Scientific stochastic volatility models for the European carbon markets: forecasting and extracting conditional moments

This paper builds and implements a multifactor stochastic volatility model for the latent (and observable) volatility of the carbon front December forward contracts at the European Carbon Exchanges, applying Bayesian Markov chain Monte Carlo simulation methodologies for estimation, inference, and model adequacy assessment. Stochastic volatility is the main way time-varying volatility is modelled in financial markets. Our main objective is therefore to structure a scientific model specifying volatility as having its own stochastic process. Appropriate model descriptions broaden the applications into derivative pricing purposes, risk assessment and asset allocation and portfolio management. From an estimated optimal and appropriate stochastic volatility model, the paper reports risk and portfolio measures, extracts conditional one-step-ahead moments (smoothing), forecast one-step-ahead conditional volatility (filtering), evaluates shocks from conditional variance functions, analyses multi-step-ahead dynamics, and calculates conditional persistence measures. The analysis adds insight and enables forecasts to be made, building up the methodology for developing valid scientific commodity market models

Kinesisk kullimport og norsk gassproduksjon/-eksport gir CO2-utslipp reduksjoner tilsvarende 7-8 norske komplette bilparker

Internasjonale miljøforkjempere som ønsker et forbud mot økt kinesisk import av kull og redusert produksjon av norsk naturgass tar grundig feil. Det faktum at Kina driver opp kullprisen i verdensmarkedet og Norge presser prisen på naturgass ned, reduserer de globale karbonutslippene (CO2). The International Energy Agency (IEA) har definert utslipp ved bruk av naturgass som innsatsfaktor for elektrisitetsproduksjon til omtrent halvparten CO2 per mega-watt time sammenlignet med kull. IEA oppgir at Europa og USA til sammen konsumerer 7 milliarder MWh elektrisitet per år. Et bytte av innsatsfaktorer fra kull til naturgass i internasjonal elektrisitetsproduksjon er den største enkeltstående faktor for reduksjon av globale CO2 utslipp. Dette skjer uten byråkratiske virkemidler som subsidier, avgifter eller direkte reguleringer

On the Estimation of Extreme Values for Risk Assessment and Management: The ACER Method

In this paper we use an Average Conditional Exceedance Rate (ACER) method to model the tail of the price change distribution of daily spot prices in the Nordic electricity market, Nord Pool Spot. We use an AR-GARCH model to remove any seasonality, serial correlation and heteroskedasticity from the data before modelling the residuals from this filtering process with the ACER method. We show that using the conditional ACER method for Value-at-Risk forecasts give significant improvement over a standard AR-GARCH model with normal or Student’s-t distributed errors. Compared to a conditional generalized Pareto distribution (GPD) fitted with the Peaks-over-Threshold (POT) method, the conditional ACER method produces slightly more accurate quantile forecasts for the highest quantiles.publishedVersio

Covariance estimation using high-frequency data : an analysis of Nord Pool electricity forward data

The modeling of volatility and correlation is important in order to calculate hedge ratios, value at risk estimates, CAPM betas, derivate pricing and risk management in general. Recent access to intra-daily high-frequency data for two of the most liquid contracts at the Nord Pool exchange has made it possible to apply new and promising methods for analyzing volatility and correlation. The concepts of realized volatility and realized correlation are applied, and this study statistically describes the distribution (both distributional properties and temporal dependencies) of electricity forward data from 2005 to 2009. The main findings show that the logarithmic realized volatility is approximately normally distributed, while realized correlation seems not to be. Further, realized volatility and realized correlation have a long-memory feature. There also seems to be a high correlation between realized correlation and volatilities and positive relations between trading volume and realized volatility and between trading volume and realized correlation. These results are to a large extent consistent with earlier studies of stylized facts of other financial and commodity markets.publishedVersio

Modelling day-ahead Nord Pool forward-price volatility: realized rolatility versus GARCH models

The argument that better volatility estimates can be obtained by using standard time-series techniques on non-parametric volatility measures constructed from high- frequency intradaily returns has been prevalent over the past decade. This study uses high- frequency data and the concept of realized volatility to make one-day-ahead predictions of Nord Pool forward-price volatility. We compare the predictions obtained from realized volatility using standard time-series techniques with the more traditional GARCH framework. Additionally, we examine whether different approaches of decomposing the total variation, and whether inclusion of exogenous effects, improves the accuracy or not. The main findings suggest that significant improvements in the one-day-ahead Nord Pool forward-price volatility predictions can be obtained by applying high-frequency data and the concept of realized volatility.publishedVersio

Bootstrapped Nonlinear Impulse-Response Analysis: The FTSE100 (UK) and the NDX100 (US) Indices 2012-2021

This paper presents bootstrapped nonlinear impulse response function analyses for general step ahead mean and volatility densities. From strictly (ergodic and) stationary series and BIC optimal non-linear model coefficients the paper establish step ahead densities for both the conditional mean and volatility. For sampling variances using one thousand samples and conditioning all paths on the daily impulses -5, -3,…,5% all mean and volatility responses show mean reversion. For the volatility, all increases seem to arise from negative index movements suggesting strong asymmetry. Furthermore, the model coefficients for the volatility exhibit data dependence suggesting ability to predict volatility. The indices report some striking step ahead differences for both the mean and the volatility. For the mean, only the NDX100 seems to show overreactions. For the volatility, for both positive and negative impulses the NDX100 reports higher volatility responses then FTSE100. However, asymmetry is manifested for both indices suggesting that trading volatility as an asset may insure against market crashes and be an excellent diversification instrument. Finally, using a stochastic volatility model to obtain calibrated functions that give step ahead predicted values for static predictions, enrich participants derivative trading strategies (i.e. volatility swaps)

The Nordic/Baltic Spot Electric Power System Price: Univariate Nonlinear Impulse-Response Analysis

This paper revisits the conditional mean and volatility density characteristics of the System Price settled by the Nordic/Baltic Spot electric power market (1993-2017). The main purpose of this paper is an analysis of the nonlinear impulse-response features (shocks) in the non-storable commodity market. Initially, we extract all deterministic seasonality and non-stationary trend and scale features from the series. A strictly stationary model reports serial correlation for the mean and clustering, asymmetry and level effects for the volatility. For the mean, the impulse-response analysis reports linear and symmetric mean reversion for any price movements. For the volatility, small price movements report symmetric and decreasing volatility. In contrast, for larger absolute price movements, the volatility show a non-linear increase as well as fast-growing negative asymmetries. The impulse persistence is therefore relatively short. For the entrance of renewables in the energy market, the sub-period 2008-2017 reports major systematic changes for the mean, the volatility, the asymmetry and the persistence. In fact, the renewables era has made changes to all the fundamental features of the Nordic/Baltic electricity market

Step-ahead Spot Price Densities using daily Synchronous Price and Wind Forecast Changes

This paper uses non‐linear methodologies to follow the synchronously reported relationship between the Nordic/Baltic electric daily spot auction prices and geographical relevant wind forecasts in MWh from early 2013 to 2020. It is a well‐known market (auctions) microstructure fact that the daily wind forecasts are information available to the market before the daily auction bid deadline at 11 a.m. The main objective is therefore to establish conditional and marginal step ahead spot price density forecast using a stochastic representation of the lagged, synchronously reported and stationary spot price and wind forecast movements. Using an upward expansion path applying the Schwarz (Bayesian information criterion [BIC]) criterion and a battery of residual test statistics, an optimal maximum likelihood process density is suggested. The optimal specification reports a significant negative covariance between the daily price and wind forecast movements. Conditional on bivariate lags from the SNP information and using the known market information for wind forecast movements at t1, the paper establishes one‐step‐ahead bivariate and marginal day‐ahead spot price movement densities. The result shows that wind forecasts significantly influence the synchronously reported spot price densities (means and volatilities). The paper reports day‐ahead bivariate and marginal densities for spot price movements conditional on several very plausible price and wind forecast movements. The paper suggests day‐ahead spot price predictions from conditional and synchronously reported wind forecasts movements. The information should increase market participants spot market insight and consequently make spot price predictions more accurate and the confidence interval considerably narrower

Projecting and Forecasting the Latent Volatility for the Nasdaq OMX Nordic/Baltic Financial Electricity Market Applying Stochastic Volatility Market Characteristics

In this empirical study, multifactor stochastic volatility models for the financial Nordic/Baltic power markets are developed, implemented, and analyzed. Stochastic volatility projections are the primary aim, followed by volatility forecasts and market repercussions. The research provides a functional variant of the conditional distribution (f(x|y)) based on conditional moments and a long-simulated state vector realization (MCMC-GMM) that is evaluated on observed data (a non-linear Kalman Filter) and applicable for step-forward volatility forecasts. For front year and quarter financial electricity contracts, the SV model creates two mean-reverting factors: one persistent and slowly moving component and one choppy, rapidly moving component. According to these factors, static volatility predictions with optimum and generous lags have a Theil covariance percentage of well over 97 percent for the front year contracts and 86 percent for the front quarter contracts. The volatility visibility and its associated static forecasts improve market transparency and will eventually make diversification and risk management easier to implement