Calculation of Monte-Carlo Sensitivities for a portfolio of time coupled options and application to conventional power plants
Current European energy markets are significantly influenced by a strongly growing share of highly volatile renewable electricity generation, not only changing the absolute level and structure of electricity prices but also leading to an increased demand for conventional generation flexibility to compensate supply and demand variations. Standardised reserve energy products provide an established way to trade such flexibility, however imposing additional operational constraints on the involved generation portfolios. This enforces the ability of utilities to derive values and sensitivities of their asset portfolios subject to external reserve requirements in order to manage market price risks and perform state of the art portfolio optimisation. In this thesis we adopt the Proxy Simulation Scheme (PSS) method of Fries and Kampen (2007) – originally developed with a focus on fixed income markets – for the rolling intrinsic valuation of stylised power plants subject to complex technical constraints. Thereby we succeed to overcome well known numerical performance issues of standard Monte-Carlo approaches and are able to derive robust Monte-Carlo portfolio sensitivities with respect to the underlying price of electricity of both first and second order (∆ and Γ). We employ electricity prices that are affected by a strong photovoltaic production to take into account the current reality of energy markets in Europe. To our knowledge this application of the PSS methodology to energy related real option valuation has not been presented in academic literature before. Based on this approach we are able to analyse the impact of technical constraints including minimum up- and down-time and externally imposed reserve requirements on the risk profile of stand-alone power plant options in detail. We confirm the quality of our results via backtesting with a Delta-Gamma hedging framework and a Taylor series approach to replicate single step probability densities of option values via numerically derived sensitivities. Furthermore we evaluate and discuss a variety of power plant option portfolios including technically more flexible and inflexible portfolios as well as larger and smaller portfolios. Thereby we are able to analyse the impact of reserve requirements on different portfolios allowing us to provide a complete value and risk assessment of varying levels of reserve requirements in each portfolio context. Finally we compare portfolio results of simplified and numerically more cost efficient option dispatching rules with the full rolling intrinsic approach as applied otherwise throughout this thesis.