Review of stochastic differential equations in statistical arbitrage pairs trading

The use of stochastic differential equations offers great advantages for statistical arbitrage pairs trading. In particular, it allows the selection of pairs with desirable properties, e.g., strong mean-reversion, and it renders traditional rules of thumb for trading unnecessary. This study provides an exhaustive survey dedicated to this field by systematically classifying the large body of literature and revealing potential gaps in research. From a total of more than 80 relevant references, five main strands of stochastic spread models are identified, covering the ‘Ornstein–Uhlenbeck model’, ‘extended Ornstein–Uhlenbeck models’, ‘advanced mean-reverting diffusion models’, ‘diffusion models with a non-stationary component’, and ‘other models’. Along these five main categories of stochastic models, we shed light on the underlying mathematics, hereby revealing advantages and limitations for pairs trading. Based on this, the works of each category are further surveyed along the employed statistical arbitrage frameworks, i.e., analytic and dynamic programming approaches. Finally, the main findings are summarized and promising directions for future research are indicated

Convenience Yields for CO2 Emission Allowance Futures Contracts

In January 2005 the EU-wide CO2 emissions trading system (EU-ETS) has formally entered into operation. Within the new trading system, the right to emit a particular amount of CO2 becomes a tradable commodity - called EU Allowances (EUAs) - and affected companies, traders and investors will face new strategic challenges. In this paper we investigate the nature of convenience yields for CO2 emission allowance futures. We conduct an empirical study on price behavior, volatility term structure and correlations in different CO2 EUA contracts. Our findings are that the market has changed from initial backwardation to contango with significant convenience yields in future contracts for the Kyoto commitment period starting in 2008. A high fraction of the yields can be explained by the price level and volatility of the spot prices. We conclude that the yields can be interpreted as market expectation on the price risk of CO2 emissions allowance prices and the uncertainty of EU allocation plans for the Kyoto period.CO2 Emission Trading, Commodity Markets, Spot and Futures Prices, Convenience Yields.

Additive models for energy markets

This Dissertation explores the capability of additive models to describe prices in energy markets, by focusing in particular on the specific case of electricity and natural gas. In Chapter 1 we study a dynamic portfolio optimization problem designed for intraday electricity trading. In Chapter 2 we introduce a no-arbitrage tractable framework based on the Heath- Jarrow-Morton approach for a multicommodity energy forward market. Chapter 3 deals with a thorough empirical study of a two-factor model derived by the framework of Chapter 2, with an application to the German power futures market. Finally, in Chapter 4 we discuss option pricing for additive factor models by Fourier transform methods. We introduce a two-factor futures price model with jumps in order to capture the implied volatility smile of European electricity options. An application to the European Energy Exchange Power Derivatives market is presented

Four essays in commodity markets: asset allocation, pricing, and risk management

Mención Internacional en el título de doctorOur study is divided into two parts. The first part (Chapter 2 and Chapter 3) analyzes the multivariate distribution of commodity returns and its impact on portfolio selection and tail risk measures. Chapter 2 solves the portfolio selection problem of an investor with three-moment preferences when commodity futures are part of the investment opportunity set, providing a conditional copula model for the joint distribution of returns that allows for time-varying moments and state-dependent tail behavior. Chapter 3 approximates the exposure of physical and financial players to energy price risk using linear combinations of energy futures; it also analyzes the tail behavior of energy price risk using a dynamic multivariate model, in which the vector of innovations is generated by different generalized hyperbolic distributions. The second part (Chapter 4 and Chapter 5) considers the valuation of real assets and commodity derivatives in the presence of non-Gaussian shocks in a continuous time framework. Specifically, Chapter 4 employs a jump diffusion model for the price differentials and proposes a valuation tool for the connection between two electricity markets. Chapter 5 proposes a reduced-form model for the data generating process of commodity prices together with a more flexible change of measure, capable of changing the mean-reversion rate of Gaussian and jump processes under the risk-adjusted probability measure. Some parts of this thesis have been presented in different seminars, workshops, and conferences. Chapter 2 was presented at the 2011 INFINITI Conference on International Finance (Trinity College, Dublin), the 2011 Conference of the Multinational Finance Society (LUISS, Rome), the 2012 International Conference of the Financial Engineering and Banking Society (ESCP, London), the 2012 International Finance and Banking Society Conference (Valencia), the 2012 Meetings of the European Financial Management Association (University of Barcelona), and Universidad Autónoma de Madrid. A previous version of Chapter 3 was presented at the 2010 AEEE Conference on Energy Economics (University of Vigo). Chapter 4 was presented at the 2010 Finance Forum (CEU, Elche), the 2011 AEEE Conference on Energy Economics (University of Barcelona), University of Duisburg-Essen, and Birkbeck-University of London. Previous drafts of Chapter 5 were presented at the 2009 Conference on Energy Finance (Universities of Oslo and Agder), the 2010 Industrial-Academic Forum on Commodities, Energy Markets, and Emissions Trading (Fields Institute, Toronto), and the 2011 Energy and Finance (Erasmus School of Economics).Programa Oficial de Posgrado en Investigación en Economía de la Empresa y Métodos CuantitativosPresidente: Alfonso Novales Cinca; Secretario: Rüdiger Kiesel; Vocal: David Vereda

Stochastics of Environmental and Financial Economics

Systems Theory, Contro