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Abstract:
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 plant.

Commodity, Hedging, Risk Management, Power Plant

Abstract:
This work discusses the calibration of instantaneous Libor correlations in the Libor market model. We extend existing calibration strategies by incorporation of spread option implied correlation information. The correlation structure implied by CMS spread options observed in the present-day’s market motivates us to extend existing parameterizations of ratio correlations by a new three parameter approach. For the first time, this paper presents an extensive empirical study of different parameterizations and their capability of matching market correlations. We can show that our approach leads to stable calibrations and gives a satisfactory fit to the market. We conclude our investigation with a pricing of a callable swap on cms spread using the parameterizations compared before.

LMM, Libor Market Model, calibration, correlation, market analysis, CMS spread option

Abstract:
This paper provides a two-factor model for electricity futures, which captures the main features of the market and fits the term structure of volatility. The approach extends the one-factor-model of Clewlow and Strickland to a two-factor model and modifies it to make it applicable to the electricity market. We will especially take care of the existence of delivery periods in the underlying futures. Additionally, the model is calibrated to options on electricity futures and its performance for practical application is discussed.

Energy derivatives, Futures, Option, Two-Factor Model, Volatility Term Structure