Stochastic equilibrium models for generation capacity expansion

Capacity expansion models in the power sector were among the first applications of operations research to the industry. The models lost some of their appeal at the inception of restructuring even though they still offer a lot of possibilities and are in many respect irreplaceable provided they are adapted to the new environment. We introduce stochastic equilibrium versions of these models that we believe provide a relevant context for looking at the current very risky market where the power industry invests and operates. We then take up different questions raised by the new environment. Some are due to developments of the industry like demand side management: an optimization framework has difficulties accommodating them but the more general equilibrium paradigm offers additional possibilities. We then look at the insertion of risk related investment practices that developed with the new environment and may not be easy to accommodate in an optimization context. Specifically we consider the use of plant specific discount rates that we derive by including stochastic discount rates in the equilibrium model. Linear discount factors only price systematic risk. We therefore complete the discussion by inserting different risk functions (for different agents) in order to account for additional unpriced idiosyncratic risk in investments. These different models can be cast in a single mathematical representation but they do not have the same mathematical properties. We illustrate the impact of these phenomena on a small but realistic example.capacity adequacy, risk functions, stochastic equilibrium models, stochastic discount factors

Incomplete Market Models of Carbon Emissions Markets

New regulatory frameworks have been developed with the aim of decreasing global greenhouse gas emissions over both short and long time periods. Incentives must be established to encourage the transition to a clean energy economy. Emissions taxes represent a price incentive for this transition, but economists agree this approach is suboptimal. Instead, the quantity instrument provided by cap-and-trade markets are superior from an economic point of view. This thesis focuses on the cap-and-trade instrument. Carbon emissions markets have recently been implemented in different countries. We summarize the state of world cap-and-trade schemes. We also provide a literature review of existing research that offer pricing and hedging tools. Based on the European Union Emissions Trading Scheme, we study the impact of the market design on the observed spread between futures contracts with different maturities. Moreover we investigate the relationship between their returns. First we study the spread using a discrete-time model. We propose a pricing procedure arising from quadratic risk minimization hedging strategies. We suggest recommendations for both traders and the regulator in order to efficiently encourage market participation. We also present a continuous-time model that investigates the way in which the market structure affects the impact of an unexpected release of information on futures returns. We propose a pricing solution based on the Follmer-Schweizer decomposition. The optimal hedging strategy depends on all traded futures and minimizes the mean conditional square error of the cumulative cost process. Both discrete and continuous time model parameters are estimated to fit real data, and economic conclusions are drawn

Econometrics: A Bird’s Eye View

As a unified discipline, econometrics is still relatively young and has been transforming and expanding very rapidly over the past few decades. Major advances have taken place in the analysis of cross sectional data by means of semi-parametric and non-parametric techniques. Heterogeneity of economic relations across individuals, firms and industries is increasingly acknowledged and attempts have been made to take them into account either by integrating out their effects or by modeling the sources of heterogeneity when suitable panel data exists. The counterfactual considerations that underlie policy analysis and treatment evaluation have been given a more satisfactory foundation. New time series econometric techniques have been developed and employed extensively in the areas of macroeconometrics and finance. Non-linear econometric techniques are used increasingly in the analysis of cross section and time series observations. Applications of Bayesian techniques to econometric problems have been given new impetus largely thanks to advances in computer power and computational techniques. The use of Bayesian techniques have in turn provided the investigators with a unifying framework where the tasks of forecasting, decision making, model evaluation and learning can be considered as parts of the same interactive and iterative process; thus paving the way for establishing the foundation of “real time econometrics”. This paper attempts to provide an overview of some of these developments.history of econometrics, microeconometrics, macroeconometrics, Bayesian econometrics, nonparametric and semi-parametric analysis

Essays on asset pricing

The dissertation consists of three chapters that represent separate papers in the area of asset pricing. The first chapter studies investors optimal asset allocation problem in which mean reversion in stock prices is captured by explicitly modeling transitory and permanent shocks. The second chapter focuses on option pricing with stochastic dividend yield. In this work, we present an option formula which does not depend on the dividend yield risk premium. In the final chapter, we work on commodity derivative pricing under the existence of stochastic convenience yield. In this paper, we discuss a Gaussian complete market model of commodity prices in which the stochastic convenience yield is assumed to be an affine function of a weighted average of past commodity price changes

On investment, uncertainty, and strategic interaction with applications in energy markets

The thesis presents dynamic models on investment under uncertainty with the focus on strategic interaction and energy market applications. The uncertainty is modelled using stochastic processes as state variables. The specific questions analyzed include the effect of technological and revenue related uncertainties on the optimal timing of investment, the irreversibility in the choice between alternative investment projects with different degrees of uncertainty, and the effect of strategic interaction on the initiating of discrete investment projects, on the abandonment of a project, and on incremental capacity investments. The main methodological feature is the incorporation of game theoretic concepts in the theory of investment. It is argued that such an approach is often desirable in terms of real applications, because many industries are characterized by both uncertainty and strategic interaction between the firms. Besides extending the theory of investment, this line of work may be seen as an extension of the theory of industrial organization towards the direction that views market stability as one of the factors explaining rational behaviour of the firms.reviewe

An analysis of spending behaviour under liquidity constraints with an application to financial hedging

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Measuring Default Risk Premia from Default Swap Rates and EDFs

This paper estimates the degree of variation over time in the price for bearing exposure to U.S. corporate default risk during 2000-2004, based on the relationship between default probabilities, as estimated by Moody’s KMV EDFs, and default swap (CDS) market rates. The default-swap data, obtained through CIBC from 39 banks and specialty dealers, allow us to establish a strong link between actual and risk-neutral default probabilities in the three sectors that we analyze: broadcasting and entertainment, healthcare, and oil and gas. We find dramatic variation over time in risk premia, from peaks in the third quarter of 2002, dropping by roughly 50% to late 2003.

An asset and liability management model incorporating uncertainty

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Asset and Liability Management (ALIvI) is a well-established method, which enables companies to match future liabilities with future cash flow streams of assets. The first stage is to develop a deterministic model with forecast cash flow streams. In reality this can lead to results that are often volatile to deviations of future cash flows from their predicted values. There are two main stages to this problem. Firstly, there is the issue of representing the future uncertainties. To this end we have developed a scenario generator that forecasts alternative realizations of future cash flows streams of different assets using alternative scenarios about a financial Index and the Capital Asset Pricing Model (CAPM). Considering this with the deterministic model leads to the creation of ALM models which incorporate uncertainty. Having represented the uncertainty, we use an optimisation model to generate the current decisions concerning acquisition and disposal of assets. This model is a two stage stochastic programming model that aims to achieve targeted cash flows for each future year. Risk is represented in the form of assigning shares to different risk groups. In this thesis we describe our models of randomness and how they are captured in the two-stage stochastic programming model. We compare our model to a mean-variance representation. Both models are simulated through time. Backtesting is used to investigate the quality of both approaches