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MODELLING & MANAGING FULL/RESIDUAL SUPPLY GAS CONTRACTS IN CONTINENTAL MARKETS

ALEPH CONSULTING

ENERGY – RISK – FINANCE

Padova, 10 Maggio 2013

Stefano Fiorenzani

ALEPH - Director & Founder –

What is Aleph?

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• Aleph is a project created by Stefano Fiorenzani in order to provide Energy

Companies, Consulting Firms and Financial Institutions specialized services in the area of Energy Trading and Risk Management.

• Aleph’s particular focus is on training and consulting quantitative methods

applied to Energy Finance.

• Aleph’s strength is the professional and theoretical experience of its founder

and team.

• Aleph is in contact with other business entities able to integrate its services

with pure IT, Legal, Accounting, Fiscal and Commercial aspects.

Full/Residual supply gas contracts

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• Full supply contracts (or Full Serve/Full Requirements) are typically structured to satisfy supply

needs of big/medium/small size energy consumers.

• FS are highly structured deals. Only the general framework is common for different markets.

Many different contract features can characterize different markets and/or specific sectors (eg. Industrial large consumers, Distributors, Municipalities, SME etc).

• In FS contracts the writer (seller) has the obligation to fully satisfy the consumption need

(demand) of the buyer for the payment of a monetary price defined per unit of consumed volume (€/MWh).

• Contract price may be a fixed price or an indexed one. Indexed price contracts may be subject to

fixing prior to delivery.

• Contract’s buyer should provide indications about future consumption needs based on

consumption history. Nomination rules may apply in order to segregate volume flexibility from pure unbalancing (a different pricing may apply).

Full/Residual supply gas contracts

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Payoff Structure:

𝐺𝐺 = 𝑀𝑢 𝑄𝑢 − 𝐺𝑢

𝑢∈Ψ

+ Δ𝑀𝑢 𝑄𝑢 + 𝑞𝑞𝑞𝑞𝑞𝑞𝑞 − 𝐶𝐺𝑢 𝐺𝐺 = 𝑀𝑢 𝑄𝑢 − 𝐺𝑢

𝑢∈Ψ

+ Δ𝑀𝑢 𝑄𝑢 + 𝑞𝑞𝑞𝑞𝑞𝑞𝑞 − 𝐶𝐺𝑢

d-1 nominated (forecastable d-1) load delivery period contractual price spot price unbalanced load unbalancing penalty unbalancing price

Full/Residual supply gas contracts

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• Residual supply contracts are typically

structured to partially satisfy supply needs of big size energy consumers which have already contracted a part of its supply.

• The seller of RS contracts are required to

complement and balance (proportionally or globally) the consumption demand of the buyer net of a previously contracted supply which could be a ToP band, a ToP Profile, an

• ther RS contract.
• The RS contract’s buyer shall provide

the seller full evidence of previously contracted supplies.

• RS contracts can have different

contractual schemes according to counterparty nature (shipper/non shipper) and distribution rules.

ToP Band RS Supplier Consumer RS Supplier ToP (Hub) ToP (Hub) FS (DP) RS Contractual Scheme

Full/Residual supply gas contracts

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Payoff Structure:

𝑆𝐺 = (𝑀𝑢 − 𝐺𝑀𝑢) 𝑄𝑢 − 𝐺𝑢

𝑢∈Ψ

+ Δ𝑀𝑢 𝑄𝑢 + 𝑞𝑞𝑞𝑞𝑞𝑞𝑞 − 𝐶𝐺𝑢

Load supplied by alternative supplier

Volumetric flexibility and balancing service apply to the whole consumption => proportional impact

• f risk premium and balancing

service is much higher than in FS contracts.

Full/Residual supply gas contracts

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Physical Constraints (potentially present):

• Capacity Constraints => working at daily level (Max/Min MWh/d), mirroring the physical capacity of the

transportation facility.

• Energy Constraints => working at yearly/season/quarter level (Max/Min MWh/period), aiming to constraint

volumetric flexibilities. If they are present they should be supported by appropriate penalty structure (no pure indications).

• Make up /Carry Forward => linked to energy constraints, pretty infrequent in non Hub delivered contracts

(swings).

Daily Consumption Min Capacity Max Capacity Cumulated Consumption Max Energy Min Energy

Full/Residual supply gas contracts

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Sell Back Options (potentially present):

• The main difference between volumetric flexibility sold to a wholesale trader (with a swing

contract typically) or to a final consumer (industrial or retail) is related to the delivery point and hence to the opportunity to re-sell gas in the market instead of consuming it.

• This opportunity present in swings and not typically in FS allows contract owner to optimize and

extract value from contact’s flex otherwise impossible to extract.

• In particular cases also in FS contracts sell back
• ptions can be present:

 Within portfolio construction schemes + RS contracts => opportunity to buy and sell back portfolio building blocks (only) before delivery.  Complete sell back opportunity up to d-2 (in this case FS become almost a pure swing despite the delivery point).

Portfolio Construction Framework

The wider is the sell back opportunity the higher is the contract’s value.

Framing the pricing problem

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FS contracts are non-perfectly hedgiable products, hence the pricing problem should be tackled in different steps in order to obtain a coherent even if subjective valuation:

1. Construct (typically by simulations) the complete conditional distribution of contract’s payoff structure (conditional distribution of the “naked position”); 2. Determine the contract price which sets the conditional expectation of contract’s payoff to zero (“break even price”); 3. Determine the optimal “static” or “dynamic” hedging strategy which minimize overall risk (at deal level) and construct the complete conditional distribution of “hedged position” (remember that we usually work under the assumption that hedging strategies with linear instruments does not contribute to overall expected payoff); 4. Determine the subjective minimum risk remuneration (“risk premium”), eventually disentangled in different risk components such as pure volumetric risk, unbalancing risk, liquidity risk etc.

Framing the pricing problem

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FS Payoff Simulation

• The main challenge is determining and implementing a realistic and robust joint

dynamics of the triplet of stochastic processes [L(t), S(t), P(t)] (we can also reduce the triplet to a couple price/ load [L(t), Prices(t)] with Prices(t)= [S(t), P(t)] ).

• The designated model should be able to correctly represents individual dynamics but

also joint behavior (dependence structure).

• The designated model should be consistent with observed forward price structures

and with historically measured load paths (or forecasted ones).

• Two alternative modeling approaches: semi fundamental models, reduced form

models.

𝐺𝐺 = 𝑀𝑢 𝑄𝑢 − 𝐺𝑢

𝑢∈Ψ

+ Δ𝑀𝑢 𝑄𝑢 + 𝑞𝑞𝑞𝑞𝑞𝑞𝑞 − 𝐶𝐺𝑢

Framing the pricing problem

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Un-hedged Payoff Distributions The more load and price are correlated in their movements the more FS payoff structure becomes non-linear wrt price (form y=-c*x to y=c*x-x^2)

Framing the pricing problem

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Un-hedged Payoff Distributions Load-Price correlation induce non linearity in the payoff structure as can be reflected also in distribution variance and asymmetry.

• 3
• 2.5
• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 x 10

5

0.2 0.4 0.6 0.8 1 1.2 x 10

• 5

Payoff Distribution

Framing the pricing problem

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Optimal hedging in a static and dynamic framework  FS contracts cannot be perfectly hedged (daily granularity, volume risk), nevertheless the better is the hedge the lower is the payoff risk (left tail of payoff distribution).  When we face the pricing problem we should necessarily consider hedge possibilities and effectiveness (we can’t price the contract based on payoff expectations!) Static Hedging Problem (hedging with respect to static payoff expectation) determine optimal contract pricing (P0) and hedging (θ(t)) which maximize expected utility ??

• determine your utility function (risk charged expected profit?)
• avoid trivial problems
• consider the market (liquidity, maturity, bid-ask spreads…etc)

𝐺𝐺 = 𝑛𝑞𝑛𝑄0,𝜄0,𝑢 𝐹 𝑉 𝑀𝑢 𝑄𝑢 − 𝐺𝑢

𝑢∈Ψ

+ Δ𝑀𝑢 𝑄

𝑢 + 𝑞𝑞𝑞𝑞𝑞𝑞𝑞 − 𝐶𝐺𝑢 + 𝜄0,𝑢 𝐺 0, 𝑞 − 𝐺𝑢

Framing the pricing problem

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Optimal hedging in a static and dynamic framework (plausible pricing/hedging targets) I. Determine the break even price and the minimum risk hedging strategy. II. Determine the minimum contract price (more competitive price) which allows to guarantee a target expected profit given a certain (controlled) risk level.

𝑔 𝑄

0, 𝜄0,𝑢 =

• 𝑀𝑢

𝑄𝑢 − 𝐺𝑢

𝑢∈Ψ

+ Δ𝑀𝑢 𝑄

𝑢 + 𝑞𝑞𝑞𝑞𝑞𝑞𝑞 − 𝐶𝐺𝑢 + 𝜄0,𝑢 𝐺 0, 𝑞 − 𝐺𝑢

determine P(0) -> E[f] = 0 Θ -> Var[f] is minimized 𝑔 𝑄

0, 𝜄0,𝑢 =

• 𝑀𝑢

𝑄𝑢 − 𝐺𝑢

𝑢∈Ψ

+ Δ𝑀𝑢 𝑄

𝑢 + 𝑞𝑞𝑞𝑞𝑞𝑞𝑞 − 𝐶𝐺𝑢 + 𝜄0,𝑢 𝐺 0, 𝑞 − 𝐺𝑢

determine min P(0) -> E[f] > target profit Θ -> Percentile[f] < target abs risk

Framing the pricing problem

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Optimal hedging in a static and dynamic framework (plausible pricing/hedging targets) I. Determine the minimum contract price (more competitive price) which allows to guarantee a target risk adjusted return on capital (RaRoC). II. Determine the minimum contract price (more competitive price) which allows to guarantee a target risk adjusted return on capital (RaRoC) subject to controlled (absolute) risk level. Note: under standard assumptions hedging (with linear instruments) does not contribute to strategy’s expected profit.

𝑔 𝑄

0, 𝜄0,𝑢 =

• 𝑀𝑢

𝑄𝑢 − 𝐺𝑢

𝑢∈Ψ

+ Δ𝑀𝑢 𝑄

𝑢 + 𝑞𝑞𝑞𝑞𝑞𝑞𝑞 − 𝐶𝐺𝑢 + 𝜄0,𝑢 𝐺 0, 𝑞 − 𝐺𝑢

determine P(0) -> E[f] / Percentile [f] > target hurdle rate (RaRoC) Θ -> Var[f] is minimized 𝑔 𝑄

0, 𝜄0,𝑢 =

• 𝑀𝑢

𝑄𝑢 − 𝐺𝑢

𝑢∈Ψ

+ Δ𝑀𝑢 𝑄

𝑢 + 𝑞𝑞𝑞𝑞𝑞𝑞𝑞 − 𝐶𝐺𝑢 + 𝜄0,𝑢 𝐺 0, 𝑞 − 𝐺𝑢

determine P(0) -> E[f] / Percentile [f] > target hurdle rate (RaRoC) Θ -> Percentile[f] < target abs risk

Framing the pricing problem

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Dynamic Hedging Problem (properly consider hedging rebalancing costs)

• Simulate (consistently and simultaneously) spot and forward price dynamics.
• The problem may become an SDP problem.
• The relationship between hedging adjustments and forward price changes has an

impact both on pricing and risk measurement of FS contract (positive dependence, negative dependence, independence).

• Computationally more intense exercise.

𝐺𝐺 = 𝑛𝑞𝑛𝑄0,𝜄0,𝑢,∆𝜄𝑡,𝑢 𝐹 𝑉

• 𝑀𝑢

𝑄

𝑢 − 𝐺𝑢 𝑢∈Ψ

+ Δ𝑀𝑢 𝑄

𝑢 + 𝑞𝑞𝑞𝑞𝑞𝑞𝑞 − 𝐶𝐺𝑢 + 𝜄0,𝑢 𝐺 0, 𝑞 − 𝐺𝑢 𝑡∈Ω

+ Δ𝜄𝑡,𝑢 ∙ Δ𝐺(𝑡, 𝑞)

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Conclusions

• Tailor Made product may imply the construction of a tailor made pricing model and

tailor made definition of risk factors evolution.

• When a product is not completely hedgiable (market incompleteness) subjective

valuation of residual risks is necessary.

• In FS contracts valuation and hedging is played by Load-Price dependence structure

which is by the way difficult to measure and model.

Contacts

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Stefano Fiorenzani is a recognized expert in Energy Trading & Risk Management. He completed his career in top European energy companies and financial institutions. He has published several scientific and business articles and three books on advanced methods in Energy Finance area. He also lectures in Masters and Postgraduate courses in various European universities. Stefano has a degree in Economic Science at the University of Florence, a Master of Science in Financial Economics at the University of Wales in Cardiff and a PhD in Mathematical Finance at the University of Brescia.

Web: www.aleph-energy.com E-mail : stefano.fiorenzani@aleph-energy.com Mobile: +39-3481724153

Thanks a lot for your attention!!!!