A quantitative approach to carbon price risk modeling - CiteSeerX

350
300
250
40
35
30
25
EUA Intraday
Switch Coal-Gas
Euro/t CO2
200
150
20
15
10
5
01/04 01/05 01/06 01/07 01/08 01/09 01/10
100
50
0
01/05/05 01/07/05 01/09/05 01/11/05 01/01/06 01/03/06
Figure 2: The price for EUA versus fuel switching price calculated for
gas/coal spot prices.
The strategy to perform fuel switch helps to meet the emission cap, since instead
of the business-as-usual allowance demand Γ i merely Γ i − ∑ T −1
t=0 ξi t ton of carbon
dioxide are to be covered at the end of the compliance period. Thus, we correct
Γ i in the equation (6) by Γ i − ∑ T −1
t=0 ξi t which with (2) expresses the win/loss of
the producer i by
I θi ,ξ i ,A,i
T
= V θi ,A
T
− θT i A T − π(Γ i − ∑ T −1
t=0 ξi t − θT i )+ − ∑ T −1
t=0 ξi tEt. i (7)
Assumption To avoid problems in existence of expected values for (7) and (13),
we suppose that
Γ i , E i t are integrable for i = 1, . . . , N , t = 0, . . . , T − 1. (8)
We substantiate further argumentation using Banach spaces L 1 and L ∞ of P –
integrable and essentially bounded F T –measurable random variables respectively.
Further, we introduce the following spaces of adapted processes
L 1 := {(Ξ t ) T t=0 −1 t ∈ L 1 , t = 0, . . . , T − 1}
L ∞ := {(ξ t ) T t=0 −1 t ∈ L ∞ , t = 0, . . . , T − 1}
U i := {(ξt) i T t=0 −1 i]-valued process}
U := × N i=1U i
Following the conception that each market participant maximizes the own wealth
by trading allowances and applying fuel switching, we formulate the individual
optimization problem, given the fuel switch process A = (A t ) T t=0 as
L 1 × L 1 × U i → R,
(θ i , ξ i ) ↦→ E(I A,i
T (θi , ξ i )). (9)
8