Pricing forward contracts in power markets by the certainty equivalence principle : explaining the sign of the market risk premium.

In this paper we provide a framework that explains how the market risk premium, defined as the difference between forward prices and spot forecasts, depends on the risk preferences of market players and the interaction between buyers and sellers. In commodities markets this premium is an important indicator of the behavior of buyers and sellers and their views on the market spanning between short-term and long-term horizons. We show that under certain assumptions it is possible to derive explicit solutions that link levels of risk aversion and market power with market prices of risk and the market risk premium. We apply our model to the German electricity market and show that the market risk premium exhibits a term structure which can be explained by the combination of two factors. Firstly, the levels of risk aversion of buyers and sellers, and secondly, how the market power of producers, relative to that of buyers, affects forward prices with different delivery periodsContango; Backwardation; Market price of risk; Electricity forwards; Market risk premium; Forward risk premium; Forward bias; Market power;

Pricing forward contracts in power markets by the certainty equivalence principle: Explaining the sign of the market risk premium.

In this paper we provide a framework that explains how the market risk premium, defined as the difference between forward prices and spot forecasts, depends on the risk preferences of market players and the interaction between buyers and sellers. In commodities markets this premium is an important indicator of the behavior of buyers and sellers and their views on the market spanning between short-term and long-term horizons. We show that under certain assumptions it is possible to derive explicit solutions that link levels of risk aversion and market power with market prices of risk and the market risk premium. We apply our model to the German electricity market and show that the market risk premium exhibits a term structure which can be explained by the combination of two factors. Firstly, the levels of risk aversion of buyers and sellers, and secondly, how the market power of producers, relative to that of buyers, affects forward prices with different delivery periodsContango; Backwardation; Market price of risk; Electricity forwards; Market risk premium; Forward risk premium; Forward bias; Market power;

Cross-commodity analysis and applications to risk management.

The understanding of joint asset return distributions is an important ingredient for managing risks of portfolios. Although this is a well-discussed issue in fixed income and equity markets, it is a challenge for energy commodities. In this study we are concerned with describing the joint return distribution of energy-related commodities futures, namely power, oil, gas, coal, and carbon. The objective of the study is threefold. First, we conduct a careful analysis of empirical returns and show how the class of multivariate generalized hyperbolic distributions performs in this context. Second, we present how risk measures can be computed for commodity portfolios based on generalized hyperbolic assumptions. And finally,we discuss the implications of our findings for risk management analyzing the exposure of power plants, which represent typical energy portfolios. Our main findings are that risk estimates based on a normal distribution in the context of energy commodities can be statistically improved using generalized hyperbolic distributions. Those distributions are flexible enough to incorporate many characteristics of commodity returns and yield more accurate risk estimates. Our analysis of the market suggests that carbon allowances can be a helpful tool for controlling the risk exposure of a typical energy portfolio representing a power plantCommodities; Risk;

Cross-Commodity Analysis and Applications to Risk management.

The understanding of joint asset return distributions is an important ingredient for managing risks of portfolios. While this is a well-discussed issue in fixed income and equity markets, it is a challenge for energy commodities. In this paper we are concerned with describing the joint return distribution of energy related commodities futures, namely power, oil, gas, coal and carbon. The objective of the paper is threefold. First, we conduct a careful analysis of empirical returns and show how the class of multivariate generalized hyperbolic distributions performs in this context. Second, we present how risk measures can be computed for commodity portfolios based on generalized hyperbolic assumptions. And finally, we discuss the implications of our findings for risk management analyzing the exposure of power plants which represent typical energy portfolios. Our main findings are that risk estimates based on a normal distribution in the context of energy commodities can be statistically improved using generalized hyperbolic distributions. Those distributions are flexible enough to incorporate many characteristics of commodity returns and yield more accurate risk estimates. Our analysis of the market suggests that carbon allowances can be a helpful tool for controlling the risk exposure of a typical energy portfolio representing a power plantCommodities; Risk;

Carbon default swap – disentangling the exposure to carbon risk through CDS

Using Credit Default Swap spreads, we construct a forward-looking, market-implied carbon risk factor and show that carbon risk affects firms’ credit spread. The effect is larger for European than North American firms and varies substantially across industries, suggesting the market recognizes where and which sectors are better positioned for a transition to a low-carbon economy. Moreover, lenders demand more credit protection for those borrowers perceived to be more exposed to carbon risk when market-wide concern about climate change risk is elevated. Lenders expect that adjustments in carbon regulations in Europe will cause relatively larger policy-related costs in the near future

Carbon default swap – disentangling the exposure to carbon risk through CDS

Using Credit Default Swap spreads, we construct a forward-looking, market-implied carbon risk factor and show that carbon risk affects firms’ credit spread. The effect is larger for European than North American firms and varies substantially across industries, suggesting the market recognizes where and which sectors are better positioned for a transition to a low-carbon economy. Moreover, lenders demand more credit protection for those borrowers perceived to be more exposed to carbon risk when market-wide concern about climate change risk is elevated. Lenders expect that adjustments in carbon regulations in Europe will cause relatively larger policy-related costs in the near future

Cross-Commodity Analysis and Applications to Risk management

The understanding of joint asset return distributions is an important ingredient for managing risks of portfolios. While this is a well-discussed issue in fixed income and equity markets, it is a challenge for energy commodities. In this paper we are concerned with describing the joint return distribution of energy related commodities futures, namely power, oil, gas, coal and carbon. The objective of the paper is threefold. First, we conduct a careful analysis of empirical returns and show how the class of multivariate generalized hyperbolic distributions performs in this context. Second, we present how risk measures can be computed for commodity portfolios based on generalized hyperbolic assumptions. And finally, we discuss the implications of our findings for risk management analyzing the exposure of power plants which represent typical energy portfolios. Our main findings are that risk estimates based on a normal distribution in the context of energy commodities can be statistically improved using generalized hyperbolic distributions. Those distributions are flexible enough to incorporate many characteristics of commodity returns and yield more accurate risk estimates. Our analysis of the market suggests that carbon allowances can be a helpful tool for controlling the risk exposure of a typical energy portfolio representing a power plan

Nonparametric statistical methods and the pricing of derivative securities

In this review paper we summarise several nonparametric methods recently applied to the pricing of financial options. After a short introduction to martingale-based option pricing theory, we focus on two possible fields of application for nonparametric methods: the estimation of risk-neutral probabilities and the estimation of the dynamics of the underlying instruments in order to construct an internally consistent model

Strong Laws And Summability for Sequences of φ-Mixing Random Variables in Banach Spaces

In this note the almost sure convergence of stationary, '-mixing sequences of random variables with values in real, separable Banach spaces according to summability methods is linked to the fulfillment of a certain integrability condition generalizing and extending the results for i.i.d. sequences. Furthermore we give via Baum-Katz type results an estimate for the rate of convergence in these laws. 1 Introduction and main result Let (\Omega ; A; IP ) be a probability space rich enough so that all random variables used in the sequel can be defined on this space. If X 0 ; X 1 ; : : : is a sequence of independent, identically distributed (i.i.d.) real valued random variables, then the almost sure (a.s.) convergence of such a sequence according to certain summability methods is equivalent to the fulfillment of certain integrability conditions on X 0 , see e.g.[5, 6, 12, 19, 24]. Some of the above results have been extended to sequences of stationary, '-mixing sequences of real-valued ran..