Natural Gas Storage Assets:
Value, Trading Strategy and Financial Investment
Youyi Feng1
1
James Pang2
Department of System Engineering and Engineering Management
Chinese University of Hong Kong, Hong Kong, China
2
Department of Mathematics and Statistics
University of Calgary, Calgary, Alberta, Canada
Seminar of Finance Lab, 2008
Y. Feng, Z. Pang
Gas Storage Valuation
Outline
1
Introduction
Fundamentals of Natural Gas Storage
Literature Review
2
The Model
Valuing a Peak-load Storage Facility
Optimal Trading Strategy in a Dynamic Context
Valuing a Base-Load Storage Facility
Valuing a Firm Storage Contract
3
Numerical Analysis
Example 1: Valuing a natural gas storage facility
Example 2: Valuing a firm storage contract
Y. Feng, Z. Pang
Gas Storage Valuation
Outline
1
Introduction
Fundamentals of Natural Gas Storage
Literature Review
2
The Model
Valuing a Peak-load Storage Facility
Optimal Trading Strategy in a Dynamic Context
Valuing a Base-Load Storage Facility
Valuing a Firm Storage Contract
3
Numerical Analysis
Example 1: Valuing a natural gas storage facility
Example 2: Valuing a firm storage contract
Y. Feng, Z. Pang
Gas Storage Valuation
Outline
1
Introduction
Fundamentals of Natural Gas Storage
Literature Review
2
The Model
Valuing a Peak-load Storage Facility
Optimal Trading Strategy in a Dynamic Context
Valuing a Base-Load Storage Facility
Valuing a Firm Storage Contract
3
Numerical Analysis
Example 1: Valuing a natural gas storage facility
Example 2: Valuing a firm storage contract
Y. Feng, Z. Pang
Gas Storage Valuation
Fundamentals of Natural Gas Storage
1
Storage’s role is changing
Traditional role: balancing the variability in demand and smoothing the
production/supply.
After deregulation: independent charged service and arbitrate instruments
2
Natural Gas Storage Players
Local distribution company (LDC) (obligated to serve, focuses on operational
needs )
Energy marketer (Arbitrager and speculator)
3
Operational Characteristics
Base (cushion) and working gas capacities;
Deliverability, injection/withdrawal rates
Cycling
4
Cost Structure
Injection/withdrawal variable cost (≤ 2% per mmBtu)
Injection/withdrawal fuel cost (≤ 1%)
Y. Feng, Z. Pang
Gas Storage Valuation
Fundamentals of Natural Gas Storage
1
Classification by Operational Characteristics
Depleted Reservoir Storages (Low capital investment, 50% base gas, low
deliverability, 80% )
Aquifer Storages (high deliverability, 80% base gas, less popular)
Salt caverns or salt dome storages (low base gas [25%], high deliverability,
high capital investment)
2
Classification by Functions
Base load facilities (Depleted gas storages)
Peak load storage facilities (Salt caverns)
3
Natural gas storages add value in two ways.
Arbitrage mechanism that allow the exploration of the time spread (buy low
in summer and sell high in winter). (Intrinsic value)
Operational flexibility to react to price fluctuations. (Extrinsic value)
Hedging affects optionality
Valuing the storage with spot trading strategy (instead of forward-based
valuation).
Y. Feng, Z. Pang
Gas Storage Valuation
Relation to American and Swing Options
Storage contract is similar to American options in timing decision of the
exercises (injection/withdraw rights); but with more decision options and
volumetric restrictions at any time.
Similar to swing options with multiple exercises rights but with physical
constraints and transaction costs.
Y. Feng, Z. Pang
Gas Storage Valuation
Leasing Contracts of Natural Gas Storage
1
Term of Service, Injection/Withdrawal Dates
2
Capacities
Maximum Storage Quantity (MSQ) ($MDth)
Maximum Daily Injection Quantity (MDIQ) ($ per Dth/d)
Maximum Daily Withdrawal Quantity (MDWQ) ($ per Dth/d)
3
RATES AND CHARGES (monthly)
Monthly Reservation Charge:
Capacity Reservation Rate ($ per Dth/mo)
Deliverability ($ per Dth/mo)
Usage Charge:
Injection Rate ($ per Dth)
Withdrawal Rate ($ per Dth)
Inventory Charge ($ per Dth/day)
Authorized Overrun Charge
Fuel Reimbursement: In Kind
Y. Feng, Z. Pang
Gas Storage Valuation
Related Literature
1
Real options: Dixit and Pindyck [1994], Trigeorgis [1996], Smit and
Trigeorgis [2004], and Amram and Kulatilaka [2005])
2
Existing literature on gas storage valuation
Financial derivative based valuation: rolling intrinsic approach (Gary and
khandelwal [2004]), calendar spread call options (Eydeland and Wolyniec
[2003], virtual storage (Ahn et al. [2002]).
Computational contribution: finite difference approach (Ahn et al. [2002],
Thompson et al. [2003], Weston [2002], Chen and Forsyth [2006]), Monte
Carlo simulation approach (see e.g., Ludkovski and Carmona [2005],
Boogert and de Jong [2006]) and stochastic programming (Nowak and
Römisch [2000]).
3
Inventory models: Song and Zipkin (1993) and Li, Porteus and Zhang
(2001).
4
Our focus: Characterizing the structure of the storage model and the
optimal spot trading strategy, and the impacts of operational
characteristics and market dynamics, to exploit its financial implications
as the fundamentals of investment analysis.
Y. Feng, Z. Pang
Gas Storage Valuation
The Model
Valuing a Peak-load Storage Facility
1
Introduction
Fundamentals of Natural Gas Storage
Literature Review
2
The Model
Valuing a Peak-load Storage Facility
Optimal Trading Strategy in a Dynamic Context
Valuing a Base-Load Storage Facility
Valuing a Firm Storage Contract
3
Numerical Analysis
Example 1: Valuing a natural gas storage facility
Example 2: Valuing a firm storage contract
Y. Feng, Z. Pang
Gas Storage Valuation
Model Specifications
Consider a marketer who is rational and risk-neutral and rents a storage
facility to trade in energy market, aiming to maximize total expected profit
over the finite horizon of her rental. The financial market is complete and
the marketer is a price-taker.
Time horizon T , risk free interest rate r .
Inventory level of working gas at time t is Xt with the realization x.
Assume that the maximum injection rate α(x) is strictly decreasing and
concave in x and the maximum withdrawal rate β(x) is strictly increasing
and concave in x.
Let q ∈ [−β(x)1{x >0} , α(x)1{x <M} ] be the amount of gas being injected
to (q > 0) or release from (q < 0) storage.
Fuel charges (proportion) for injection/withdrawal L(q) = ρi q + + ρw q − ,
ρi , ρw ∈ [0, 1).
Injection and withdrawal charge C(q) = ci q + + cw q −
Inventory holding cost h(x, s) is increasing and convex in x for any spot
price s.
Terminal value ν(x, s) is non-decreasing and concave in x for any s.
Y. Feng, Z. Pang
Gas Storage Valuation
Dynamics of Spot Price
Risk-adjusted natural gas spot price follows a Markov process {St }
which can be described by the following stochastic differential equation:
dSt = µ(St , t)dt + σ(St , t)dzt +
K
X
χk (t, St , ξk )dNk (t)
k =1
(For the sake of simplicity, we consider only the single-factor model.)
Some canonical examples:
GBM Process: µ(St , t) = µSt , σ(St , t) = σSt
Ornstein-Uhlenbeck Process: µ(St , t) = κ(η − St ), σ(St , t) = σ or
σ(St , t) = σSt .
Geometric Mean-Reverting Process:
µ(St , t) = κ(η − log(St ))St , σ(St , t) = σSt
Y. Feng, Z. Pang
Gas Storage Valuation
Dynamics of Storage System
Let π(t, Xt , St , qt ) the instant payoff rate at time t given the inventory level Xt ,
spot price St and the injection/withdrawal rate qt . Then, the dynamics of
payoff rate and inventory level can be represented as follows.

 Injection (qt > 0): π(t, Xt , St ; qt ) = −St qt (1 + ρi ) − ci qt − h(Xt , St )
Store (qt = 0): π(t, Xt , St ; qt ) = −h(Xt , St )
 Withdrawal (q < 0): π(t, X , S ; q ) = −S q (1 − ρ ) + c q − h(X , S )
w
w t
t
t
t
t
t t
t
t
Y. Feng, Z. Pang
Gas Storage Valuation
dXt = qt dt
dXt = 0
dXt = qt dt
The Stochastic Control Problem
Define J u (t, x, s) = E
RT
t
e−r (τ −t) π(τ, Xτu , Sτ ; qτu )dτ + e−rT ν(XTu , ST )S(t) = s
for any admissible strategy u ∈ U .
The optimal stochastic control problem is
J(t, x, s) = sup J u (t, x, s)
u∈U
subject to the dynamic of
dSt
=
µ(St , t)dt + σ(St , t)dz +
K
X
χ(t, St , ξk )dNk , S0 = s,
k =1
dXtu
=
(qtu + L(qtu , Xtu ))dt, qtu ∈ [−β(Xtu )1{X u >0} , α(Xtu )1{X u <M} ],
t
t
and terminal and boundary conditions
J u (T , x, s)
lim J u (t, x, s)
s→∞ ss
→ 0,
Y. Feng, Z. Pang
=
ν(x, s),
and
u
lim Jss
(t, x, s) → 0,
s→0
Gas Storage Valuation
(1)
(2)
The HJB Equation
0
=
L J(t, x, s) +
max
{−s[q + L(q)] − C(q, x) + qJx (t, x, s)} − h(x, s)
q∈[−β(x ),α(x )]
where
K
X
1 2
L J(t, x , s) = Jt (t, x , s)+ σ (s, t)Jss (t, x , s)+µ(x , t)Js (t, x , s)+
λk [EV (t, x , s+χk (t, x , ξk ))−V (t, x , s)]
2
k =1
The optimal control:


 α(x)
q ∗ (t, x, s) = −β(x)

0
where
if (t, x, s) ∈ IR
if (t, x, s) ∈ WR
if (t, x, s) ∈ NT.
IR
=
{(t, x, s) ∈ D : Jx (t, x, s) > s(1 + ρi ) + ci },
WR
NT
=
=
{(t, x, s) ∈ D : Jx (t, x, s) < s(1 − ρw ) − cw },
{(t, x, s) ∈ D : s(1 − ρw ) − cw ≤ Jx (t, x, s) ≤ s(1 + ρi ) + ci }.
Y. Feng, Z. Pang
Gas Storage Valuation
The Structure Properties
Theorem
1
J(t, x, s) is strictly concave in x for any fixed (t, s).
2
For any fixed (t, s), there is an inject-up-to gas load level I(t, s) and a
withdraw-down-to level W (t, s), which are given by
I(t, s) = inf x ∈ [0, M) : Jx (t, x, s) ≤ (1 + ρi )s + ci ,
W (t, s) = inf x ∈ (0, M] : Jx (t, x, s) ≤ (1 − ρw )s − cw .
Further, I(t, s) ≤ W (t, s). It is optimal to inject gas at rate α(x) if and
only if x < I(t, s), and to withdraw gas at rate β(x) if and only if
x > W (t, s), and to do nothing otherwise. That is,

if x ∈ [0, I(t, s))
 a(t, x, s)
0
if x ∈ [I(t, s), W (t, s)] .
q ∗ (t, x, s) =

−w(t, x, s) if x ∈ (W (t, s), M]
Y. Feng, Z. Pang
Gas Storage Valuation
Structure of Optimal Trading Strategy
x
M
Withdrawal
β (x)
W(t,s)
No Transaction
I(t,s)
Injection
α (x)
0
s
Y. Feng, Z. Pang
Gas Storage Valuation
The Model
Optimal Trading Strategy in a Dynamic Context
1
Introduction
Fundamentals of Natural Gas Storage
Literature Review
2
The Model
Valuing a Peak-load Storage Facility
Optimal Trading Strategy in a Dynamic Context
Valuing a Base-Load Storage Facility
Valuing a Firm Storage Contract
3
Numerical Analysis
Example 1: Valuing a natural gas storage facility
Example 2: Valuing a firm storage contract
Y. Feng, Z. Pang
Gas Storage Valuation
Some Facts
Is it always true to buy low and sell high ?
Y. Feng, Z. Pang
Gas Storage Valuation
Monotonicity on Price Dynamics
Assumption
(A) The spot price process {S(t) : t ≥ 0} is stochastically increasing
in the sense that for any s1 ≥ s2 and any s ≥ 0 and t > t ′
P[S(t) ≥ s|S(t ′ ) = s1 ] ≥ P[S(t) ≥ s|S(t ′ ) = s2 ].
Theorem
Suppose (A) holds.
1. If µ(t, s) = κ(η − s)(mean-reverting drift), q(t, x, s) is decreasing in s.
2. If µ(t, s) = µs (exponential growth drift) and µ > r holds, q(t, x, s) is
increasing in s.
Y. Feng, Z. Pang
Gas Storage Valuation
Pressure of Contract Duration
Theorem
When implementing the optimal operating strategy, the present value of
dynamic marginal storage profit e −rt Jx (t, Xt , St ) is a super-martingale, i.e., for
any time interval δ ∈ (0, T − t),
E[e−r (t+δ) Jx (t + δ, Xt+δ , St+δ )|St = s, Xt = x] ≤ e−rt Jx (t, x, s).
Theorem
Suppose h(x, s) = 0 and ν(x, s) = 0.
J(t, x, s) is increasing in x for any (t, s), J(t, x, s) is decreasing in t for
any (x, s). Moreover, Jx (t, x, s) is decreasing in t.
For any x and s, q(t, x, s) is decreasing in t).
Y. Feng, Z. Pang
Gas Storage Valuation
(3)
The Model
Valuing a Base-Load Storage Asset
1
Introduction
Fundamentals of Natural Gas Storage
Literature Review
2
The Model
Valuing a Peak-load Storage Facility
Optimal Trading Strategy in a Dynamic Context
Valuing a Base-Load Storage Facility
Valuing a Firm Storage Contract
3
Numerical Analysis
Example 1: Valuing a natural gas storage facility
Example 2: Valuing a firm storage contract
Y. Feng, Z. Pang
Gas Storage Valuation
Valuing a Base-Load Storage Asset
Low injection injection and deliverability rates ( seasonal storage such as
depleted reservoirs )
Single-cycle per year which turnovers twice annually.
The injection season is from April to October and the withdrawal season
is from November to March in the following year.
The HJB equation: for t ∈ [τ, T ] and x < M,
0
=
L˜J(t, x, s) − h(x, s) +
max
{−s(1 + ρi )q − C(q, x) + qJx (t, x, s)},
q∈[0,α(x )]
and for t ∈ [0, τ ] and x > 0,
0
=
L˜J(t, x, s) − h(x, s) +
max
{−s(1 − ρw )q − C(q, x) + qJx (t, x, s)}.
q∈[−β(x ),q]
Y. Feng, Z. Pang
Gas Storage Valuation
Valuing a firm storage contract
1
Introduction
Fundamentals of Natural Gas Storage
Literature Review
2
The Model
Valuing a Peak-load Storage Facility
Optimal Trading Strategy in a Dynamic Context
Valuing a Base-Load Storage Facility
Valuing a Firm Storage Contract
3
Numerical Analysis
Example 1: Valuing a natural gas storage facility
Example 2: Valuing a firm storage contract
Y. Feng, Z. Pang
Gas Storage Valuation
Sensitivity of Operational Constraints
Theorem
Defining a firm storage contract with C = (α, β, M, ci , cw , p).
1. At a time t, J(t, x, s; C) is concave in (x, α, β, M) and supermodular in
(x, −α), (x, β) and (x, M), respetively .
2. Optimal thresholds I(t, s; C) and W (t, s; C) are increasing in M and β,
respectively, and decreasing in α. Thus, q(t, x, s) = a(t, x, s) − w(t, x, s)
is increasing in M and β and decreasing in α.
3. J(t, x, s; C) is submodular in (α, ci ) and (β, cw ), respectively.
Y. Feng, Z. Pang
Gas Storage Valuation
Optimal Capacity Decision
Let p be the marginal capacity reservation fee, then the investment
return:
Z
T
Π(C) = J(0, x0 , s0 ; C) −
e −rt pMdt
0
Theorem
1. Π(C) is increasing and concave in α and β, and concave in M. In
addition, it is submodular in (α, ci ), (β, cw ), and (M, p), respectively.
2. For fixed (α, β, ci , cw ), if there is no limit on the contractual capacity, then
the optimal capacity of an FSS contract, M ∗ (p), is determined by the
first-order condition:
∂Π(M ∗ (p), α, β, p, ci , cw )
= 0.
∂M
In addition, M ∗ (p) is decreasing in p.
Y. Feng, Z. Pang
Gas Storage Valuation
Numerical Analysis
Example 1: Valuing a natural gas storage facility
1
Introduction
Fundamentals of Natural Gas Storage
Literature Review
2
The Model
Valuing a Peak-load Storage Facility
Optimal Trading Strategy in a Dynamic Context
Valuing a Base-Load Storage Facility
Valuing a Firm Storage Contract
3
Numerical Analysis
Example 1: Valuing a natural gas storage facility
Example 2: Valuing a firm storage contract
Y. Feng, Z. Pang
Gas Storage Valuation
Example 1: Valuing a natural gas storage facility
Example
A natural gas storage facility
Capacity (M=1Bcf), injection cost ($0.0218/mmBtu), withdrawal cost ($
0.0195/mmBtu). There is 3.59% injection fuel loss and no withdrawal
fuel cost.
Maximum injection/withdrawal rates are stepwise functions:
x/M
0 − 10%
50 − 100%
α(x)(Btu/month)
0.167M
0.140M
x/M
0 − 10%
10 − 16%
16 − 30%
30 − 35%
35 − 100%
α(x)(Btu/month)
0.250M
0.333M
0.375M
0.475M
0.500M
Table: Injection/Withdrawal Rates (Ratchets) a
a
This example is provided by Dr. Kevin G. Kindall, Commercial Division, ConocoPhillips
Y. Feng, Z. Pang
Gas Storage Valuation
Example 1: Valuing a natural gas storage facility
Example
Price Calibration
We refer to Thompson et al. (2003) for a calibrated gas price process
with jumps:
dSt = 0.25(2.5 − St )dt + 0.2St dWt + (ξ − St )dQ.
where Q is a Poisson process with intensity 2 and ξ ∈ N(6, 4).
The risk-free interest rate is 10% per year and T = 1 (year).
The terminal value function ν(x, s) = 0.
Y. Feng, Z. Pang
Gas Storage Valuation
Example 1: Valuing a natural gas storage facility
Value of Storage
7
x 10
2
1.8
Value of Storage ($)
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
1
20
15
0.5
10
Working Gas in Storage (Bcf)
5
0
Gas Price ($/MMBtu)
0
Figure: The Value of Storage
Y. Feng, Z. Pang
Gas Storage Valuation
Example 1: Valuing a natural gas storage facility
Net Withdrawal Rate
Net Withdrawal Rate
6
6
5
Net Withdrawal Rate (Bcf/Year)
Net Withdrawal Rate (Bcf/Year)
5
4
3
2
1
0
−1
4
3
2
1
0
−1
−2
−2
−3
−3
1
20
1
20
15
0.5
15
0.5
10
Working in Gas in Storage (Bcf)
5
0
5
0
Figure: Net withdrawal rate at t= 0
Gas Price ($/MMBtu)
0
Figure: Net withdrawal rate at t=
Net Withdrawal Rate
1
4
Net Wihdrawal Rate
6
6
5
5
Net Withrawal Rate (Bcf/Year)
Netwithdrawal Rate (Bcf/Year)
10
Working Gas in Storage (Bcf)
Gas Price ($/MMBtu)
4
3
2
1
0
−1
4
3
2
1
0
−1
−2
−2
−3
−3
1
1
20
20
15
15
0.5
0.5
10
5
Working Gas in Storage (Bcf)
0
0
Figure: Net withdrawal rate at t=
10
5
Working Gas in Storage (Bcf)
Gas Price ($/MMBtu)
0
1
2
Y. Feng, Z. Pang
0
Gas Price ($/MMBtu)
Figure: Net withdrawal rate at t=
Gas Storage Valuation
3
4
Numerical Analysis
Example 2: Valuing a firm storage contract
1
Introduction
Fundamentals of Natural Gas Storage
Literature Review
2
The Model
Valuing a Peak-load Storage Facility
Optimal Trading Strategy in a Dynamic Context
Valuing a Base-Load Storage Facility
Valuing a Firm Storage Contract
3
Numerical Analysis
Example 1: Valuing a natural gas storage facility
Example 2: Valuing a firm storage contract
Y. Feng, Z. Pang
Gas Storage Valuation
Example 2: Valuing a firm storage contract
Example
Price calibration and contract specification
We refer to de Jong and Walet (2003) for a calibrated gas price process :
d log(St ) = 17.1(log(3) − log(St ))dt + 1.33dWt .
Total capacity (8 Bcf), duration (T = 1 year), initial inventory level
(x0 = 4Bcf ).
The terminal payoff ν(x, s) = −2 · s · max{4 − x, 0}.
Maximum injection rate α(x) = 0.06 · 365(Bcf /year ) and the maximum
withdrawal rate β(x) = 0.25 · 365(Bcf /year ).
injection/withdrawal costs ci = $0.02/MMBtu, cw = $0.01/MMBtu,
injection/withdarwal fuel charges ρi = ρw = 1%.
The risk-free interest rate is 0.06% per year.
Y. Feng, Z. Pang
Gas Storage Valuation
Example 2: Valuing a firm storage contract
Example
Sensitivity to price characteristics
7
7
x 10
1.8
Value of Storage (US$)
Value of Storage (US$)
x 10
1.6
2
1.5
1
s=1
s=2
s=3
1.4
1.2
1
s=1
0.8
s=2
s=4
0.5
s=3
s=5
s=4
0.6
s=6
s=5
s=7
s=6
s=7
0
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
0.4
0
2
4
6
Volatility (σ)
8
10
12
14
16
18
20
Mean−reverting Rate (κ)
Figure: Sensitivity to volatility
Y. Feng, Z. Pang
Figure: Sensitivity to mean-reverting rate
Gas Storage Valuation
Example 2: Valuing a firm storage contract
Example
Sensitivity to operational constraints
Value of Storage (V (0, 4, s)) (106 $)
α
0.01
0.05
0.1
0.15
0.2
β
0.25
0.25
0.25
0.25
0.25
8
8
8
8
8
α
β
M
0.06
0.06
0.06
0.06
0.06
0.06
0.1
0.15
0.2
0.25
8
8
8
8
8
α
β
M
0.06
0.06
0.06
0.06
0.06
0.25
0.25
0.25
0.25
0.25
Initial Spot Price ($/MMBtu)
3
4
5
M
5
6
7
8
10
1
2
2.5423
9.4928
13.1912
15.1745
16.4279
2.3357
8.5354
11.5808
13.1512
14.1359
1
2
6.3395
7.9626
9.1611
9.9335
10.4716
5.3021
6.8845
8.0631
8.8256
9.3591
1
2
7.1643
8.699
9.7442
10.4716
11.3535
6.8641
7.9732
8.7767
9.3591
10.0849
2.2564
8.1254
10.8936
12.274
13.1374
Y. Feng, Z. Pang
2.4056
8.5653
11.5381
13.0264
13.9542
3.1484
9.9344
13.0373
14.5814
15.5374
Initial Spot Price ($/MMBtu)
3
4
5
4.988
6.4894
7.6244
8.3655
8.8823
5.4565
7.0029
8.1445
8.8745
9.3736
6.0913
7.8918
9.2624
10.152
10.7798
Initial Spot Price ($/MMBtu)
3
4
5
6.9375
7.78
8.4163
8.8823
9.4718
7.9434
8.572
9.0376
9.3736
9.7825
9.5578
10.1022
10.4985
10.7798
11.1075
Gas Storage Valuation
6
7
4.8093
12.0395
15.1968
16.7584
17.724
7.2195
14.7544
17.9282
19.4908
20.4561
6
7
6.9094
9.0997
10.85
12.035
12.9017
7.8978
10.5956
12.8533
14.4373
15.6221
6
7
11.7898
12.2908
12.6499
12.9017
13.1852
14.5758
15.0512
15.388
15.6221
15.8795
Summary
Valuation of natural gas storage needs to capture the extrinsic value as
well as intrinsic value.
Understanding the impacts of operational flexibility and market dynamics
on the options value and trading strategy is important.
How to identify momentum opportunity is key to success for a marketer.
We are still thinking about ......
How to price the storage interruptible contract?
Storage facility as a risk management instrument
A contracting game between a risk-averse storage owner and a risk-neutral
marketer
How storage capacity affects the energy (gas/electricity) prices?
Applying to oil markets, soft commodity markets and even electricity markets
(through pumped-storage hydropower stations).
Y. Feng, Z. Pang
Gas Storage Valuation