Schedule for: 19w5229 - New Challenges in Energy Markets - Data Analytics, Modelling and Numerics

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions.

Price integration is extensively studied in commodity markets as a means of examining the degree of integration between regions of a geographically diverse market. In this paper, we use an inverse optimization approach to provide an analysis of price integration as a function of underlying transportation network features. Results include a price decomposition which explicitly isolates the influences of market forces (supply and demand), transportation costs and congestion surcharges on price integration. Using this price decomposition, we develop a novel methodology that captures price shocks indicative of structural disruptions in the underlying network using pricing data alone. Applying the methodology to gasoline prices in the South-Eastern US, we find the methodology is able to capture the effects of well-documented network disruptions, and evidence of capacity-driven price disruptions during normal operations.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Meet in the Corbett Hall Lounge for a guided tour of The Banff Centre campus.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

An important but rarely-addressed option pricing question is how to choose appropriate strikes for implied volatility inputs when pricing more exotic multi-asset derivatives. By means of Malliavin Calculus we construct an asymptotically optimal log-linear strike convention for exchange options under stochastic volatility models. This novel approach allows us to minimize the difference between the corresponding Margrabe computed price and the true option price. We show that this optimal convention does not depend on the specic stochastic volatility model chosen and furthermore that parameter estimation can be dramatically simplifed by using market observable as inputs. Numerical examples are given which provide strong support to the new methodology.

We consider various PDE-based approaches for pricing several types of financial derivatives, where the underlying factors exhibit stochastic correlation. One of the approaches considers correlation structures guided by a stochastic mean-reverting process, and numerically solves an associated PDE with an extra dimension. Another approach considers a regime switching correlation structure, and numerically solves an associated system of PDEs. A third approach is based on an asymptotic analytical approximation to the solution, when a stochastic mean-reverting correlation process is considered. We present results from these approaches and compare with Monte Carlo simulations. Joint work with Nat H.C. Leung

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

In the context of energy price modelling, prices are formed from exponential maps of underlying factor processes, and the mathematical convenience this offers means that this is no surprise. In this talk we will show various ways in which models based on polynomial maps of polynomial processes (PMPP models) can function in a similar way. Polynomial processes have the property that expectations of polynomial functions of the future state of the process, conditional on the current state, are themselves polynomial functions of the current state. It is this property that means that PMPP models also provide a level of mathematical convenience (for forming futures prices). But they also provide an additional level of flexibility, which means that they are capable of capturing the extreme dynamics that are commonly seen in energy market prices even with relatively tame dynamics in the underlying factor process. We will end by discussing numerical methods for the valuation of energy contracts in the PMPP setting.

Under the two-asset Merton jump-diffusion model, the value of a European-style option satisfies a two-dimensional time-dependent partial integro-differential equation (PIDE). We study seven recent and novel operator splitting schemes when applied to this PIDE, with a keen focus on implicit-explicit (IMEX) and alternating direction implicit (ADI) methods. Each of the schemes conveniently treats the nonlocal integral part in an explicit fashion. Through ample numerical experiments we investigate the convergence behaviour of the different splitting schemes and study their relative performance. Joint work with Lynn Boen, UAntwerp

This talk overviews my recent results in energy market modelling (including option pricing formula for a mean-reversion asset, variance and volatility swaps in energy markets, applications of weather derivatives in energy markets, pricing crude oil options using Levy processes, energy contracts modelling with delayed and jumped volatilities), and also some latest results on energy-switching and carbon pricing. I will also talk about the clean renewable energy prospective and a vision to transition to 100% wind, water & solar energy in Canada.

SREC markets are a relatively novel market-based system to incentivize the production of energy from solar means. A regulator imposes a floor on the amount of energy each regulated firm must generate from solar power in a given period and provides them with certificates for each generated MWh. Firms offset these certificates against the floor and pay a penalty for any lacking certificates. Certificates are tradable assets, allowing firms to purchase/sell them freely. In this work, we formulate a stochastic control problem for generating and trading in SREC markets from a regulated firm's perspective. We account for generation and trading costs, the impact both have on SREC prices, provide a characterization of the optimal strategy, and develop a numerical algorithm to solve this control problem. Through numerical experiments, we explore how a firm who acts optimally behaves under various conditions. We find that an optimal firm's generation and trading behaviour can be separated into various regimes, based on the marginal benefit of obtaining an additional SREC, and validate our theoretical characterization of the optimal strategy. We also conduct parameter sensitivity experiments and conduct comparisons of the optimal strategy to other candidate strategies.

Recently, optimal investment and generation of solar renewable energy contracts (SREC) have been formulated in a single-agent setting, where each firm is affected by their own actions (decoupled from other firms) and aim to minimize their own cost. In real markets, however, a large number of firms operate in regulated SREC markets, and the average trading and generation rates of all firms affect prices, and hence form a large-population stochastic game. In this work, we model the SREC market as a large-population non-cooperative game, where each firm wishes to minimize their own cost while their actions are coupled to other firms through the average trading and generation rates in the price dynamics. We use mean field game theory to find the best response strategies for individual firms which, together, yield an equilibrium. In this talk, we present our ongoing work.

In this study, we aim to improve inference capabilities of risk models for energy commodities by employing statistical procedures to identify outliers in the prices for crude oil and natural gas futures contracts traded on the CME over the period of December 2003 through March 2017. Our results show that it is important to investigate and control for potential outlier effects when performing parametric estimation of risk parameters because outliers can have a large impact on the estimation of Value at Risk (VaR) and Expected Shortfall (CVaR or ES). We illustrate using crude oil and natural gas futures contracts how risk metrics based on raw data can lead to higher than expected actual losses. As a result, a firm may be placing itself unknowingly at precarious financial risk. Our research demonstrates that it is crucial to include intervention parameters to address outlier impacts in order to obtain robust risk metrics. Outlier intervention models will allow manager in firms with trading operations and financial services to make more informed decisions in regards to risk management, credit management, governance and compliance activities.

Fuel costs are a substantial component of the shipping industry, making bunker fuel price risk a major consideration for shipping firms. We analyse the hedging effectiveness of different proxy hedges with oil futures as well as OTC forwards for the bunker fuel market. Using different hedge ratios and a VECM-GARCH modeling approach it is found that oil futures’ hedging effectiveness has significantly improved over the past 20 years. Despite this improvement, in the minimum-variance framework, the forward contracts’ higher correlation still yields better hedging results. However, given the high amount of transaction costs for OTC products, the exchange-traded oil futures contracts can deliver higher mean-variance utilities and can thus be considered a viable candidate when hedging fuel for ships. We explore the tradeoff between liquidity and correlation that dominates this important energy market challenge.

We discuss oligopoly games with a continuum of players that have mean field structure. These may be of Bertrand (price setting) or Cournot (quantity setting) type and may apply to analysis of consumer goods or energy markets respectively. Key advantages over finite player nonzero sum differential games are analytical and numerical tractability of the associated PDEs. Models for energy markets with competition between producers with heterogeneous costs (fossils vs. renewables) are presented as motivation. Sources of uncertainty in the stochastic version of the problem include controlled random discovery of reserves, and uncertain demand environments.

This paper evaluates the effect of market integration on prices and welfare, in a model where two Lucas trees grow in separate regions with similar investors. We find equilibrium asset price dynamics and welfare both in segmentation, when each region holds its own asset and consumes its dividend, and in integration, when both regions trade both assets and consume both dividends. Integration always increases welfare. Asset prices may increase or decrease, depending on the time of integration, but decrease on average. Correlation in assets' returns is zero or negative before integration, but significantly positive afterwards, explaining some effects commonly associated with financialization.

Energy infrastructure is big, expensive, and can often be operated so as to react to market and other conditions. The resulting coupled valuation/optimal operation problem is one of real options. In my talk I will present issues in real options for energy arising from incorporation of realistic market and operational properties and constraints.

Current distribution systems cannot support simultaneous and identical actions of a large number of distributed flexible energy resources reacting to an identical signal. This talk presents a transactive energy market framework when their access to transactions is restricted. A nonlinear pricing structure incentivizes small transactions spread out among arrivals of operation opportunities. A self-exciting point process expresses operation permissions. The problem of optimal operations in this market to maximize the cumulated revenue is modeled as a piecewise deterministic Markov decision process. Various properties of the optimal value and sensitivity to market parameters are studied. 

In the hedging of electricity increasingly option contracts which are well-known in finance and risk management play an important role. The efficient pricing of option contracts is essential to facilitate their use in real-world hedging. In this talk we present a class of high-order compact finite difference schemes which are very efficient and at the same time parsimonious and memory-efficient to implement. We discuss stability and convergence results, and present results of numerical experiments.

We will thus outline the calibration of a financial asset price model in the context of financial option pricing. We will briefly explain the COS method, which is based on Fourier cosine expansions and the availability of the asset's characteristic function as the PDe solution technique. Particularly, to provide an efficient calibration framework, a data-driven approach, by means of an Artificial Neural Network (ANN), is proposed to learn the solutions of financial models and to reduce the corresponding computation time significantly. This ANN-based method is extended to calibrate financial models. Specifically, fitting model parameters is formulated as training hidden neurons within a machine-learning framework. The rapid on-line computation of ANNs combined with a flexible optimization method (i.e. Differential Evolution) provides us fast calibration without getting stuck in local minima.

In this study, we propose a model for the electricity demand in the German intraday market. The increase in percentage of renewable energy resources in electricity production (e.g. from 31.6% in 2016 to 36.2% in 2017 [5]) has a substantial effect on the German intra- day market. The renewable energy production results in a more volatile environment due to forecast errors and the owner of a renewable energy resource tends to trade in the intraday market to be able to adjust the forecast and their position more precisely [1]. In particular, in the German intraday market the trading continues up to 30 minutes before the delivery, so the market participants have the opportunity to react to the forecasted offer of renewable energy even closer to real-time. This indeed makes the intraday market more attractive for the traders. For instance, the traded volume in German intraday market has increased from 41 TWh in 2016 to 47 TWh in 2017, i.e. 15.1% [4]. Hence, it can be concluded that intraday markets are gaining more importance and also growing by the increase of renewable energy resources. Therefore, it is necessary to introduce a model for the spot price or the electricity demand which closely captures the real dynamics of the intraday market. With this motivation, we propose a statistical model for the electricity demand in the intra- day market by following a similar approach to the one given in [3]. In our setting, statistical modeling refers to time series analysis of the actual consumption data in Germany which covers the time span from 01.01.2015 to 31.12.2018 with 15-minutes resolution of 140215 data points. We exploit statistical information contained by the data in order to capture the stylized features of the electricity demand and further to get an insight for the modeling concerns. We primarily consider the Jacobi process, which is initially given in [2] as a model for the dynamic behaviour of the interest rate in a target zone as follows \[d r_t =α(r_μ −r_t)dt+β\sqrt{􏰀(r_t −r_m)(r_M −r_t)}d W_t\] where $r_μ$ is the mean reversion level, $r_m$ and $r_M$ are lower and upper bounds bounds for the process $r_t$ , respectively. We further modify the Jacobi process by utilizing the data analysis results. Finally, we present the model calibration results of the proposed model.

The rapid growth of renewables in Germany in the last decade has led to various new modeling challenges for many energy firms. Wind park owners and operators in particular require valuation and risk analysis techniques which capture the high volatility and intermittency of wind power generation, the dynamics of intraday prices and their correlation with changes in wind forecast levels. Under typical contract terms, owners of wind parks receive production volume times the spot price minus a premium $p$, while managers receive revenues dependent on how they nominate the power and rebalance their positions in the day-ahead and intraday markets. Here we present a trading and hedging strategy for determining a fair premium $p$, which can vary significantly across wind parks, for example due to their forecast variability and whether they are more or less correlated with overall wind in Germany, which drives market prices. This valuation problem is of significant interest to many market participants, including investors and policy makers looking to further grow the penetration of renewables.