Shi-Jie Deng

Exotic electricity options and the valuation of electricity generation and transmission assets

We present and apply a methodology for valuing electricity derivatives by constructing replicating portfolios from electricity futures and the risk-free asset. Futures-based replication is 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 both spark and locational spread options for both geometric Brownian motion and mean reverting price processes. These valuation results are in turn used to construct real options-based valuation formulae for generation and transmission 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. q 2001 Elsevier Science B.V. All rights reserved.

INCORPORATING OPERATIONAL CHARACTERISTICS AND START-UP COSTS IN OPTION-BASED VALUATION OF POWER GENERATION CAPACITY

We describe a stochastic dynamic programming approach for “real option”-based valuation of electricity generation capacity incorporating operational constraints and start-up costs. Stochastic prices of electricity and fuel are represented by recombining multinomial trees. Generators are modeled as a strip of cross-commodity call options with a delay and a cost imposed on each option exercise. We illustrate implications of operational characteristics on the valuation of generation assets under different modeling assumptions about the energy commodity prices. We find that the impacts of operational constraints on real asset valuation are dependent on both the model specification and the nature of operating characteristics.

A REAL OPTIONS APPROACH FOR PRICING ELECTRICITY TOLLING AGREEMENTS

An electricity tolling agreement (or, tolling contact) is a supply contract in which the buyer reserves the right to take the output of an underlying electricity generation asset by paying a predetermined premium to the asset owner. We propose a real options approach to value a tolling contract incorporating operational characteristics of the generation asset and contractual constraints. Dynamic programming and value function approximation by Monte Carlo based least-squares regression are employed to solve the valuation problem. The effects of different electricity price assumptions on the valuation of tolling contracts are examined through numerical examples.

Priority Network Access Pricing for Electric Power

We propose a priority-pricing scheme for zonal access to the electric power grid that is uniform across all buses in a zone. The independent system operator (ISO) charges bulk power traders a per unit ex ante transmission access fee. The zonal access fee serves as an access insurance premium that entitles a bulk power trader to either physical injection of one unit of energy or a compensation payment. The access fee per MWh depends on the injection zone and a self-selected strike price that serves as an insurance “deductible” that determines the scheduling priority of the insured transaction and the compensation level in case of curtailment. Inter-zonal transactions are charged (or credited) with an additional ex post congestion fee equal to the differences in zonal spot prices. The compensation for curtailed transactions equals the difference between the realized zonal spot price and the selected strike price (deductible level). The ISO manages congestion so as to minimize net compensation payments and thus, curtailment probabilities increase with strike price and for any particular strike price may vary from bus to bus. We calculate the rational expectations equilibrium for three-, four- and six-node systems and demonstrate that the efficiency losses of the proposed second best scheme relative to the efficient dispatch solutions are modest.

Spark spread options and the valuation of electricity generation assets

The 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.

Levy process-driven mean-reverting electricity price model: the marginal distribution analysis

We propose a class of stochastic mean-reverting models for electricity prices with Levy process-driven Ornstein-Uhlenbeck (OU) processes being the building blocks. We first fit marginal distributions of power price series to two special classes of distributions defined by quantile functions (termed Class I and Class II distributions). A theoretical correlation structure is then used to fit the empirical autocorrelation structure. Lastly, based on results from the first two steps, we construct a stochastic process by superposing two OU processes. The focus of this paper is on fitting the marginal distribution. A Class I distribution has closed-form formulas for probability density, cumulative distribution function, and quantile function, while a Class II distribution may have extremely unbalanced tails. Both classes of distributions admit realistic modelling of the marginal distribution of electricity prices. This approach effectively captures not only the anomalous tail behaviors but also the correlation structure present in the electricity price series.

The inherent inefficiency of the point-to-point congestion revenue right auction

Empirical evidence shows that the clearing prices for point-to-point congestion revenue rights, also known as financial transmission rights (FTRs), resulting from centralized auctions conducted by independent system operators differ significantly and systematically from the realized congestion revenues that determine the accrued payoffs of these rights. The question addressed by this paper is whether such deviations are due to price discovery errors which will eventually vanish or due to inherent inefficiencies in the auction structure. We address this question by studying a hypothetical DC-flow approximation model of a six-node system with known outage probabilities of each element and known statistical demand variability. We show that even with perfect foresight of average congestion rents the clearing prices for the FTRs depend on the bid quantity and therefore may not be priced correctly in the financial transmission right (FTR) auction. In particular, we demonstrate that if all FTR bid quantities are equal to the corresponding average transaction volumes and the bid values are set at the expected congestion rent level, then the resulting auction prices systematically deviate from the known FTR values. We conclude that price discovery alone would not remedy the discrepancy between the auction prices and the realized values of the FTRs. Secondary markets or frequent reconfiguration auctions are necessary in order to achieve such convergence.

Volumetric hedging in electricity procurement

Load serving entities (LSE) providing electricity service at regulated prices in restructured electricity markets, face price and quantity risk. We address the hedging problem of such a risk averse LSE. Exploiting the correlation between consumption quantities and spot prices, we developed an optimal, zero-cost hedging function characterized by payoff as function of spot price. We then show how such a hedging strategy can be implemented through a portfolio of call and put options.

An inverse-quantile function approach for modeling electricity price

We propose a class of alternative stochastic volatility models for electricity prices using the quantile function modeling approach. Specifically, we fit marginal distributions of power prices to two special classes of distributions by matching the quantile of an empirical distribution to that of a theoretical distribution. The distributions from the first class have closed form formulas for probability densities, probability distribution functions, and quantile functions, while the distributions from the second class may have extremely unbalanced tails. Having rich tail behaviors, both classes allow realistic modeling of the power price dynamics. The appealing features of this approach are that it can effectively model the heavy tail behavior of electricity prices caused by jumps and stochastic volatility and that the resulting distributions are easy to simulate. This latter feature enables us to perform both parameter estimation and derivative pricing tasks based on price data directly observed from real markets.

An alternative mechanism for carbon emission permit price volatility mitigation

In this paper, we propose a stylized model to investigate the impact of financial options on mitigating carbon permit price volatility under a cap and trade system. We show that both the spot price level and the price volatility of carbon permits can be reduced via financial options, while ensuring market efficiency and achieving the emission target. The existence of an option market also provides a way to hedge the uncertainty of future spot prices and is a stimulus for investment in carbon emission abatement technologies. A comparison of the policy implications of this mechanism, a safety valve and banking/borrowing is also described.