Short-term Hedging for an Electricity Retailer.

• Author: Dupuis, Debbie J.

1. INTRODUCTION

   With the recent liberalization of electricity markets and the disentanglement of the vertical integration in the electricity supply chain in Nordic countries, continental Europe, North America and Australia, new risks have arisen for some of the participants of the electricity markets. One such risk-facing participant is the retailer buying from wholesalers to sell to end-users. These retailers (1) sign contracts giving them the obligation to supply electricity to consumers. Retailers often need to supply a quantity of electricity at a price that is predetermined while acquiring it at a variable market price (Von der Fehr and Hansen 2010, Johnsen 2011), exposing the retailers to price risk. Furthermore, as the quantity of electricity which must be supplied to consumers is uncertain, retailers also face load (or volumetric) risk (Deng and Oren 2006).

   Electricity is not easily storable and retailers cannot build up electricity reserves upon which to draw to cover an unexpectedly high load demand or an electricity price increase. The non-storability of electric power fuels extreme price volatility as highly inelastic demand can cause spot prices to skyrocket when shortages occur. For retailers, the volatility can affect profitability since an unexpected high cost of electricity can lead to major losses. "The profit margin for a retailer is so small in relation to the price risk that the profit margin can quickly disappear if the price risk is not hedged" (NordREG 2010). In some cases, there was eventual bankruptcy as with the Pacific Gas and Electric Company in 2001 and Texas Commercial Energy in 2003. To prevent such events, some government regulatory initiatives were even implemented to force retailers to hedge their obligation to serve electricity loads. For example, the California Public Utility Commission now requires load serving entities (LSE) to use forward contracts and options (with mandatory physical settlement) to reduce their risk exposure (State of California 2004).

   It is clear that deficient risk management can lead to financial hardship for retailers and developing effective hedging methodologies in the electricity market has become paramount. Different approaches, using different electricity derivatives, have been proposed in the literature. (Deng and Oren 2006) survey available derivatives and list the papers that implement methods pertaining to each. Hedging procedures can be divided into two main categories: (i) static, and (ii) dynamic. For static hedging, hedging instruments are bought at one point in time and the hedging portfolio is never rebalanced. For dynamic hedging, the composition of the hedging portfolio is adjusted through time as additional information becomes available. Dynamic hedging procedures can be divided into two sub-categories, which we refer to as local and global hedging. Local hedging procedures minimize the risk associated with the portfolio until the next rebalancing whereas global hedging procedures minimize the risk related to the terminal cash flow.

   Several papers apply static hedging without considering load uncertainty. Stoft et al. (1998) describe simple hedging strategies with vanilla derivatives. Bessembinder and Lemmon (2002) identify the optimal position in forward contracts for electricity producers and retailers through an equilibrium scheme. Tanlapco et al. (2002) compare the performance of direct versus cross hedging, the latter practice consisting of the use of futures on other commodities to hedge an exposure to electricity prices. Fleten et al. (2010) optimize the static futures contract position of a hydro-power electricity producer in Nord Pool. Other papers studying static hedging incorporate load uncertainty in their model. Wagner et al. (2003) and Woo et al. (2004) investigate static hedges with forward and futures contracts under different risk constraints. Nasakkala and Keppo (2005) consider an agent with a time-varying load estimate and propose a mean-variance optimization scheme with forward contracts for the optimization of the static hedge ratio and the hedging time. Deng and Xu (2009) examine hedging strategies using interruptible contracts in a one-period setting. In a series of papers, Vehvilainen and Keppo (2003), Oum et al. (2006), Oum and Oren (2009), and Oum and Oren (2010) propose a static hedging procedure maximizing the expected utility of a LSE or a generator using a portfolio of derivatives. Kleindorfer and Li (2005) optimize the expected return of an electricity portfolio corrected by a risk measure (either variance or value-at-risk). The literature on dynamic hedging strategies includes some local procedures. For example, Ederington (1979) suggests to hedge an underlying asset with its futures in a way to minimize the one-period variance of the total portfolio. Bystrom (2003), Madaleno and Pinho (2008), Zanotti et al. (2010), Liu et al. (2010), and Torro (2011) adapt this procedure to the electricity market, but with different model specifications for the spot and futures prices. [Bystrom(2003)] applies one-week horizon hedges on Nord Pool, comparing conditional and unconditional hedge ratios. The unconditional version of hedge ratios outperforms the conditional models. Madaleno and Pinho (2008) and Zanotti et al. (2010) compare different correlation models for the spot and futures prices to compute optimal hedge ratios on European electricity markets. Liu et al. (2010) use copulas to represent the relationship between the spot and futures prices. Torro (2011) studies the case of early dismantlement of the hedging portfolio in the Nord Pool market. Alizadeh et al. (2008) propose a regime-switching process with stochastic volatility for the joint dynamics of the spot price of a commodity and its associated futures, allowing for the calculation of a regime dependent optimal hedge ratio.

   Alternative dynamic hedging schemes are discussed in Eydeland and Wolyniec (2003). For example, there is delta hedging, a method which consists in building a portfolio with value variations that mimic those of the hedged contingent claim. Eydeland and Wolyniec (2003) apply delta hedging to achieve perfect replication when a LSE hedges the price of a fixed amount of load to be served. When perfect replication cannot be achieved, they propose local mean-variance optimization to tackle hedging problems.

   Local procedures are attractive because they are simple to implement. Local risk minimization procedures are myopic however as they do not necessarily minimize the risk through the entire period of exposure (see Remillard 2013). Global hedging procedures remedy this drawback by taking into account the outcomes of all future time periods at any point in time; they evaluate the adequacy of a hedge by looking at the terminal hedging error, i.e. at the maturity of the hedged contingent claim. The following is a non-exhaustive list of papers which study this methodology in general financial contexts. Schweizer (1995) minimizes the global quadratic hedging error in a discrete-time framework for European-type securities. Remillard et al. (2010) extend his work for American-type derivatives. Follmer and Leukert (1999) minimize the probability of incurring a hedging shortfall. Follmer and Leukert (2000) minimize an expected function of the terminal hedging error.

   There have been attempts to apply global hedging procedures in electricity markets. Goutte et al. (2013) use the global quadratic hedging scheme from Schweizer (1995) to hedge various vanilla contingent claims involving a deterministic amount of load with futures. Supposing that the market share of the retailer is a specific functional form of the price charged to customers, Hatami et al. (2009) propose a scheme for the joint optimization of the retail price and the derivatives investment policy. They only consider open-loop (2) solutions. Rocha and Kuhn (2012) consider a retailer that optimizes its global procurement cost with respect to a mean-variance objective measure over a given period of time by purchasing futures and vanilla options. They propose two simplifications to increase tractability: time steps are aggregated into sub-periods and only decision variables that are linear functions of past realized state variables are considered. Kettunen et al. (2010) use a two-dimensional binomial scenario tree representing spot price and load uncertainty to compute the optimal futures hedging portfolio of a retailer incurring electricity procurement costs while maximizing its expected terminal cash value under conditional-cash-flow-at-risk (CCFAR) constraints. Futures are assumed to be priced with a risk premium that only depends on time to maturity. Other work in the literature considers dynamic portfolio management with the perspective of electricity generators. For example, Fleten et al. (2002) propose a global portfolio optimization (both generation scheduling and financial contract management) scheme for electricity generators under scenarios built with a mix of construction and simulation. A total of 256 scenarios are considered within a five-stage stochastic program.

   The current paper contributes to the literature on global hedging procedures for electricity markets and offers three main contributions. First, we develop a dynamic global hedging methodology that makes use of futures contracts for a retailer facing load risk, price risk, basis risk and transaction costs. Obtaining global solutions to such hedging problems is non-trivial and often requires advanced numerical schemes. Our model has the unique advantage that the optimal hedging strategy is computed using a dynamic program that requires neither simplifying the optimization problem (e.g. restricting admissible strategies to linear ones as in Rocha and Kuhn (2012)) nor reducing the dynamics of the state variables (e.g. using binomial trees as in Kettunen et al. (2010) or a low number of scenarios as in...