http://www.erasmusenergy.com en-us N/A dejong@maycroft.com Fri, 25 Jul 2008 18:04:41 CEST 20 http://www.erasmusenergy.com/articles/165/1/Effective-pricing-of-wind-power/Page1.html 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.
]]> no@spam.com (Cyriel de Jong) Mon, 24 Mar 2008 21:40:16 CET http://www.erasmusenergy.com/articles/165/1/Effective-pricing-of-wind-power/Page1.html http://www.erasmusenergy.com/articles/142/1/Spark-Spread-Options-and-the-Valuation-of-Electricity-Generation-Assets/Page1.html Published in: Proceedings of the 32nd Hawaii International Conference on System Sciences Volume 3
Publication year: 1999
Co-author 1: Aram Sogomonian
Co-author 2: Blake Johnson

This paper presents and applies a methodology for valuing electricity derivatives by constructing replicating portfolios from electricity futures and the risk free asset. Futures based replication is argued to be made necessary by the non-storable nature of electricity, which rules out the traditional spot market, storage-based method of valuing commodity derivatives. Using the futures based approach, valuation formulae are derived for spark spread options for both geometric Brownian motion and mean reverting price processes. The valuation result is in turn used to construct real options based valuation formula for generation assets. Finally, the valuation formula derived for generation assets is used to value a sample of assets that have been recently sold, and the theoretical values calculated are compared to the observed sales prices of the assets.]]> no@spam.com (Shijie Deng) Mon, 07 Jan 2008 11:33:56 CET http://www.erasmusenergy.com/articles/142/1/Spark-Spread-Options-and-the-Valuation-of-Electricity-Generation-Assets/Page1.html http://www.erasmusenergy.com/articles/123/1/Valuation-of-the-early-exercise-price-for-options-using-simulation-and-nonparametric-regression/Page1.html Published in: Insurance mathematics & economics
Publication year: 1996

This article shows how to value the optimal stopping time for any Markovian process in finite discrete time. Specifically, the article focuses on the valuation of American options using simulations of stochastic processes. It also shows that the estimation of the decision rule to exercise early is equivalent to the estimation of a series of conditional expectations. For Markov processes, these conditional expectations can be estimated with nonparametric regression techniques. This article shows how to approximate the conditional expectations and the resulting early-exercise decision rule with spline and local regression.]]> no@spam.com (Jacques F. Carriere) Mon, 17 Dec 2007 15:22:52 CET http://www.erasmusenergy.com/articles/123/1/Valuation-of-the-early-exercise-price-for-options-using-simulation-and-nonparametric-regression/Page1.html http://www.erasmusenergy.com/articles/120/1/Valuation-of-Power-Generation-Assets-A-Real-Option-Approach/Page1.html Published in: Algo Research Quarterly
Publication year: 2000
Co-author 1: Yiping Zhuang

Real options theory is an increasingly popular tool for valuing physical assets such as power generation plants. In this paper, we describe a model for power plant valuation that accounts for such important operating characteristics as minimum on- and off-times, ramp time, nonconstant heat rates, response rate and minimum electricity dispatch level. The power plant values and optimal operating policies are obtained by employing stochastic dynamic programming. Sample numerical results, using electricity price data from the New England power pool, show that operating constraints can have a significant impact on power plant values and optimal operating policies.]]> no@spam.com (Doug Gardner) Thu, 13 Dec 2007 19:21:49 CET http://www.erasmusenergy.com/articles/120/1/Valuation-of-Power-Generation-Assets-A-Real-Option-Approach/Page1.html http://www.erasmusenergy.com/articles/119/1/Short-term-generation-asset-valuation-a-real-option-approach/Page1.html Published in: Operations research
Publication year: 2002
Co-author 1: Graydon Barz

This paper discusses using real options to value power plants with unit commitment constraints over a short-term period. We formulate the problem as a multistage stochastic problem and propose a solution procedure that integrates forward-moving Monte Carlo simulation with backward-moving dynamic programming. We assume that the power plant operator maximizes expected profit by deciding in each hour whether or not to run the unit, that a certain lead time for commitment and decommitment decisions is necessary to start up and shut down a unit, and that these commitment decisions, once made, are subject to physical constraints such as minimum uptime and downtime. We also account for the costs associated with starting up and shutting down a unit. Last, we assume that there are hourly markets for both electricity and the fuel used by the generator and that their prices follow Ito processes. Using numerical simulation, we show that failure to consider physical constraints may significantly overvalue a power plant.]]> no@spam.com (Chung-Li Tseng) Thu, 13 Dec 2007 19:02:07 CET http://www.erasmusenergy.com/articles/119/1/Short-term-generation-asset-valuation-a-real-option-approach/Page1.html http://www.erasmusenergy.com/articles/118/1/Use-of-real-options-in-asset-valuation/Page1.html Published in: The Electricity Journal
Publication year: 2002

An enhanced real option methodology and an alternative volatility measure, applied to the real option framework, allow a valuation to capture the holistic nature of real assets and the reality of the transaction involving them.]]> no@spam.com (Gary Gitelman) Thu, 13 Dec 2007 18:58:10 CET http://www.erasmusenergy.com/articles/118/1/Use-of-real-options-in-asset-valuation/Page1.html http://www.erasmusenergy.com/articles/115/1/What-Is-It-Worth-Application-of-Real-Options-Theory-to-the-Valuation-of-Generation-Assets/Page1.html Published in: The electricity journal
Publication year: 2001
Co-author 1: Nazli Uludere

An analysis of two generation assets in a regional market in the Northeast demonstrates how a real options-based valuation framework uncovers and quantifies the value of efficient plant operation in the face of volatile electricity market prices. The analysis shows that a peaking gas-fired facility may be more valuable than a mid-merit coal-fired plant, even though traditional methodologies would favor the coal-fired asset given its lower marginal cost.]]> no@spam.com (Julia Frayer) Thu, 13 Dec 2007 17:05:40 CET http://www.erasmusenergy.com/articles/115/1/What-Is-It-Worth-Application-of-Real-Options-Theory-to-the-Valuation-of-Generation-Assets/Page1.html http://www.erasmusenergy.com/articles/114/1/Generation-Asset-Valuation/Page1.html Published in: Energy risk
Publication year: 2005
Co-author 1: Chris Strickland
Co-author 2: Oleg Zakharov
Co-author 3: Geoff Carroll

In this latest article of our series on practical applications of Monte Carlo simulation we focus on the valuation issues associated with a physical asset, namely a merchant power plant. Typically these assets are valued on a simple net present value basis with respect to a static forward, or forecast, curve. The analysis that will be employed here takes into account both the stochastic nature of the fuel and output prices and also the physical constraints associated with operating the plant. This methodology is often termed “real options theory” and is an increasingly popular tool for valuing physical assets.]]> no@spam.com (Les Clewlow) Mon, 10 Dec 2007 18:01:22 CET http://www.erasmusenergy.com/articles/114/1/Generation-Asset-Valuation/Page1.html http://www.erasmusenergy.com/articles/112/1/Valuing-American-options-by-simulation-A-simple-least-squares-approach/Page1.html Published in: The review of financial studies
Publication year: 2001
Co-author 1: Eduardo Schwartz

This article presents a simple yet powerful new approach for approximating the value of American options by simulation. The key to this approach is the use of least squares to estimate the conditional expected payoff to the optionholder from continuation. This makes this approach readily applicable in path-dependent and multifactor situations where traditional finite difference techniques cannot be used. we illustrate this technique with several realistic examples including valuing an option when the underlying asset follows a jump-diffusion process and valuing an American swaption in a 20-factor string model of the term structure.]]> no@spam.com (Francis Longstaff) Mon, 10 Dec 2007 15:53:06 CET http://www.erasmusenergy.com/articles/112/1/Valuing-American-options-by-simulation-A-simple-least-squares-approach/Page1.html http://www.erasmusenergy.com/articles/109/1/An-Analysis-of-a-Least-Squares-Regression-Method-for-American-Option-pricing/Page1.html Published in:
Publication year: 2001
Co-author 1: Damien Lamberton
Co-author 2: Philip Protter

Recently, various authors proposed Monte-Carlo methods for the computation of American option prices, based on least squares regression. The purpose of this paper is to analyze an algorithm due to Longstaff and Schwartz. This algorithm involves two types of approximation. Approximation one: replace the conditional expectations in the dynamic programming principle by projections on a finite set of functions. Approximation two: use Monte-Carlo simulations and least squares regression to compute the value function of approximation one. Under fairly general conditions, we prove the almost sure convergence of the complete algorithm. We also determine the rate of convergence of approximation two and prove that its normalized error is asymptotically Gaussian.
]]> no@spam.com (Emmanuelle Clement) Mon, 10 Dec 2007 14:42:42 CET http://www.erasmusenergy.com/articles/109/1/An-Analysis-of-a-Least-Squares-Regression-Method-for-American-Option-pricing/Page1.html