A Power Market Forward Curve with Hydrology Dependence - An Approach based on Artificial Neural Networks

This paper develops an hourly forward curve for power markets where the intra-day and intra-week shapes (profiles) depend on the level of the hydrological balance. The shaping model is based on a feed-forward Artificial Neural Network (ANN), which is trained on a historical data set of hourly electricity spot prices from the Nord Pool market and weekly measurements of the Nordic hydrological balance. The yearly seasonal cycle is estimated with historical electricity forward prices from the Nasdaq OMX Commodities exchange. We calibrate the shaping model to prevailing electricity forward prices and proceed to demonstrate its most important properties. By using comparative static analysis we particulary focus on the hydro dependence of the shapes. We conclude the paper with a real world valuation task. By combining our proposed forward curve with a simple Ornstein-Uhlenbeck process we price a strip of hourly call options on the electricity spot price under different hydrological scenarios

Closed Form Valuation of Three-Asset Spread Options With a view towards Clean Dark Spreads

We perform a slight generalization of the Bjerksund and Stensland (2011) spread option valuation formula to cover three-asset spread options. We investigate the pricing performance of the model against the corresponding version of the Kirk formula and the true price calculated with Monte Carlo methods. The numerical setting of the evaluation is designed to mimic a real market situation in the German OTC market for clean dark spread options.The results show that both models give similar and accurate price estimates (compared to the true option price). Comparing the performance between the models we conclude that the three-asset Bjerksund-Stensland formula performs marginally better compared to the three-asset Kirk formula (counting the number of test cases with the lowest absolute pricing error against the true option price)

Essays on Financial Risks

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Essays on Financial Risks and Derivatives with Applications to Electricity Markets and Credit Markets

Contracts traded on international financial and commodity markets are associated with complex risk structures. In this dissertation we are concerned with two specific types of risks; market risks and credit risks. The first chapter investigates market risks in the context of the Nordic electricity market. The paper performs in- and out-of-sample backtesting of a VaR model based on GARCH volatility with NIG innovations. Furthermore, the Cornish-Fisher expansion is applied to get analytical approximations of the NIG based VaR estimates. Backtesting shows that the model is a promising alternative to the well known Gaussian GARCH. Results also show that the Cornish-Fisher approximation gives reasonable outcomes for the less extreme quantiles, especially when the return distribution is close to normality. The second chapter continues to explore market risks on the Nordic electricity market. A mean-reverting jump diffusion stochastic volatility model for the electricity spot price is suggested. The model is estimated with a combination of standard statistical methods and a Markov Chain Monte Carlo (MCMC) algorithm. Results indicate that the model captures large parts of the trajectorial and statistical properties of the spot price. Hence, the model is a candidate for applications in risk management and derivative pricing. The third chapter is again concerned with market risks. The spot price model from chapter two is applied to pricing of the forward curve in the Nordic electricity market. A semi-closed solution for the forward curve is derived, and then calibrated to market data. Results show that the model outperforms its benchmark. The final chapter of the dissertation goes in the direction of credit risks. The paper extends Merton’s classical corporate bond credit risk model to an international setting with stochastic domestic and foreign interest rates. In an extensive comparative static analysis we study how the credit spread in the model depends on the currency and related variables

Markov Chain Monte Carlo Estimation of a Multi-Factor Jump Diffusion Model for Power Prices

In this paper we generalize the electricity spot price model of Lucia and Schwartz by a two-factor model with jumps and stochastic volatility. We estimate the model on daily spot price data from the Nordic market using an approach that combines traditional statistical methods with a Markov chain Monte Carlo algorithm. Results show that the model captures most of the trajectorial and the statistical characteristics of the electricity spot price. Further, we find that the inclusion of stochastic volatility is crucial to separate spikes from the normal price process. Moreover, we estimate that the correlation between the spot price and its stochastic volatility is negative

Pricing Electricity Swaptions under a Stochastic Volatility Term-Structure Model

This paper suggests a stochastic volatility term-structure model applied to the pricing of electricity swaptions in the Nord Pool market. The volatility structure in the model is specified as a product of a time-dependent function that handles the maturity effect, and a Cox-Ingersoll-Ross process that captures the volatility smile. We employ a Fourier based approach to price electricity swaptions and perform an empirical analysis by calibrating the model to a data set consisting of more than 12000 implied volatilities corresponding to swaption prices from the Nord Pool market. To our knowledge this is one of the first studies of the volatility smile in the market for electricity swaptions. We show that our model outperforms the log-normal benchmark in-sample and out-of-sample

Cross-Commodity News Transmission and Volatility Spillovers in the German Energy Markets

This study investigates volatility spillovers to electric power from large exogenous shocks in the prices of gas, coal, and carbon emission allowances in the German energy market. Our sample ranges from 2008 to 2016 and covers periods of different market conditions. We use a general VAR-BEKK model and the volatility impulse response function methodology to analyze and evaluate the spillover effects. Special attention is paid to selecting an appropriate econometric volatility model. Our results show that the spillover effects often are of a significant magnitude and display considerable variation over time and across commodities. Coal and gas generate non-negligible spillovers during almost the entire sample period. Carbon has very little impact during the early and late parts of the sample, but generates significant, and highly variable, spillovers during the period from 2011 to the end of 2014

Cross-Commodity News Transmission and Volatility Spillovers in the German Energy Markets

This study investigates volatility spillovers to electric power fromlarge exogenous shocks in the prices of gas, coal, and carbon emissionallowances in the German energy market. Our sample ranges from 2008 to 2016and covers periods of different market conditions. We use a general VAR-BEKKmodel and the volatility impulse response function methodology to analyze andevaluate the spillover effects. Special attention is paid to selecting anappropriate econometric volatility model. Our results show that the spillovereffects often are of a significant magnitude and display considerablevariation over time and across commodities. Coal and gas generatenon-negligible spillovers during almost the entire sample period. Carbon hasvery little impact during the early and late parts of the sample, butgenerates significant, and highly variable, spillovers during the period from2011 to the end of 2014