Comments on: "Forward market integration", by
Thomas Tangeras
Thomas-Olivier Léautier
Toulouse School of Economics
June 2014
Léautier (TSE)
Forward integration
06/14
1 / 11
Outline of the article
Initial observation: introducing a forward market is procompetitive in a single
market when producers compete à la Cournot (Allaz and Vila, 1993)
Léautier (TSE)
Forward integration
06/14
2 / 11
Outline of the article
Initial observation: introducing a forward market is procompetitive in a single
market when producers compete à la Cournot (Allaz and Vila, 1993)
Research question: What is the impact of introducing a single forward market
in a set of multiple spot markets?
Léautier (TSE)
Forward integration
06/14
2 / 11
Outline of the article
Initial observation: introducing a forward market is procompetitive in a single
market when producers compete à la Cournot (Allaz and Vila, 1993)
Research question: What is the impact of introducing a single forward market
in a set of multiple spot markets?
Policy application: zonal pricing of electricity. Single day-ahead market vs.
multiple nodal real-time markets
Léautier (TSE)
Forward integration
06/14
2 / 11
Policy application: zonal pricing (1/2)
Unconstrained (day ahead) dispatch
Léautier (TSE)
Forward integration
06/14
3 / 11
Policy application: zonal pricing (2/2)
Constrained (real-time) dispatch
Léautier (TSE)
Forward integration
06/14
4 / 11
Separate spot and forward markets
Forward contract: producers l in market m produces qlm at cost cm , sells klm
at the forward price f and (qlm klm ) at the spot price
P (Qm ) = am bQm . Pro…ts are
π
Léautier (TSE)
= (P (Qm )
= (P (Qm )
cm ) (qlm klm ) + klm (f cm )
cm ) qlm + klm (f P (Qm ))
Forward integration
(1)
06/14
5 / 11
Separate spot and forward markets
Forward contract: producers l in market m produces qlm at cost cm , sells klm
at the forward price f and (qlm klm ) at the spot price
P (Qm ) = am bQm . Pro…ts are
π
= (P (Qm )
= (P (Qm )
cm ) (qlm klm ) + klm (f cm )
cm ) qlm + klm (f P (Qm ))
(1)
Equilibrium output is
qlm
Léautier (TSE)
1
=
L+1
am
cm
b
Forward integration
+ Lklm
∑ kim
i 6 =l
!
06/14
5 / 11
Separate spot and forward markets
Forward contract: producers l in market m produces qlm at cost cm , sells klm
at the forward price f and (qlm klm ) at the spot price
P (Qm ) = am bQm . Pro…ts are
π
= (P (Qm )
= (P (Qm )
cm ) (qlm klm ) + klm (f cm )
cm ) qlm + klm (f P (Qm ))
(1)
Equilibrium output is
qlm
1
=
L+1
am
cm
b
+ Lklm
∑ kim
i 6 =l
!
No arbitrage in the forward market:
f = P (Qm ) ) π = (P (Qm )
Léautier (TSE)
Forward integration
cm ) qlm
06/14
5 / 11
Separate spot and forward markets
Forward contract: producers l in market m produces qlm at cost cm , sells klm
at the forward price f and (qlm klm ) at the spot price
P (Qm ) = am bQm . Pro…ts are
π
= (P (Qm )
= (P (Qm )
cm ) (qlm klm ) + klm (f cm )
cm ) qlm + klm (f P (Qm ))
(1)
Equilibrium output is
qlm
1
=
L+1
am
cm
b
∑ kim
+ Lklm
i 6 =l
!
No arbitrage in the forward market:
f = P (Qm ) ) π = (P (Qm )
cm ) qlm
Equilibrium forward market volume is
A
Km
=
Léautier (TSE)
1
1+
L +1
L (L 1 )
Forward integration
am
cm
b
06/14
5 / 11
Integrated forward market (separate spot markets)
Forward contract: producers l in market m produces qlm at cost cm , sells klm
at the forward price f and (qlm klm ) at the spot price P (Qm )
Léautier (TSE)
Forward integration
06/14
6 / 11
Integrated forward market (separate spot markets)
Forward contract: producers l in market m produces qlm at cost cm , sells klm
at the forward price f and (qlm klm ) at the spot price P (Qm )
Equilibrium pro…t hence output unchanged
Léautier (TSE)
Forward integration
06/14
6 / 11
Integrated forward market (separate spot markets)
Forward contract: producers l in market m produces qlm at cost cm , sells klm
at the forward price f and (qlm klm ) at the spot price P (Qm )
Equilibrium pro…t hence output unchanged
No arbitrage in the forward market delivery price
f =
1
M
M
∑
P (Qm )
m =1
)
π = (P (Qm )
Léautier (TSE)
cm ) qlm + klm
Forward integration
1
M
M
∑ P (Qi )
i =1
P (Qm )
!
06/14
6 / 11
Integrated forward market (separate spot markets)
Forward contract: producers l in market m produces qlm at cost cm , sells klm
at the forward price f and (qlm klm ) at the spot price P (Qm )
Equilibrium pro…t hence output unchanged
No arbitrage in the forward market delivery price
f =
1
M
M
∑
P (Qm )
m =1
)
π = (P (Qm )
1
M
cm ) qlm + klm
M
∑ P (Qi )
i =1
P (Qm )
!
Equilibrium forward market volume is
KI =
Léautier (TSE)
1
1+
L +1
ML (L 1 )
∑M
m = 1 ( am
b
Forward integration
cm )
06/14
6 / 11
Impact of forward markets integration
Higher forward sales
KI
M
∑
m =1
Léautier (TSE)
A
=
Km
L (L 1 )
L +1
+
M 1
M
L (L 1 )
1
M
L +1
Forward integration
∑M
m = 1 ( am
b
+1
cm )
0
06/14
7 / 11
Impact of forward markets integration
Higher forward sales
KI
M
∑
m =1
A
=
Km
L (L 1 )
L +1
+
M 1
M
L (L 1 )
1
M
L +1
∑M
m = 1 ( am
b
+1
cm )
0
Lower average price cost markup (Proposition 1)
Léautier (TSE)
Forward integration
06/14
7 / 11
Application to zonal pricing
Day-ahead supply-demand equilibrium per zone
Léautier (TSE)
Forward integration
06/14
8 / 11
Application to zonal pricing
Day-ahead supply-demand equilibrium per zone
Within each zone, nodal rebalancing between day-ahead and real-time to
meet transmission constraints
Léautier (TSE)
Forward integration
06/14
8 / 11
Application to zonal pricing
Day-ahead supply-demand equilibrium per zone
Within each zone, nodal rebalancing between day-ahead and real-time to
meet transmission constraints
Related to previous problem: single forward (day-ahead) price, multiple
possible real-time (nodal) prices
Léautier (TSE)
Forward integration
06/14
8 / 11
Application to zonal pricing
Day-ahead supply-demand equilibrium per zone
Within each zone, nodal rebalancing between day-ahead and real-time to
meet transmission constraints
Related to previous problem: single forward (day-ahead) price, multiple
possible real-time (nodal) prices
Zonal pricing is shown to have desirable e¢ ciency properties (Propositions 2
and 3)
Léautier (TSE)
Forward integration
06/14
8 / 11
Observations and suggestions for further work
De…nition of the single forward contract in multiple markets
Léautier (TSE)
Forward integration
06/14
9 / 11
Observations and suggestions for further work
De…nition of the single forward contract in multiple markets
Representation of countertrading in zonal pricing
Léautier (TSE)
Forward integration
06/14
9 / 11
De…nition of the single contract in multiple markets
1
Physical contract
Léautier (TSE)
Forward integration
06/14
10 / 11
De…nition of the single contract in multiple markets
1
Physical contract
Pro…t
π = (P (Q m )
Léautier (TSE)
cm ) (qlm
Forward integration
klm ) + klm (f
cm )
06/14
10 / 11
De…nition of the single contract in multiple markets
1
Physical contract
Pro…t
π = (P (Q m )
cm ) (qlm
klm ) + klm (f
cm )
What is the delivery point of the forward contract? Market m? If so, no
arbitrage would imply P (Qm ) = f . Mix of di¤erent markets, consistent with
f = M1 ∑M
m =1 P (Qm )? If so, how does a producer guarantee delivery in other
markets?
Léautier (TSE)
Forward integration
06/14
10 / 11
De…nition of the single contract in multiple markets
1
Physical contract
Pro…t
π = (P (Q m )
cm ) (qlm
klm ) + klm (f
cm )
What is the delivery point of the forward contract? Market m? If so, no
arbitrage would imply P (Qm ) = f . Mix of di¤erent markets, consistent with
f = M1 ∑M
m =1 P (Qm )? If so, how does a producer guarantee delivery in other
markets?
2
Financial contract
Léautier (TSE)
Forward integration
06/14
10 / 11
De…nition of the single contract in multiple markets
1
Physical contract
Pro…t
π = (P (Q m )
cm ) (qlm
klm ) + klm (f
cm )
What is the delivery point of the forward contract? Market m? If so, no
arbitrage would imply P (Qm ) = f . Mix of di¤erent markets, consistent with
f = M1 ∑M
m =1 P (Qm )? If so, how does a producer guarantee delivery in other
markets?
2
Financial contract
Pro…t
π
=
=
(P (Q m )
(P (Q m )
cm ) qlm + klm (f
cm ) (qlm
y)
klm ) + klm (f
cm ) + klm (P (Qm )
y)
where y is the delivery price of the underlying
Léautier (TSE)
Forward integration
06/14
10 / 11
De…nition of the single contract in multiple markets
1
Physical contract
Pro…t
π = (P (Q m )
cm ) (qlm
klm ) + klm (f
cm )
What is the delivery point of the forward contract? Market m? If so, no
arbitrage would imply P (Qm ) = f . Mix of di¤erent markets, consistent with
f = M1 ∑M
m =1 P (Qm )? If so, how does a producer guarantee delivery in other
markets?
2
Financial contract
Pro…t
π
=
=
(P (Q m )
(P (Q m )
cm ) qlm + klm (f
cm ) (qlm
y)
klm ) + klm (f
cm ) + klm (P (Qm )
y)
where y is the delivery price of the underlying
Additional basis risk (P (Qm ) y ) compared to equation (1)
Léautier (TSE)
Forward integration
06/14
10 / 11
Di¤erences between the model and practice
Counter trading is pay-as-bid. Pro…t of …rm l in market m that has o¤ered
klm in the unconstrained (day ahead) market and is constrained to qlm in the
constrained (real time) market is
π = (P (Qm )
cm ) qlm + (z
cm ) (klm
qlm )
which appears di¤erent from equation (5) in the article
π = (P (Qm )
Léautier (TSE)
cm ) qlm + (z
Forward integration
P (Qm )) klm
06/14
11 / 11
Di¤erences between the model and practice
Counter trading is pay-as-bid. Pro…t of …rm l in market m that has o¤ered
klm in the unconstrained (day ahead) market and is constrained to qlm in the
constrained (real time) market is
π = (P (Qm )
cm ) qlm + (z
cm ) (klm
qlm )
which appears di¤erent from equation (5) in the article
π = (P (Qm )
cm ) qlm + (z
P (Qm )) klm
Possible extension: counter trading is determined by available transmission
capacity. Equilibrium in each market requires supply plus net imports (often,
transmission capacity constraint) equals demand
Léautier (TSE)
Forward integration
06/14
11 / 11
Di¤erences between the model and practice
Counter trading is pay-as-bid. Pro…t of …rm l in market m that has o¤ered
klm in the unconstrained (day ahead) market and is constrained to qlm in the
constrained (real time) market is
π = (P (Qm )
cm ) qlm + (z
cm ) (klm
qlm )
which appears di¤erent from equation (5) in the article
π = (P (Qm )
cm ) qlm + (z
P (Qm )) klm
Possible extension: counter trading is determined by available transmission
capacity. Equilibrium in each market requires supply plus net imports (often,
transmission capacity constraint) equals demand
Desirability of zonal pricing weakened by the inc-dec game (Holmberg and
Lazarczyk, 2014)
Léautier (TSE)
Forward integration
06/14
11 / 11