Electricity contracts differ substantially from financial contracts making traditional derivatives inapplicable. The main difference lies in the inability to store electricity causing the production to cover demand instantaneously. Therefore, electricity prices often jump to a multiple of their current value only to come back to normal level within a few hours. Spot price volatility is driven by demand whereas prices in the long run are rather affected by the physical ability of technology and generation capacity. A one factor price model like the geometric Brownian motion is insufficient to capture the mean-reverting behaviour of the electricity prices. The model needs to be extended by an additional stochastic factor to reflect electricity price movements realistically.
The evolution of sophisticated models and numerical techniques had a lasting effect on the risk perception of companies active in these markets. Facing the problem of managing their risk exposure, market participants seek to offset their risk by hedging and rebalancing their positions. The approach is referred to as the ‘Greeks' or sensitivity analysis whereby each risk factor is assigned to a 'Greek Letter'. An alternative risk management technique which summarizes the total risk in a single number is known as VaR. Despite its popularity, the VaR concept should be handled with caution when it is applied to electricity markets.
This work aims at providing further insights into risk management in electricity markets in general and into sensitivity analysis in particular. The goal of this paper is a systematic analysis and comparison of the ‘Greeks' under the assumption of different price dynamics. Moreover, it tries to demonstrate the limits of traditional risk management methods such as VaR and their modification. In the last part, model test are carried out in order prove the accuracy of the used software tool for option valuation.
Similar to the classical Markowitz approach it is possible to apply a mean-variance criterion to a multiperiod setting to obtain efficient portfolios. To represent the stochastic dynamic characteristics necessary for modelling returns a process of asset returns is discretized with respect to time and space and summarized in a scenario tree. The resulting optimization problem is solved by means of stochastic multistage programming. The optimal solutions show equivalent structural properties as the classical approach, however, by taking rebalancing activities into consideration a different efficient frontier is obtained.
For many banks, deals based on interest rate differences are one of the most important sources of income. In this context, the uncertainty regarding future interest rates and cash flows forms the central challenge in asset and liability management for every bank.
This paper investigates some common interest rate models for scenario generation in financial applications of stochastic optimization. We discuss conditions for the underlying distributions of state variables which preserve convexity of value functions in a multistage stochastic program. One- and multi-factor term structure models are estimated based on historical data for the Swiss Franc. An analysis of the dynamic behavior of interest rates generated with these models reveals several deficiencies which have an impact on the performance of investment policies derived from the stochastic program. While barycentric approximation is used here for the generation of scenario trees, these insights may be generalized to other discretization techniques as well.
