels of the commodity as predicted by the theory of storage. We empirically test both models using weekly crude oil futures data from 5th of March 1999 to the 15th of October 2003. In both cases, we estimate the model's parameters using the Kalman filter.
Book Synopsis Mathematical Models of Financial Derivatives by : Yue-Kuen Kwok
Download or read book Mathematical Models of Financial Derivatives written by Yue-Kuen Kwok and published by Springer Science & Business Media. This book was released on 2008-07-10 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition, now featuring new material, focuses on the valuation principles that are common to most derivative securities. A wide range of financial derivatives commonly traded in the equity and fixed income markets are analysed, emphasising aspects of pricing, hedging and practical usage. This second edition features additional emphasis on the discussion of Ito calculus and Girsanovs Theorem, and the risk-neutral measure and equivalent martingale pricing approach. A new chapter on credit risk models and pricing of credit derivatives has been added. Up-to-date research results are provided by many useful exercises.
Book Synopsis Optimal Mean Reversion Trading by : Tim Leung (Professor of industrial engineering)
Download or read book Optimal Mean Reversion Trading written by Tim Leung (Professor of industrial engineering) and published by World Scientific. This book was released on 2015-11-26 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Optimal Mean Reversion Trading: Mathematical Analysis and Practical Applications provides a systematic study to the practical problem of optimal trading in the presence of mean-reverting price dynamics. It is self-contained and organized in its presentation, and provides rigorous mathematical analysis as well as computational methods for trading ETFs, options, futures on commodities or volatility indices, and credit risk derivatives. This book offers a unique financial engineering approach that combines novel analytical methodologies and applications to a wide array of real-world examples. It extracts the mathematical problems from various trading approaches and scenarios, but also addresses the practical aspects of trading problems, such as model estimation, risk premium, risk constraints, and transaction costs. The explanations in the book are detailed enough to capture the interest of the curious student or researcher, and complete enough to give the necessary background material for further exploration into the subject and related literature. This book will be a useful tool for anyone interested in financial engineering, particularly algorithmic trading and commodity trading, and would like to understand the mathematically optimal strategies in different market environments."--
Book Synopsis Optimal Sampled-Data Control Systems by : Tongwen Chen
Download or read book Optimal Sampled-Data Control Systems written by Tongwen Chen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the many techniques for designing linear multivariable analogue controllers, the two most popular optimal ones are H2 and H-infinity optimization. The fact that most new industrial controllers are digital provides strong motivation for adapting or extending these techniques to digital control systems. This book, now available as a corrected reprint, attempts to do so. Part I presents two indirect methods of sampled-data controller design: These approaches include approximations to a real problem, which involves an analogue plant, continuous-time performance specifications, and a sampled-data controller. Part II proposes a direct attack in the continuous-time domain, where sampled-data systems are time-varying. The findings are presented in forms that can readily be programmed in, e.g., MATLAB.
