Ambiguous Aggregation of Expert Opinions: The Case of Optimal R&D Investment

How should a decision-maker allocate R&D funds when a group of experts provides divergent estimates on a technology's potential effectiveness? To address this question, we propose a simple decision-theoretic framework that takes into account ambiguity over the aggregation of expert opinion and a decision-maker's attitude towards it. In line with the paper's focus on R&D investment, decision variables in our model may affect experts' subjective probability distributions of the future potential of a technology. Using results from convex optimization, we are able to establish a number of analytical results including a closed-form expression of our model's value function, as well as a thorough investigation of its differentiability properties. We apply our framework to original data from a recent expert elicitation survey on solar technology. The analysis suggests that more aggressive investment in solar technology R&D is likely to yield significant dividends even, or rather especially, after taking ambiguous aggregation into account.Aggregation, Ambiguity, R&D, Expert Opinions, Convex/Conic Optimization

Financial engineering models for electricity market : futures pricing, liquidity risks and investment

The dissertation addresses some important topics arising in restructured electricity markets. A first part is dedicated to the pricing of power contingent claims. Electricity is a derivative product, structurally related to other energy assets: it is mainly produced by fuel fired thermal power stations. For pricing power derivatives, we propose a hybrid model that accounts for these structural relationships and which can be understood as a combination of both the fundamentals of power generation and the classical stochastic framework. It is recognized that financial markets deviate to varying degrees from the perfect paradigm and in particular that electricity markets significantly remain less liquid than other commodity markets. We assess the effect of limited liquidity in power exchanges by using an equilibrium model where illiquid contracts prevent agents from hedging up to their desired level and study the implications of the introduction of such market frictions in the theory of derivatives pricing. In the second part of the thesis we elaborate on investment valuations in stochastic generation capacity expansion models. Designed originally as optimization problems for the regulated monopoly industry, those models can be interpreted as equilibrium models in a competitive environment. We specifically develop a procedure to accurately estimate the distribution of the margin profit in a standard stochastic program. We eventually focus on the risk averse problem using the good-deal risk measure, which can be seen as an extension of the stochastic discount factor constructed from standard corporate finance theories such as the CAPM and the APT.(FSA 3) -- UCL, 201

Liquidity risks on power exchanges

Financial derivatives are important hedging tool for asset’s manager. Electricity is by its very nature the most volatile commodity, which creates big incentive to share the risk among the market participants through financial contracts. But, even if volume of derivatives contracts traded on Power Exchanges has been growing since the beginning of the restructuring of the sector, electricity markets continue to be considerably less liquid than other commodities. This paper tries to quantify the effect of this insufficient liquidity on power exchange, by introducing a pricing equilibrium model for power derivatives where agents can not hedge up to their desired level. Mathematically, the problem is a two stage stochastic Generalized Nash Equilibrium and its solution is not unique. Computing a large panel of solutions, we show how the risk premium and player’s profit are affected by the illiquidity

Liquidity risks on power exchanges: a generalized Nash equilibrium model

The extreme volatility of electricity prices makes their financial derivatives important instruments for asset managers. Even if the volume of derivative contracts traded on Power Exchanges has been growing since the inception of the restructuring of the sector, electricity remains considerably less liquid than other commodity markets. This paper assesses the effect of limited liquidity in power exchanges using an equilibrium model where agents cannot hedge up to their desired level. Mathematically, the problem is formulated as a two stage stochastic Generalized Nash equilibrium with possibly multiple equilibria. Computing a large panel of solutions, we show how the risk premium and players profits are affected by illiquidity. We also dhow that the illiquidity in the FTR market affects the trades in the electricity futures market

The valuation of power futures based on optimal dispatch

The pricing of contingent claims in the wholesale power market is a controversial topic. Important challenges come from the non-storability of electricity and the number of parameters that impact the market. We propose an equilibrium model based on the fundamentals of power generation. In a perfect competitive market, spot electricity prices are determined by the marginal cost of producing the last unit of power. Electricity can be viewed as a derivative of demand, fuels prices and carbon emission price. We extend the Pirrong-Jermakayan model such as to incorporate the main factors driving the marginal cost and the non-linearities of electricity prices with respect to fuels prices. As in the Pirrong-Jermakayan framework, any contingent claims on power must satisfy a high dimensional PDE that embeds a market price of risk, as load is not a traded asset. Analyzing the specificity of the marginal cost in power market, we simplify the problem for evaluating power futures so that it becomes computationally tractable. We test our model on the German EEX for ”German Month Futures” with maturity of June and September 2008

Investment with incomplete markets for risk: the need for long-term contracts

Barring subsidies, investment in the power generation sector has come to an almost complete halt in the restructured European power sector. Market and regulatory failures such as the well known missing money (see Joskow, (2006)) but also normal market features such as risk, possibly also affected by market failures like market incompleteness are mentioned as common causes for the situation. This paper discusses incomplete risk trading and its impact on investment. The analysis applies computable stochastic equilibrium models on a simple market model of the Energy Only type. The paper first compares the cases of complete and fully incomplete markets (full risk trading and no risk trading). It continues by testing the impact of different risk trading contracts on both welfare and investment. We successively consider Contracts for Difference, Reliability Options with and without physical back up that we add to our Energy Only market model. We test the impact of market liquidity on the results. Finally, we compare these methods to a Forward Capacity Market that we also add to the energy only model. We complete the paper by interpretation of these results in terms of hurdle rate implied by these risk-trading situations

On the multiplicity of solutions in generation capacity investment models with incomplete markets: a risk-averse stochastic equilibrium approach

Investment in generation capacity has traditionally been evaluated by computing the present value of cashflows accruing from new equipment in a market with globally optimized capacity mix. The competition and risk that now prevail in the sector may require a more refined analysis. We consider a competitive market with agents investing in some mix of capacities: the risk exposure of a plant and the attitude towards risk of the owner depend on the plant and the portfolio of its capacities. They may also depend on hedging contracts acquired by the investor on the market if such contracts exist. We represent these effects through equilibrium models of generation capacity in incomplete markets. The models come in different versions depending on the portfolio of physical plants and hedging contracts. These modify the long-term risk of the plants, the attitude of the owners towards risk, and hence the incentive to invest. The models involve risk-averse producers and consumers, and their behavior is represented by convex risk measures. We use degree theory to prove existence and explore multiplicity of equilibrium solutions

Risk exposure and Lagrange multipliers of nonanticipativity constraints in multistage stochastic problems

We take advantage of the interpretation of stochastic capacity expansion problems as stochastic equilibrium models for assessing the risk exposure of new equipment in a competitive electricity economy. We develop our analysis on a standard multistage generation capacity expansion problem. We focus on the formulation with nonanticipativity constraints and show that their dual variables can be interpreted as the net margin accruing to plants in the different states of the world. We then propose a procedure to estimate the distribution of the Lagrange multipliers of the nonanticipativity constraints associated with first stage decisions; this gives us the distribution of the discounted cash flow of profitable plants in that stage

Ambiguous Aggregation of Expert Opinions: The Case of Optimal R&D Investment

How should a decision-maker allocate R&D funds when a group of experts provides divergent estimates on a technology's potential effectiveness? To address this question, we propose a simple decision-theoretic framework that takes into account ambiguity over the aggregation of expert opinion and a decision-maker's attitude towards it. In line with the paper's focus on R&D investment, decision variables in our model may affect experts' subjective probability distributions of the future potential of a technology. Using results from convex optimization, we are able to establish a number of analytical results including a closed-form expression of our model's value function, as well as a thorough investigation of its differentiability properties. We apply our framework to original data from a recent expert elicitation survey on solar technology. The analysis suggests that more aggressive investment in solar technology R&D is likely to yield significant dividends even, or rather especially, after taking ambiguous aggregation into account

Demand response in Indian electricity market

This paper outlines a methodology for implementing cost of service regulation in retail market for electricity in India when wholesale market is liberalised and operates through an hourly spot market. As in a developing country context political considerations make tariff levels more important than supply security, satisfying the earmarked level of demand takes a back seat. Retail market regulators are often forced by politicians to keep the retail tariff at suboptimal level. This imposes budget constraint on distribution companies to procure electricity that it requires to meet the earmarked level of demand. This is the way demand response is introduced in the system and has its impact on spot market prices. We model such a situation of not being able to serve the earmarked demand as disutility to the regulator which has to be minimised and we compute associated equilibrium. This results in systematic mechanism for cutting loads. We find that even a small cut in ability of the distribution companies to procure electricity from the spot market has profound impact on the prices in the spot market. © 2012 Elsevier Ltd