Derivatives pricing in energy markets: an infinite dimensional approach

Based on forward curves modelled as Hilbert-space valued processes, we analyse the pricing of various options relevant in energy markets. In particular, we connect empirical evidence about energy forward prices known from the literature to propose stochastic models. Forward prices can be represented as linear functions on a Hilbert space, and options can thus be viewed as derivatives on the whole curve. The value of these options are computed under various specifications, in addition to their deltas. In a second part, cross-commodity models are investigated, leading to a study of square integrable random variables with values in a "two-dimensional" Hilbert space. We analyse the covariance operator and representations of such variables, as well as presenting applications to pricing of spread and energy quanto options

Uncovering predictability in the evolution of the WTI oil futures curve

Accurately forecasting the price of oil, the world's most actively traded commodity, is of great importance to both academics and practitioners. We contribute by proposing a functional time series based method to model and forecast oil futures. Our approach boasts a number of theoretical and practical advantages including effectively exploiting underlying process dynamics missed by classical discrete approaches. We evaluate the finite-sample performance against established benchmarks using a model confidence set test. A realistic out-of-sample exercise provides strong support for the adoption of our approach with it residing in the superior set of models in all considered instances.Comment: 28 pages, 4 figures, to appear in European Financial Managemen

Pooling, Pricing and Trading of Risks

Abstract. Exchange of risks is considered here as a transferableutility, cooperative game, featuring risk averse players. Like in competitive equilibrium, a core solution is determined by shadow prices on state-dependent claims. And like in finance, no risk can properly be priced only in terms of its marginal distribution. Pricing rather depends on the pooled risk and on the convolution of individual preferences. The paper elaborates on these features, placing emphasis on the role of prices and incompleteness. Some novelties come by bringing questions about existence, computation and uniqueness of solutions to revolve around standard Lagrangian duality. Especially outlined is how repeated bilateral trade may bring about a price-supported core allocation.Keywords: cooperative game; transferable utility; core; risks; mutual insurance; contingent prices; bilateral exchange; supergradients; stochastic approximation.

Arbitrage Pricing in Electricity Markets.

Electricity market; Pricing;

Existence of GE: Are the Cases of Non Existence a Cause of Serious Worry?

In this work, we attempt to characterize the main theoretical difficulties to prove the existence of competitive equilibrium in infinite dimensional models. We shall show cases in which it is not possible to prove the existence of equilibrium and some others in which, however the existence of equilibrium can be proved, the equilibrium prices seem not to have natural economic interpretation. Nevertheless in pure exchange economies, most of these difficulties may be avoided by mild restrictions on the model. In productive economies new specifics problem appear, for instance non convexity of the production sets or non boundedness of the feasible allocation sets. To prove the existence and the efficiency of the equilibrium in productive economies we need some strong hypothesis about the technological possibilities of each firm.

Hedging electricity swaptions using partial integro-differential equations

AbstractThe basic contracts traded on energy exchanges are swaps involving the delivery of electricity for fixed-rate payments over a certain period of time. The main objective of this article is to solve the quadratic hedging problem for European options on these swaps, known as electricity swaptions. We consider a general class of Hilbert space valued exponential jump-diffusion models. Since the forward curve is an infinite-dimensional object, but only a finite set of traded contracts are available for hedging, the market is inherently incomplete. We derive the optimization problem for the quadratic hedging problem under the risk neutral measure and state a representation of its solution, which is the starting point for numerical algorithms

Metabolizing Capital: Writing, Information, and the Biophysical World

While the discipline of rhetoric and composition has looked at a variety of topics related to the materiality of writing, the majority of materialist approaches limit their scope to local, situated writing practices. However, with the spread of digital media and the establishment of a global, networked infrastructure for communication and inscription, the abundant textuality that has emerged in the early 21st century demands that we develop more rigorous materialist approaches to the study and teaching of writing. This growing textual environment has been called, in popular and academic discourse, Web 2.0—a more “social Web” than its early form in the late 1990s, one that encourages more interaction and collaboration between users. The ethos of sharing that defines Web 2.0 has been celebrated by writing scholars as a qualitatively new public sphere where we are writing and participating more than ever. Yet, underlying our exuberance of Web 2.0 is the problematic assumption that more writing is an intrinsic good. As more writing is produced, the logic goes, the richer the opportunities for human agency. In a world of infinite resources, such a productivist ethos makes sense; but in a world of finite resources, one whose health is intertwined with our global network of writing technologies, unrestrained textual production has become a threat to other human and nonhuman systems. In this dissertation, I analyze current materialist approaches to writing to theorize how the usefulness of Web 2.0 technologies--and the writing labor they harness—have become necessary agents in the production of capitalist, consumer culture. Drawing on ecological models of writing and supplementing them with Marxian concepts of value, metabolism, and capital circulation, I explore the historical and dialectical relations that have given rise to a new phase of digital culture, one called Web 3.0, where the celebrated use value of Web 2.0 writing is eclipsed by the ascendant exchange value of Big Data--the massive substratum of consumer data that is produced as a by-product of our writing. Because the economic value of user data depends on two critical resources--the labor of our writing and the finite natural resources of the planet—our celebration of the productivity of Web 2.0 is in direct antagonism with other natural systems, including the organic system of the writing body. I conclude with a sequence of writing activities designed to help students foster critical, ecological literacies that will prepare them to grapple with the social and ecological problems emerging in Web 3.

Existence and Uniqueness of Equilibrium in a Reinsurance Syndicate

In this paper we consider a reinsurance syndicate, assuming that Pareto optimal allocations exist. Under a continuity assumption on preferences, we show that a competitive equilibrium exists and is unique. Our conditions allow for risks that are not bounded, and we show that the most standard models satisfy our set of sufficient conditions, which are thus not too restrictive. Our approach is to transform the analysis from an infinite dimensional to a finite dimensional setting.Existence of equilibrium; uniqueness of equilibrium; Pareto optimality; reinsurance model; syndicate theory; risk tolerance; exchange economy; probability distributions; Walras’ law

A logical reconstruction of pure exchange economics

The basic core of the theory of exchange is reconstructed in set-theoretical terms. The central notions of the models are the following: person, kind of good, total endowment of goods, endowment of persons, price, equilibrium and utility. All these notions are used in the central hypothese of maximization of utility. Some simple standard theorems and some special hypotheses are formulated concisely. The theory is described in the structuralistic frame of (Sneed, 1971). The notions of utility and equilibrium are treated as theoretical terms relative to the theoryof pure exchange economics