Keywords: power plant valuation, VPP, plant start, dynamic programming, Monte Carlo simulations, least squares Monte Carlo
Published in: World Power
Publication year: 2010
Co-author 1: Dirk van Abbema, ING Bank
Co-author 2: Henk Sjoerd Los, KYOS Energy Consulting
Co-author 3: Cyriel de Jong, KYOS Energy Consulting

Gas-fired power plants provide the primary source of production flexibility in many power markets. An economically optimal use of the start-stop flexibility of gas plants is paramount to retrieving the maximum value from the asset. With the increasing penetration of wind power, this flexibility will become essential to balance the system. While starts and stops allow the owner to choose the production hours with the largest margin, they are also associated with various explicit and implicit costs. In this article we demonstrate the impact of various start-stop constraints and costs. This impact analysis is possible by applying advanced techniques for generating realistic Monte Carlo price simulations in combination with techniques for optimizing the production pattern.

An important insight that we gain is that different ways to limit starts lead to subtle differences in the actual use of the power plant and the corresponding value. We also find that the common modeling assumption of having perfect foresight about the future spark spreads may lead to a significant overstatement of plant value. This latter result contrasts our previous belief [Los et al, 2009], and statements of some other researchers [cf Clewlow et al, 2009] who claim that perfect foresight is a reasonable assumption. In particular, when there is a fixed limit to the number of allowed starts, as is common in many VPP contracts, uncertainty about future margins is definitely reducing plant value. We are able to show this result using the concept of least-squares Monte Carlo as applied to energy assets in e.g. Deng (2006, power plants) and De Jong and Boogert (2008; gas storage).

Published in: Energy Economics

Publication year: 2009
Co-Author 1: Robert J. Elliot

This paper presents a method for valuing power derivatives using a supply–demand approach. Our method extends work in the

field by incorporating randomness into the base load portion of the supply stack function and equating it with a noisy demand process. We obtain closed form solutions for European option prices written on average spot prices considering two different supply models: a mean-reverting model and a Markov chain model. The results are extensions of the classic Black–Scholes equation. The model provides a relatively simple approach to describe the complicated price behaviour observed in electricity spot markets and also allows for computationally efficient derivatives pricing.

Published in: Energy Economics
Publication year: 2008
Co-author 1: Kazuhiko Ohashi

Despite the worldwide popularity of CDD- and HDD-type weather derivatives based on temperature, a different class of weather derivatives, so-called summer day options, is more popular in Japan; the payoffs are determined by the number of summer days (i.e., the days whose average temperature is above 25 °C) during the contract period.

In this paper, we price such summer day options by the good-deal bounds of Cochrane and Saa-Requejo [Cochrane, J.H., and J. Saa-Requejo, 2000, Beyond Arbitrage: Good-Deal Asset Price Bounds in Incomplete Markets, Journal of Political Economy 108, 79–119.], using temperature data for Tokyo

.

Keywords: wind power, pricing, price - wind correlation, hedging, investments
Published in: WorldPower 2008
Publication year: 2008
Co-author 1: Hans van Dijken

Effective Pricing of Wind Power - Uncertainties in Wind Production Often Priced at Too Low Levels

This article describes the pricing and hedging of wind power contracts. It demonstrates that substantial discounts relative to baseload power prices are reasonable to cover the negative wind-price correlation and to cover the difficulty of hedging price risks.

In this article, we outline a sound approach to the assessment of wind power projects, based on a careful analysis of project returns. In particular, we describe a number of hedge mechanisms and highlight some common pitfalls in
structuring wind power purchase agreement (PPA) deals. Wind power is one of the most viable options to meet renewable energy targets. The attractiveness to investors depends on investment costs, expected future power price and (heavily) on the subsidy regime. But with the steady increase of wind
production, the ability to secure future cashflows and to manage the risks becomes a key issue as well.

Wind power contracts typically contain discounts relative to the market forward prices. This derives from the difficulty in forecasting wind production and the variability in wind production, the correlation with market prices (imbalance and day-ahead). In the case presented, the correlation between day-ahead prices and wind production was already responsible for a discount of €6/MWh. A typical discount for imbalance costs has about the same magnitude, leading to an expected revenue shortfall of €12/MWh – without
even taking into account the effects of the continuous increase of wind production on spot power prices. The analysis also demonstrates that a
considerable proportion of the price risks, both short-term and long-term, are
unhedgeable and should be incorporated in additional discounts. It is our experience that these risks are easily overlooked and wind power priced too optimistically.

Keywords:
Published in: Energy Risk
Publication year: 2004

Salt-dome storage facilities are a flexible way to take advantage of arbitrage opportunities in the natural gas market. Kislay Sinha and colleagues at Arizona Public Service discuss the valuation of a storage asset, examine ways of capturing arbitrage opportunities in forward gas markets and consider how reliability constraints affect trading strategies.

Keywords: Monte Carlo, Valuation, Gas Storage
Published in: Journal of Derivatives
Publication year: 2008 (Spring)
Co-Author 1: Alexander Boogert

Developed countries increasingly rely on gas storage for security of supply. Widespread deregulation has created markets that help assign an objective value to existing and new to build storages. Storage valuation is nevertheless a challenging task if we consider both the financial and physical aspects of storage. In this paper we develop a Monte Carlo valuation method, which can incorporate realistic gas price dynamics and complex physical constraints. In specific we extend the Least Squares Monte Carlo method for American options to storage valuation. We include numerical results and show ways to improve computational speed.

Keywords:
Published in:
Publication year:
Co-Author 1: Thomas Bolinger
Co-Author 2: Jochen Maurer
Co-Author 3: Marco Semadeni

To optimally operate a pumped-storage hydropower plant, the strategy is essentially to determine the right time for production – typically when prices are high at peak-load during the day – and for pumping back up extra water to the reservoir using cheap off-peak electricity when the demand is low. This strategy aims to maximize net income. The evaluation of a storage hydropower plant based on a conventional swing option is in general not sufficient. In order to improve the evaluation and risk management of storage hydropower plants, the concept of the swing option has been extended. Besides the spot price development and the external inflows, the water levels of the basins, is accounted for. In general, the number of times the option is exercised to generate electricity and the number of pumping events is unlimited. Further, the model accounts for the impact of operation constraints on the hydropower scheme. With this approach, the plant operator gains detailed and accurate information to value and risk-analyse the power plant. The model also provides the optimal operation modus of the plant. The potential of the model is demonstrated on a stylised pumped storage hydropower plant.

Keywords:
Published in:
Publication year: 1999
Co-Author 1: Chris Strickland

In this paper we develop a single-factor modeling framework which is consistent with market observable forward prices and volatilities. The model is a special case of the multi-factor model developed in Clewlow and Strickland [1999b] and leads to analytical pricing formula for standard options, caps, floors, collars and swaptions. We also show how American style and exotic energy derivatives can be priced using trinomial trees, which are constructed to be consistent with the forward curve and volatility structure. We demonstrate the application of the trinomial tree to the pricing of a European and American Asian option. The analysis in this paper extends the results in Schwartz [1997] and Amin, et al. [1995].

Keywords: contingent claims on power, non-Markovian price processes, power prices with spikes
Published in: Journal of Engineering Mathematics
Publication year: 2004

A new approach to modeling spikes in power prices proposed earlier by the author is presented and further developed. In contrast to the standard approaches, power prices with spikes as a non-Markovian stochastic process are modeled that allows for modeling spikes directly as self-reversing jumps. It is shown how this approach can be used to value and hedge European contingent claims on power with spikes. It is also shown that the values of European contingent claims on power with spikes satisfy the Cauchy problem for a certain linear evolution equation. In this way, the values of European contingent claims on power with spikes can be represented in terms of the Green’s function for this Cauchy problem and the Green’s function itself can be interpreted in terms of the values of the Arrow-Debreu securities on power with spikes.

Keywords: American options, simulation methods, swing options, take-or-pay options, commodities, energy securities
Published in: Mathematical Finance
Publication year: 2004

This paper introduces the application of Monte Carlo simulation technology to the valuation of securities that contain many (buying or selling) rights, but for which a limited number can be exercised per period, and penalties if a minimum quantity is not exercised before maturity. These securities combine the characteristics of American options, with the additional constraint that only a few rights can be exercised per period and therefore their price depends also on the number of living rights (i.e. American-Asian-style payoffs), and forward securities. These securities give flexibility-of-delivery options and are common in energy markets (e.g., take-or-pay or swing options) and as real options (e.g., the development of a mine). First, we derive a series of properties for the price and the optimal exercise frontier of these securities. Second, we price them by simulation, extending the Ibanez and Zapatero (2004) method to this problem.