Can market power in the electricity spot market translate into market power in the hedge market?

Toby Daglish and Gabriel Fiuza de Bragança

New Zealand Institute for the Study of Competition and Regulation and Instituto de Pesquisa Econômica Aplicada

Background

Forward pricing in electricity markets is troublesome.

- Electricity non-storability implies that usual commodity pricing literature (and arbitrage/ cost of carry arguments) may not hold.

Electricity markets frequently present additional complications.

- Oligopoly, uniform-price auction and vertical integration.

Theoretical literature discusses how forward contracts affect spot market power. How does spot market power affect forward prices?

The hybrid pricing approach

Several papers try to mimic electricity price’s stochastic behaviour in order to value its derivatives.

- Focus on seasonality and spikes (short-lived and abrupt oscillations).

- Ex. Schwartz (1997), Schwartz and Smith (2000), Deng (2000), Lucia and Schwartz (2002) and Cartea and Villaplana (2005).

Alternative: hybrid pricing approach.

- Build on an equilibrium framework, explaining instantaneous price behaviour in terms of observable state variables (demand and supply). Keep track of fundamentals.

- Assume state variables follow dynamic processes and apply no-arbitrage methodologies to calculate derivatives.

Skantze, Gubina, and Ilic (2000), Barlow (2002), Pirrong and Jermakyan (2008), Cartea and Villaplana (2008) and Lyle and Elliott (2009).

Equilibrium ground is too simple and based on a competitive spot market.

Some definitions

There are N firms (K generators and R retailers). Firms can participate in both markets (I=K+R-N gentailers).

State variables:

The consumers’ demand:

Generator i’s cost function:

Contracts:

Generators/gentailers’ auction problem

The conditional cumulative function of market clearing price is:

Generator/Gentailer i’s maximization problem:

At any time, assume supply function is additively separable:

Then, extending Hortaçsu & Puller (2008), we have the following supply schedule:

Which is equivalent to:

Optimal supply schedule

elasticity of net residual demand

If we further assume that there are K>2 generators/gentailers and that marginal costs and demand can be approximated by a linear function…

…by the spot market clearing condition, we have:

Equilibrium spot price

There are two state variables: an inelastic demand and a cost shifter, say the water inflows. Interest rate is constant (forward=future).

Under these assumptions the spot price equation simplifies to the following:

Where

Forward pricing

Assume that the demand oscillates around a deterministic function of time (seasonality). Cost shifter oscillates around a long term mean.

Then, by Lucia & Schwartz (2002) two factor model, we have:

Forward pricing II

.

.

.

Results

Market power and forward prices as a function of contract maturity (same parameters as previous figure with b adjusting for a fixed marginal cost).

Results II

Results III

Market power and forward prices as a function of contract maturity (same assumptions as previous figure except for QC = 10).

Empirical Strategy

Challenge: to find 2 good proxies for the state variables (demand and cost shifter).

Test: See if the theoretical assumptions are supported by the data.- The estimation procedure is divided in two steps: First, spot price model

estimation. Second, forward price calibration (to find the market price of risk– lambdas).

Simulation: See how changes in concentration affect forward prices.

Assume we have an economy where K=N, which means all retailers participate of the generation market.

Assume also that only generators/gentailers transact in the forward market.

Approximation

Ex: New Zealand: Market shares in 2008

Source: Companies' annual reports 2008 and NZ Electricity Commission.

Under these assumptions the spot price equation simplifies to the following:

Notice that in this case the generators’ quantity contracted does not affect spot prices. But the number of generators still does. Price is equal to average marginal cost.

Spot price model estimation Model discretized:

The New Zealand electricity market is characterized by the dominance of hydro and gas power . Shadow prices are natural candidates for .

In particular, Evans, Guthrie and Lu (2010), show that the shadow price of water is the same as the shadow price of gas under regular conditions. However, shadow prices are not observable. The challenge is to find the best proxy or proxies. Primary candidates?

Unfortunately several combinations of variables such as hydro inflows, storage and thermal production fail to attain serially uncorrelated results.

Solution: Since marginal costs are closely related to spot prices, we use the latest observed spot price (lagged spot price) as a proxy of marginal cost shifters for empirical purposes.

Therefore:

Haywards node spot price. Source: Electricity Commission.

National offtake in GWh. Source: Electricity Commission.

Observed(Lagged) spot price as proxy.

Haywards forward price. Monthly and quarterly contracts. Source: www.energyhedge.co.nz (accessed in december/2010).

We use daily frequency from 22/01/2004 to 30/11/2010. Consistent with forward price series available.

Spot Price

0

100

200

300

400

500

2004 2005 2006 2007 2008 2009 2010

NZD/MWh (CPI adjusted)

Demand (National offtake GWh)

70

80

90

100

110

120

130

2004 2005 2006 2007 2008 2009 2010

F(t) Demand

Results Estimation method: Seemingly Unrelated Regression (SUR)- Objective: To estimate expected spot price conditioned on state variables. No endogeneity.

System of Equations

Estimation Method: Seemingly Unrelated Regression Observations: 2505R-squared 0.76 Mean dependent var 72.66

Sample: 22/01/2004 30/11/2010 Adjusted r-squared 0.76 S.D. dependent var 56.90Included observations: 2505 S.E. of regression 28.04 Sum squared resid 1,967,258

Durbin Watson stat 2.61Total system (balanced) observations: 7515

Coefficient Std. Error t-Statistic Prob.

-14.83 1.75 -8.46 0.00 R-squared 0.62 Mean dependent var 103.12

0.76 0.08 9.29 0.00 Adjusted r-squared 0.62 S.D. dependent var 9.44

0.99 0.003 368.79 0.00 S.E. of regression 5.84 Sum squared resid 85,173

102.97 0.29 358.65 0.00 Durbin Watson stat 1.55

-8.23 0.39 -21.15 0.00

4.96 0.01 674.03 0.00

148.12 5.59 26.50 0.002.89 206.28 0.01 0.99

R-squared 0.75 Mean dependent var 72.66Adjusted r-squared 0.75 S.D. dependent var 56.90S.E. of regression 28.29 Sum squared resid 2,004,258

Determinant Residual covariance 3.15E+16 Durbin Watson stat 2.62

Equation:

Equation:

Equation:

Forward Pricing Calibration

Theoretical forward pricing formula:

Integrated formula/ Calibration:

Calculating the lambdas that minimize the non linear least squares

for the 1651 forward prices of our sample, we have:

Results

Hybrid pricing models offer a promising framework to relate equilibrium fundamentals to derivative pricing.

Our model shows that, in a case where contracts are not significant in influencing clearing spot prices, the spot market power may still affect the whole forward curve.

If market power affect forward prices, it may affect the optimal quantity contracted.

Unlike the assumptions of most of the IO theoretical literature on the subject, neither forward contracts or forward prices are exogenous. Its is important to fully understand its determinants to evaluate its relationship with market power.

Conclusion