# ppt - Electric Power Optimization Centre

```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:
Optimal supply schedule

At any time, assume supply function is additively separable:

Then, extending Hortaçsu & Puller (2008), we have the following supply
schedule:

Which is equivalent to:
elasticity of net residual demand
Equilibrium spot price

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:
Forward pricing

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 II

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:
Results

.
.


.
Results II

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 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.
Approximation


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.
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
500
400
300
200
100
0
2004
2005
2006
2007
2008
2009
2010
Demand (National offtake GWh)
130
120
110
100
90
80
70
2004
2005
2006
2007
F(t)
2008
Demand
2009
2010
Results

Estimation method: Seemingly Unrelated Regression (SUR)
- Objective: To estimate expected spot price conditioned on state variables. No endogeneity.
System of Equations
Equation:
Estimation Method: Seemingly Unrelated Regression
Observations: 2505
R-squared
S.E. of regression
Durbin Watson stat
Sample: 22/01/2004 30/11/2010
Included observations: 2505
0.76
0.76
28.04
2.61
Mean dependent var
S.D. dependent var
Sum squared resid
72.66
56.90
1,967,258
103.12
Total system (balanced) observations: 7515
Coefficient
Std. Error
t-Statistic
Prob.
Equation:
-14.83
1.75
-8.46
0.00
R-squared
0.62
Mean dependent var
0.76
0.08
9.29
0.00
0.62
S.D. dependent var
0.99
0.003
368.79
0.00
S.E. of regression
5.84
Sum squared resid
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
2.89
5.59
206.28
26.50
0.01
0.00
0.99
Determinant Residual covariance
3.15E+16
9.44
85,173
Equation:
R-squared
S.E. of regression
Durbin Watson stat
0.75
0.75
28.29
2.62
Mean dependent var
S.D. dependent var
Sum squared resid
72.66
56.90
2,004,258
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
Conclusion

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.
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