Setting Up Standard Power Options to Hedge Price-Quantity Risk in a Competitive Electricity Market: The Colombian Case

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 26, NO. 3, AUGUST 2011 1493

Setting Up Standard Power Options to HedgePrice-Quantity Risk in a Competitive Electricity

Market: The Colombian CaseGabriel A. Vizcaíno Sánchez, Juan Manuel Alzate, Angela I. Cadena, and Juan M. Benavides

Abstract—This paper applies the conceptual framework appliedin the work of Oum et al. to hedge retailers against price-quan-tity fluctuations in spot electricity markets, and extends it to powergenerators, in order to design suitable power options with optimalstrike prices from a market maker’s perspective. These optionsare then used to hedge agents against price and quantity fluctu-ations by maximizing a static expected utility problem. An infi-nite collection of derivatives (“exotic option”) emerges as the so-lution of both price and quantity hedging. This exotic option isapproximated with a portfolio composed by bonds, forward/fu-tures contracts, and a fixed number of put and call options, em-ploying a plausible replicating strategy. The theoretical frameworkis tested within the context of the Colombian power market, andis applied to month-ahead and quarterly-ahead hedging duringon-peak hours. The proposal addresses major problems such aslack of liquidity and anonymity of the current bilateral electricitytrading scheme in Colombia.

Index Terms—Dynamic hedging, electricity markets, energyrisk, volumetric hedging.

I. INTRODUCTION

O VER the last two decades, the electricity sector world-wide has undergone a profound restructuring process

starting from the vertical unbundling of the generation, trans-mission, distribution, and retailing activities as well as otherdeeper reforms towards deregulation [2]. These policies haveencouraged the penetration of private investors and apparentlyhave led to improvements in the efficiency and quality ofpower generation, to a reduction of electricity prices, to anenhancement of market transparency, and also have allowed theemergence of a liquid financial trading of electricity [3]–[5].This is the case of the Nordic market which is one of themost outstanding examples next to experiences in the UnitedKingdom, Switzerland, Australia, among others [6], [7].

Certainly, this liberalization of the power markets has implieddifferent risks (price risk, quantity risk, regulatory risk, marketrisk, among others) for players due to the competitive markets

Manuscript received April 08, 2010; revised July 30, 2010; accepted October04, 2010. Date of publication November 29, 2010; date of current version July22, 2011. This work was supported by the Research Center of the EngineeringFaculty at Universidad de los Andes. Paper no. TPWRS-00281-2010.

The authors are with the Department of Electrical Engineering, Universidadde los Andes, Bogotá, Colombia (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPWRS.2010.2089474

nature, but also has brought plenty of possibilities and chances;therefore, one of the keys to success in the liberalized marketsis the ability to manage these new risks, as Unger expresses in[8].

Power derivatives have appeared as a suitable solution tomanage such risks, since lessons learned from the financialmarkets suggest that financial derivatives, when well under-stood and properly employed, are beneficial to the sharingand controlling of undesired risks through properly structuredhedging strategies, as it is discussed in [9]–[11]. There aretwo major paths about power derivatives: pricing and portfoliooptimization.

The nonstorability feature of electric energy hampers thedirect application of a no-arbitrage methodology; then, dif-ferent techniques must be developed [12]. Other authors likeVehviläinen [13] and Lucia and Schwartz [3] studied theproperties of the instruments available at Nord Pool, whereasWilhelm converts the electricity market into a virtual basemarket consisting of zero bonds and an additional risky assetto elaborate a risk-neutral price dynamic in [12]. Eydeland andGeman discuss deeper the difficulty of pricing options [14].

On the other hand, portfolio optimization has emerged as ahelpful approach for risk management purposes. There are threemajor portfolio optimization procedures: price hedging, quan-tity hedging, and price-quantity hedging. About price hedging,some authors can be mentioned: Ahn et al. in [15] minimizethe value at risk (VaR) using options and Kleindorfer and Liconsider the portfolio optimization including derivative instru-ments, subject to a VaR constraint [16]. In [7], Näsäkäkäl andKeppo found an analytical solution for a portfolio value distribu-tion, and Huisman et al. carried out a mean-variance frameworkto address the concept of structuring the portfolio and focuseson how to optimally allocate positions in peak and on-peak for-ward contracts [17].

Volumetric uncertainty is one of the main features of elec-tricity, but unfortunately quantity risk is not a tradable asset, sothere is not derivative instruments to hedge this risk directly.Thus, quantity hedging strategies usually aim to exploit theadvantages of flexible power generation technologies (mainlyhydropower plants) to manage volumetric risk. Näsäkäkäl andKeppo describe in [18] the difficulties to achieve so given loaduncertainty and the eventual correlation between spot pricesand water inflows to reservoirs, whereas Doege, Schiltknechtand Lüthi show how the volume risk can be managed throughan intelligent dispatch strategy in [19]. In [8], Unger states thatthe flexibility in some production plants, such as the hydro

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1494 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 26, NO. 3, AUGUST 2011

storage plant, even makes them suitable to hedge not only pricerisk but also volume risk, which currently is not possible in thestandardized market.

Despite the fact that there is scarce literature dealing withsimultaneous price and quantity risk hedging, there are someworks in this light. Fleten et al. in [6] discuss a risk manage-ment model (stochastic programming) for a hydropower pro-ducer, whose portfolio at risk includes own production and a setof power contracts for delivery or purchase, including contractsof financial nature. In reference [1], authors present a helpfulapproach to handle price-quantity risk supported on the posi-tive correlation between these variables, using “plain vanilla”derivative instruments.

This paper relies on the prior reference [1], seeking to applyand extend their findings in order to design an electricity deriva-tive market from a market maker’s perspective, which wouldallow agents to build up a price-quantity hedging portfolio byreplicating an optimal zero-cost hedging function with bonds,forwards/futures contracts, two put, and three call options. Bynow, we seek to optimize the strike prices for these instruments.

The proposed instruments must be easy to implement andtrade, and must control spot price volatility and market powerbehavior [20].

The number of instruments is fixed in advance in our ap-proach, regarding the transition from the current market struc-ture to the novel and flexible one, with multiplicity of alterna-tives to hedge, must be slow and soft. This will reduce tradingburden at the introduction of the instruments, and afterwards,the number of instruments could be subject to a further opti-mization problem in order to maximize agents’ price-quantityhedging.

The calculation of optimal strikes provides “demand” side in-formation about how a discrete set of call and puts could ide-ally be distributed around the current spot price. In real life,call and put options will be traded at the available strikes andwith a varying number of strikes. Negotiations in the hedgingmarket might lead to option supplies that are better suited innumber and distribution, once suppliers understand the needsand constraints of the demand side and how liquid each instru-ment might become.

The remaining of this paper is presented as follows: Section IIdescribes the core of the price-quantity risk hedging strategydeveloped in [1], and in Section III, the optimization problem isformulated to find optimal strike prices for put and call options.Section IV develops an application for the Colombian powermarket, whereas in Section V, a discussion about results andits goodness for the Colombian market is presented. Finally, inSection VI, further work and activities are mentioned.

II. PRICE-QUANTITY RISK HEDGING

A short description of the model developed in [1] is here illus-trated. In the reference authors deal with simultaneous price andquantity risk hedging by exploiting the fact that load is stronglycorrelated to spot prices due to the nonstorability feature of elec-tricity as a commodity and to a steeply rising supply function.

In Colombia, the correlation coefficient is roughly 0.62 ac-cording to recent estimations [21], which is close to prior esti-

mations in California (0.54), Spain (0.70), Britain (0.58), andScandinavia (0.53) [1].

The authors in [1] solve a static hedging problem of an LSEwho has to serve an uncertain electricity demand at a regu-lated fixed price in a single period from 0 to 1. Besides, theLSE procures the electricity to serve his customers, from thewholesale market at a spot price , and has a hedging portfolio

, depending on the realization of the spot price. The totalprofit of an LSE after receiving payoffs from the contracts inthe hedging portfolio can be defined as

(1)

To develop a competitive power derivative market bidders,askers must be considered. Hence, the analysis in [1] is extendedto a GENCO which is assumed to be continuously dispatchedwith marginal production cost and power generation . Thus

(2)

Parameter is assumed to be fixed; however, it is subject tofuel price dynamics for thermal power production, as well asto water opportunity costs for hydroelectricity. This issue couldbe treated at the time of implementing this proposal as it will beexplained in Section IV.

The risk preferences of the LSE/GENCO are characterizedwith a concave utility function defined over the corre-sponding total profit at time 1. The realization of spotprice and load are characterized by a joint probability func-tion which is defined on the probability measure .It is also defined as a risk-neutral probability measure bywhich the hedging instruments are priced, and as the prob-ability density function of under . Authors formulate theLSE/GENCO’s problem as follows:

(3)

where and denote expectations under the proba-bility measure and , respectively, and . Con-straint in (3) implies that purchasing derivative contracts maybe financed from selling other derivatives or from the moneymarket accounts. Further details about the settings of the modelon which this paper relies can be found in [1].

Then, authors derive the optimality conditions and find theLSE’s optimal payoff function for CARA and mean-vari-ance utility functions. It has to be assumed a probability dis-tribution function for spot prices and loads served or powergenerated. In the Appendix, the same optimal payoff functionis derived for the GENCOs’ case. Authors then use Carr andMadan’s argument exposed in [22] to express the optimal payofffunction as a continuum collection of risk-free bonds, for-ward/futures contracts, and put and call options, with these lastoptions underlying on the spot price

(4)

VIZCAÍNO SÁNCHEZ et al.: SETTING UP STANDARD POWER OPTIONS TO HEDGE PRICE-QUANTITY RISK 1495

where . Equation (4) requires the marketto launch a continuum spectrum of options’ strike prices toperfectly replicate payoff profile, which is an obstacleindeed, since only a few numbers of options are offered inreal markets. As a consequence, Oum et al. describe a strategydefining the amount of each instrument to be purchased (sold)to replicate the optimal payoff function . We present anenhanced replicating strategy to obtain smaller replicating er-rors, by applying the linear regression approach of generalizedleast squares (GLS).

The methodology will be further explained in Section III.

III. FINDING OPTIONS’ OPTIMAL STRIKE PRICES

From a market maker’s perspective, developments in [1]could be properly used to design the instruments to be tradedin an electricity derivatives market composed by bonds, for-ward/futures contracts, and standard options with the spot priceas underlying.

Here, the optimal payoff functions, for both LSEs andGENCOs, are calculated using (3). To aggregate agents’hedging profiles, two unique optimal payoff functions are de-fined independently, each representing the collective intentionof the retail market and the power generation market. Hereafterwe refer to these curves as retail market payoff curveand generation market payoff curve .

At this stage, a global optimization is proposed to define op-timal strike prices for a discrete fixed number of put and call op-tions assumed to be offered in the electricity derivatives market,next to forward/futures contracts and bonds. These instrumentscould then be used either by retailers or power generators tobuild up a replicating portfolio close to their own optimal price-quantity hedging function.

As previously said, we determine optimal strike prices for afixed number of instruments, seeking to ease instruments’ in-troduction burden in a traditional market. After power options’learning function decays, the optimal number of instrumentsmight be the issue to deal with.

Optimal strikes are obtained by minimizing, simultaneously,the replicating error of both retailing and generation marketpayoff curves using a discrete number of options, jointlywith the already mentioned instruments. This procedure alsoenhances complementary features of the power market sinceoptions required by LSEs can be offered by GENCOs and viceversa. In the following, a detailed description of the procedureabove is presented.

A. Aggregated Optimal Payoff Functions

The procedure to determine market payoff functions ispresented in (5):

(5)

where

corresponds to a price-cap value defined under the marketmaker’s criteria and to the number of market participants.Under this setting, and will represent the jointneeds of all the agents and could be used to determine hedginginstruments by no favoring any agent and guaranteeing samehedging opportunities for each of them.

B. Replicating Methodology

Assuming a fixed number of put and call options in themarket, (4) could be rewritten as (6):

(6)

Instruments’ coefficients are denoted by while denotesresiduals, such that as . Parameters

and have the same dimension and equals , which is thenumber of discrete prices from zero to , according to the pre-cision required to treat the problem. In a real market (with afinite number of instruments available), the market maker pur-pose will be to minimize . This can be done byapplying GLS to (6), so the coefficients can be estimated from

(7)

where

......

......

...

......

...

is a matrix of independent variables with rows definedby the set of prices from 0 to and columns, each corre-sponding to a financial instrument including the risk free bonds(unitary column) and the futures/forward contracts. Precisionwill be given by parameter which defines price thick resolu-tion. In matrix and denote the value of the put andcall option, respectively. offsets each option payment profile.

C. Global Optimization

The optimization problem presented in (8) minimizes thesquare difference between and and their corre-sponding replicating strategies, subject to constraints which1) express the agents’ market payoff function as a linear combi-nation of the available financial instruments plus an error (to beminimized); 2) estimate the coefficients related to each instru-ment, as a linear regression by using GLS; finally, 3) correspondto a compatibility constraint, shown in (8) at the bottom of thenext page. The outcomes of (8) are vectors and ,each containing strike prices for put and call options. Thesestrikes replicate retail and power production payoff curves withminimum error. is the futures electricity price and / are thelinear regression coefficients for LSEs/GENCOs. This proce-dure favors complement features among agents since optionsrequired by LSEs can be offered by GENCOs and vice versa.


Including the GLS approach represents an enhancement tothe approach in [1] since it is minimized the replicating errorsnot only by means of the strike prices but also by the coeffi-cients. In the financial sense, the approach provides the numberof instruments of each type which will minimize the replicatingerror . It might be thought that ; however, givenheterogeneous risk preferences among market participants, thiswould not necessary be the case and some times, products of-fered by the marketer will end up without buyers, and vice versa.This implies a certain level of risk for the marketer.

IV. CASE STUDY: COLOMBIAN POWER MARKET

Colombia opened up an intensive reorganization of the elec-tricity market since 1994. Under the new framework, the powergeneration and retail businesses were allowed to be competitivederegulated markets, whereas the remaining two, transmissionand distribution, were established as regulated activities.

As a result, nowadays there are four major markets at whichgeneration and retail agents can trade energy: 1) a day-aheadspot market which determines the efficient dispatch of powergeneration resources, considering the suppliers offers submitteda day ahead of actual dispatch; 2) a firm energy market for gen-eration capacity adequacy (see [23] and [24] for details); 3) anonstandardized bilateral contract market with a long trajectorybut today, under strong scrutiny given some problems that havecome to light after these years of functioning; and 4) a secondarymarket for ancillary services (e.g., AGC). See [25] for more de-tails about the Colombian power system.

According to recent findings in the Colombian powermarket, the bilateral contract system faces lack of liquidity andanonymity, not to mention the absence of an adequate and reli-able signal for future electricity prices [26]–[28]. To overcomethese situations, and regarding international experiences in thepower deregulation path, this paper proposes to establish anelectricity derivatives market which could straighten up spotand futures electricity price signals, and end up with the lack ofliquidity and anonymity present in the current bilateral contractsystem in Colombia.

Here, an application of the methodology described in the priorsection is performed with available information of the Colom-bian power market from December 2006 to October 2008 (atime interval with “homogeneous” regulatory framework). This

Fig. 1. Spot prices’ mean behavior.

application is undertaken exploiting the aforementioned corre-lation between price and quantity in the Colombia power market[21].

Hourly spot prices were analyzed (see Fig. 1) and a dailyon-peak period (hours 18, 19, and 20) and an off-peak one (theremaining hours) were defined. This application focuses onhedging instruments for on-peak hours due to higher volatilitiesfor prices and power load/production, and regarding that duringthe remaining hours agents could find hedge with forward/fu-tures contracts.

After Kolmogorov-Smirnov and Anderson-Darling goodnessof fit tests, it was possible to fit a Normal probability distribu-tion function (pdf) to loads served during on-peak periods byeach of five selected LSEs (aggregating the 72% of thenational load). Same procedure was done to the power gener-ated during on-peak periods by nine GENCOs (contributewith 52% of the national production). It was also possible tofit a log-normal pdf to on-peak spot prices according to thetests. These analyses were carried out on a monthly and quar-terly basis, expecting to implement both kinds of options in themarket.

By assuming these pdfs for and , and also assuminga mean-variance utility function to represent agents’ risk profile[see (9)], it is possible to derive an optimal payoff functionfor both kinds of agents:

(9)

(8)


Fig. 2. Application case results, May 2009.

In (9), parameter corresponds to the risk aversion coeffi-cient. Tables IV and V in the Appendix present these values, aswell as the correlation coefficients.

A. Example

Suppose a market maker wishes to find strike prices for twoput and three call monthly on-peak options to be offered in theColombian power market on May 2009 (during this monthand were not dispatched, so they were excluded of the anal-ysis). To do so, it is necessary to estimate the tariff , at whichLSEs will be remunerated during that month and the marginalproduction costs , for each power generator (this marginal cost,could be adjusted to current fuel price scenario or hydrologic ex-pectations in order to consider this parameter uncertainty).

It is also necessary to estimate the parameters of the Normalpdf fitted to and on that month, respectively (seeTables IV and V in the Appendix).

According to historic information, it is expected that on May2009, US$/MWh and that the spot price followsa log-normal pdf . The price cap

US$\/MWh, according to the way scarcity price for the firmenergy market is calculated in Colombia.

General results are presented in Fig. 2. The upper row isrelated to GENCOs and the lower to LSEs. Fig. 2(a) and (d)illustrates the optimal payoff functions and foreach LSE and GENCO considered, respectively. These func-tions were estimated as proposed in [1] [see (3)]. Right overthese curves there are also depicted in darker linescalculated as proposed in (5).

Fig. 2(b) and (e) shows and next to their corre-sponding replicating portfolio using (6) and (7). It can be seenthat the piecewise linear replicating strategies closely follow themarket curves. A zoom on a small segment of the curves on eachfigure was made in order to amplify the differences between the

TABLEL IOPTIONS’ OPTIMAL STRIKE PRICES FOR MAY 2009

lines. The x-axis tick is defined according to the optimal strikeprices found by solving (8) for two put and three call options(see Table I).

Fig. 2(c) and (f) compares, after 10 000 scenario Monte Carlosimulations, the impact on profit’s distribution (for randomlyselected agents and ) of a price-quantity hedging versusa price hedging and no hedging at all. As it can be seen, bothagents reduce the variance of its profit by giving up to a littlepercentage of the expected value in the LSE’s case, whereas inthe GENCO’s case, the profit’s mean slightly rises when fol-lowing a price-quantity hedging strategy.

This is not that intuitive for the GENCOs case; however, thezero cost constraint over the agents’ optimal payoff function

[see (3)] implies that a replicating portfolio should be fi-nanced by borrowing money through bonds or by selling otherinstruments in case of retailers and vice versa for producers.

Hence, after the assumption in the example proposed,the expected value of replicating portfolios are not equal to zerosince the premiums of the options are not properly estimatedto accurately match the payoff from bonds. This mismatch ispositive in case of producers and negative in case of retailers,which is why GENCOs’ average profit slightly soared with P-Qhedging strategy, while LSEs’ decreased.

Certainly, when options’ values are well estimated, the P-Qhedging strategy does not considerably impact average profit,but it does reduce its variance for both kinds of agents.

This outcome presented above is a straight consequence ofthe mean-variance utility function used and it is held for theremaining agents (see Table II). The expected values of retailers’


TABLE IIPROFIT DISTRIBUTION COMPARISON [US$]

TABLE IIIAGENTS’ PRICE-QUANTITY HEDGING PORTFOLIO

profit are negative because the expected spot price is greaterthan the regulated tariff of each LSE on May 2009.

Table III presents for agents and thenumber of instruments required to build up their own replicatingportfolio closer to their corresponding optimal payoff function

. It is done using the replicating procedure describedin Section III. The mean percentage errors of replication areshown in the last column.

Three major results should be highlighted from the exercise:1) the solution of the global optimization process proposed [see(8)] does not favor any agent, by giving the same hedging op-portunities to each of them. This is because the optimizationproblem is formulated in order to minimize the replicating errorof both, retailing and generation market payoff curves, and alsobecause of the way these curves are calculated. 2) Regarding theLEGO approach theory presented in [29], it is possible to repli-cate any payoff profile through a linear combination of the fourbasic financial instruments: bonds, forward/futures, swaps, andoptions.

Nevertheless, the markets are incomplete and it is not possibleto have an infinite spectrum of options’ strike prices as it is re-quired for (4) to be held, so once a finite number of options is de-termined, it is necessary to deal with a certain level of replicatingerror, which could be handled with the replicating strategy pro-posed here using GLS approach. GLS model’s suitability andgoodness is that it finds the coefficients’ estimators that mini-mize this residual error. 3) Finally, it is important to note that forthe agents whose load/production is highly correlated with spotprice and their risk aversion is high, the price-quantity hedgingstrategy gives better results in terms of expected value and dis-persion of profits than just price hedging. However, those agentswith low price-quantity correlation could achieve similar bene-fits by implementing either strategy.

V. CONCLUSION

We have developed a practical application framework toimplement the static price-quantity hedging proposed by Oumet al. in [1]. An optimization procedure is proposed to findoptimal options’ strike prices to be offered in a power marketby a market maker. The theoretical framework was tested withreal data from the Colombian power system and the analysissuggest that by offering two put and three call options on amonthly and quarterly basis, an enhancement in agents’ riskhedging positions might be achieved.

The proposal of a standardized derivatives market could over-come the lack of liquidity on the current bilateral contractingsystem in Colombia, and simultaneously, the lack of anonymitycould be solved by creating a clearing house to manage suchcontractual relationships. Add to that, by trading forward/fu-tures contracts it could also be strengthen up a futures electricityprice signal which after a while, could shift the spot price signal.Furthermore, in a long planning horizon, these products couldalso be offered to the entire region once the physical intercon-nection to other countries in the region takes place. However, itwould be necessary to be aware that a financial market could orcould not succeed, and that it will depend on factors such as thechoice of pool model, the presence of a fixing price or index, thekinds of derivatives, and the underlying asset [4].

Therefore, derivative instruments are suitable and viable toaddress some of the current Colombian power market problems,to improve and encourage competition among agents, and asChao and Wilson say in [20], could help to suppress the spotprice volatility and mitigate market power situations. Plus tothe facts that derivatives suggested correspond to plain vanillaoptions, which create an added value market by offering dif-ferent hedging strategies with simple and understandable finan-cial instruments.

Another feature is that even when power producers and re-tailers were treated as so along this paper, eventually, a nondis-patched power generator could be considered as a retailer anda retailer with excess of electricity could be treated as a powerproducer. These instruments are still suitable for any agent.

One limitation of the approach here proposed is that it doesnot consider the portfolio of technologies available for eachpower producer, which could have not only hydro power gen-eration plants but also natural gas, coal fired, diesel, or nuclearpower generation plants. This fact would light up its portfolioof investment on electricity derivatives due to its available tech-nological flexibility.

VI. FURTHER WORK

It will be first required to determine the optimal number ofinstruments to be offered by the market maker in order to in-crease power market liquidity. This is suggested to be done,once market participants dominate and fully understand optionsas hedging instruments.

A different research line could be oriented to dynamichedging strategies under this sort of electricity derivatives andto test the complementarity of demand and supply for theseinstruments throughout the time. To achieve a new electricityderivatives market in Colombia, it will be necessary to discuss


TABLE IVLSES’ PARAMETERS, MAY 2009

TABLE VGENCOS’ PARAMETERS, MAY 2009

and analyze the practical aspects of implementing these finan-cial options and create a strong institution for trading them[20]. It would be also necessary to develop a proper valuationmethodology to price this kind of options underlying on thespot price.

APPENDIX

A.

Here, it is only presented the deduction of forGENCOs, since in [1] the deduction for LSEs could be found.Regarding the utility function (9) y the assumption theoutcome of the optimization problem (3) is

Replacing (2) in the above, we obtain

Now, assuming and, then

. Given these definitions, the optimal payofffunction of a GENCO will be

B.

See Tables IV and V, where and denote the mean andstandard deviation for the electricity served/produced by agentsconsidered.

ACKNOWLEDGMENT

The authors would like to thank Prof. S. Oren at the Depart-ment of Industrial Engineering and Operations Research in theUniversity of California at Berkeley.

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Gabriel A. Vizcaíno Sánchez received the electrical engineer degree and theM.Sc. degree in operations research from the Universidad de los Andes, Bogotá,Colombia.

He worked on financial mathematics, power derivatives, market design, andenergy policy as a member of the Energy, Environment and Economics ResearchGroup at Universidad de los Andes. Currently, he is working at SIEMENS-Colombia as a Control Engineer in the Energy Automation Department.

Juan Manuel Alzate received the civil engineer degree and the M.Sc. degreein water resources management from the National University of Colombia,Medellín. He is pursuing the Ph.D. degree in engineering at the Universidad deLos Andes, Bogotá, Colombia.

He is currently working on power markets structure and architecture, thestrategic cost of hydroelectric resources, and policy design to foster renewableenergies.

Angela I. Cadena received the electrical engineer degree from the Universidadde los Andes, Bogotá, Colombia, and the Ph.D. degree in management sciencefrom HEC, School of Economy and Social Sciences, University of Geneva,Geneva, Switzerland.

She is an Associate Professor of the School of Engineering at Universidad delos Andes. She was the Head of the Colombian Energy and Mining PlanningUnit and worked in the Colombian research and development fund.

Juan M. Benavides received the electrical engineer degree from the Univer-sidad de los Andes, Bogotá, Colombia, and the Ph.D. degree in resource eco-nomics from Penn State University, State College, PA.

He is an Associate Professor of the School of the School of Business atUniversidad de los Andes. His employment experience included Regional Elec-tricity Utility and the Inter-American Development Bank. He is a national andinternational consultant on infrastructure regulation and privatization.

Documents

Setting Up Standard Power Options to Hedge Price-Quantity Risk in a Competitive Electricity Market: The Colombian Case