Modeling and Hedging the Risk in Retail Load Contracts discusses volumetric or "swing" risk in full requirements load following contracts for electricity. Swing risk is the cash flow risk from deviations in delivered load volumes from expected levels that are positively correlated with market prices. The document outlines how to estimate the expected cost of serving load including an expected "shaping factor" cost, describes delta hedging price risk but remaining exposed to swing risk, and proposes using options to construct a "gamma hedge" to manage swing risk. Regression analysis is used to estimate the relationship between historic load and price in order to model the gamma exposure and design an optimal options hedge.
The imminent release of a major update to PLEXOS will give rise to a new era in Hydro modelling with the arrival of a disruption to the 1970's SDDP methodology. The PLEXOS rolling horizon methodology offers multi-stage stochastic optimisation for long term hydro management at speeds 3 times faster than SDDP for the same high resolution.
For more information or a trial please go directly to https://energyexemplar.com/contactus/ on the Energy Exemplar website.
Normally we have taken Fire insurance for our assets (buildings/plant and machinery/stocks/contents). Current situation under lockdown where those assets are lying unattended for more than 30 days, these will be deem as Silent Risk under Fire insurance .
As proactive measure, Aera suggests please reach out to their Insurer /broker/agent about that same. Please read the note for details. Please let us know if you need any more details
The imminent release of a major update to PLEXOS will give rise to a new era in Hydro modelling with the arrival of a disruption to the 1970's SDDP methodology. The PLEXOS rolling horizon methodology offers multi-stage stochastic optimisation for long term hydro management at speeds 3 times faster than SDDP for the same high resolution.
For more information or a trial please go directly to https://energyexemplar.com/contactus/ on the Energy Exemplar website.
Normally we have taken Fire insurance for our assets (buildings/plant and machinery/stocks/contents). Current situation under lockdown where those assets are lying unattended for more than 30 days, these will be deem as Silent Risk under Fire insurance .
As proactive measure, Aera suggests please reach out to their Insurer /broker/agent about that same. Please read the note for details. Please let us know if you need any more details
Power GaN 2019: Epitaxy, Devices, Applications and Technology Trends - Yole D...Yole Developpement
First design-win for GaN HEMTs in the high-volume smartphone fast charging market.
More information on: https://www.i-micronews.com/products/power-gan-2019-epitaxy-devices-applications-technology-trends/
Polymeric Materials for Advanced Packaging at the Wafer-Level 2018 Report by...Yole Developpement
Polymeric materials market revenue will double over the next five years.
More information on that report at : https://www.i-micronews.com/report/product/polymeric-materials-for-advanced-packaging-at-the-wafer-level.html
Power Management: Technology, Industry and Trends 2019 - by Yole DéveloppementYole Developpement
China, 300mm, societal impacts, and important strategic decisions are shuffling the cards in the power
IC industry.
More on: https://www.i-micronews.com/products/power-management-technology-industry-and-trends-2019/
The page shows the global network of in-vehicle motor business, and the prospects for future business at Nidec, the world's No.1 comprehensive motor manufacturer. Nidec provides a wide lineup of high-performance, energy-efficient motors, and is quick to respond to recent customer demands in the EV and HEV vehicle markets.
Broadcom AFEM-8072 – Mid and High Band LTE RF Front-End Module (FEM) - teardo...system_plus
The first mid/high band Long Term Evolution (LTE) Radio Frequency (RF) FEM in the Apple iPhone X integrates the latest generation of Film Bulk Acoustic Resonator (FBAR) technology with advanced and innovative packaging.
More information on that report at http://www.systemplus.fr/reverse-costing-reports/broadcom-afem-8072-mid-and-high-band-lte-rf-front-end-module-fem/
Thin wafer processing and Dicing equipment market - 2016 Report by Yole Devel...Yole Developpement
Strong demand for thinner wafers and smaller die is driving the evolution of dicing technologies
Demand for thinned wafers is growing strongly!
Driven by consumer applications such as smartphones, smart cards and stacked packages, the demand for thinned wafers has increased over recent years.
We estimate that the number of thinned wafers used for MEMS devices, CMOS Image Sensors, memory and logic devices, including those with TSVs, as well as and Power devices exceeded the equivalent of 16.5 million 8-inch wafer starts per year (WSPY) in 2015. This is mainly supported by CMOS Image Sensors, followed by Power devices. We expect that this number of thinned wafers will peak at the equivalent of almost 32 million 8-inch WSPY by 2020. This would represent a 14% compound annual growth rate (CAGR) from 2015 to 2020.
Thinner wafers bring several benefits, including enabling very thin packaging, and therefore better form factors, improved electrical performance and high heat dissipation.
Miniaturization towards smaller, higher-performing, lower-cost device configurations has thinned wafers below 100 µm or even 50 µm for some applications, such as memory and power devices.
Forecasts for the number of thinned wafers by thickness and by application are analyzed in this report. It also includes insights on the number of thinning tools, breakdowns by wafer size, and technological highlights affecting the applications mentioned above...
Training Module on Electricity Market Regulation - SESSION 3 - Price RegulationLeonardo ENERGY
This session explains different forms of price control, including the classical rate of return organisation and more advanced forms of incentive regulation. It will also explain the design criteria for different price control models.
• Major price control models: Rate of return / Cap regulation / Yardstick competition / Sliding scale regulation
• Principle design criteria: Efficiency properties / Demand impact / Regulatory burden / Practicability / Coherence with industry and market design
GaN and SiC for power electronics applications 2015 Report by Yole DeveloppementYole Developpement
The SiC market is expected to treble and GaN is expected to explode - if challenges are overcome
In 2014, the SiC chip business was worth more than $133M. As in previous years, power factor correction (PFC) and photovoltaics (PV) are still the leading applications.
SiC diodes represent more than 80% of the market. In 2020, diodes will remain the main contributor across various applications, including electric and hybrid electric vehicles (EV/HEV), PV, PFC, wind, Uninterruptible Power Supplies (UPS) and motor drives.
SiC transistors will grow in parallel with diodes, driven by PV inverters. Challenges must be overcome prior to the adoption of pure SiC solutions for EV power train inverters, which is nevertheless expected by 2020.
Including the growth in both diodes and transistors we expect the total SiC market to more than treble by 2020, reaching $436M...
El shonen es uno de los géneros anime más populares en todo el mundo, básicamente el público al que va dirigido son los jóvenes, pero se puede decir que con el pasar del tiempo es uno de los más completos e interesantes.
Power GaN 2019: Epitaxy, Devices, Applications and Technology Trends - Yole D...Yole Developpement
First design-win for GaN HEMTs in the high-volume smartphone fast charging market.
More information on: https://www.i-micronews.com/products/power-gan-2019-epitaxy-devices-applications-technology-trends/
Polymeric Materials for Advanced Packaging at the Wafer-Level 2018 Report by...Yole Developpement
Polymeric materials market revenue will double over the next five years.
More information on that report at : https://www.i-micronews.com/report/product/polymeric-materials-for-advanced-packaging-at-the-wafer-level.html
Power Management: Technology, Industry and Trends 2019 - by Yole DéveloppementYole Developpement
China, 300mm, societal impacts, and important strategic decisions are shuffling the cards in the power
IC industry.
More on: https://www.i-micronews.com/products/power-management-technology-industry-and-trends-2019/
The page shows the global network of in-vehicle motor business, and the prospects for future business at Nidec, the world's No.1 comprehensive motor manufacturer. Nidec provides a wide lineup of high-performance, energy-efficient motors, and is quick to respond to recent customer demands in the EV and HEV vehicle markets.
Broadcom AFEM-8072 – Mid and High Band LTE RF Front-End Module (FEM) - teardo...system_plus
The first mid/high band Long Term Evolution (LTE) Radio Frequency (RF) FEM in the Apple iPhone X integrates the latest generation of Film Bulk Acoustic Resonator (FBAR) technology with advanced and innovative packaging.
More information on that report at http://www.systemplus.fr/reverse-costing-reports/broadcom-afem-8072-mid-and-high-band-lte-rf-front-end-module-fem/
Thin wafer processing and Dicing equipment market - 2016 Report by Yole Devel...Yole Developpement
Strong demand for thinner wafers and smaller die is driving the evolution of dicing technologies
Demand for thinned wafers is growing strongly!
Driven by consumer applications such as smartphones, smart cards and stacked packages, the demand for thinned wafers has increased over recent years.
We estimate that the number of thinned wafers used for MEMS devices, CMOS Image Sensors, memory and logic devices, including those with TSVs, as well as and Power devices exceeded the equivalent of 16.5 million 8-inch wafer starts per year (WSPY) in 2015. This is mainly supported by CMOS Image Sensors, followed by Power devices. We expect that this number of thinned wafers will peak at the equivalent of almost 32 million 8-inch WSPY by 2020. This would represent a 14% compound annual growth rate (CAGR) from 2015 to 2020.
Thinner wafers bring several benefits, including enabling very thin packaging, and therefore better form factors, improved electrical performance and high heat dissipation.
Miniaturization towards smaller, higher-performing, lower-cost device configurations has thinned wafers below 100 µm or even 50 µm for some applications, such as memory and power devices.
Forecasts for the number of thinned wafers by thickness and by application are analyzed in this report. It also includes insights on the number of thinning tools, breakdowns by wafer size, and technological highlights affecting the applications mentioned above...
Training Module on Electricity Market Regulation - SESSION 3 - Price RegulationLeonardo ENERGY
This session explains different forms of price control, including the classical rate of return organisation and more advanced forms of incentive regulation. It will also explain the design criteria for different price control models.
• Major price control models: Rate of return / Cap regulation / Yardstick competition / Sliding scale regulation
• Principle design criteria: Efficiency properties / Demand impact / Regulatory burden / Practicability / Coherence with industry and market design
GaN and SiC for power electronics applications 2015 Report by Yole DeveloppementYole Developpement
The SiC market is expected to treble and GaN is expected to explode - if challenges are overcome
In 2014, the SiC chip business was worth more than $133M. As in previous years, power factor correction (PFC) and photovoltaics (PV) are still the leading applications.
SiC diodes represent more than 80% of the market. In 2020, diodes will remain the main contributor across various applications, including electric and hybrid electric vehicles (EV/HEV), PV, PFC, wind, Uninterruptible Power Supplies (UPS) and motor drives.
SiC transistors will grow in parallel with diodes, driven by PV inverters. Challenges must be overcome prior to the adoption of pure SiC solutions for EV power train inverters, which is nevertheless expected by 2020.
Including the growth in both diodes and transistors we expect the total SiC market to more than treble by 2020, reaching $436M...
El shonen es uno de los géneros anime más populares en todo el mundo, básicamente el público al que va dirigido son los jóvenes, pero se puede decir que con el pasar del tiempo es uno de los más completos e interesantes.
This new course is designed specifically to expand participants\' knowledge and skills in the areas of risk, exposures, managing uncertainty, portfolio management, setting limits and implementing controls. Products, potential price changes and risk management with respect to trading and portfolio management are also focused upon during the course, therefore the primary aim is that of market risk.
Risk is the big topic of conversation in the compliance industry. Businesses are moving at a faster rate and operations continue to increase in complexity, and yet the need for compliance is stronger than ever. So we need to implement a systematic and objective means to maintain compliance, and keep up with the pace of business.
In just 5 minutes, you'll learn why Risk Assessment is the new benchmark, and how to create a simple Risk Matrix for use in your compliance efforts.
Risk assessment principles and guidelinesHaris Tahir
Risk assessment principles and guidelines is a presentation slides was created and presented at Mission Critical Workshop. This slides is part of Business Continuity Management (BCM) presentation which intended for professional who is responsible for BCM or Risk Assessment Program.
EmberClear BAML Global Energy Conference 2012emberclear
Albert Lin, Chief Executive Officer of EmberClear, presented at the Bank of America Merrill Lynch 2012 Global Energy Conference on Tuesday November 13, 2012 at the Fontainebleau Hotel in Miami, FL.
The 2012 Global Energy Conference is an interactive and highly productive gathering of industry leaders and top institutional investors. Bank of America Merrill Lynch’s Energy Research team will host senior leaders from more than 80 companies from the US and abroad representing a cross-section of subsectors and investment opportunities.
For more information please visit www.emberclear.com
MicroCapClub Invitational: Vertex Energy (VTNR)Ian Cassel
Vertex Energy (VTNR) is a vertically integrated hydrocarbon recovery company that has profitably grown revenues from $38m in 2009 to $110m in 2011. The company owns and operates a network of used motor oil collectors and aggregators, and then refines this feedstock using the company’s proprietary TCEP technology into higher value end products. The company has been expanding organically and by way of strategic acquisitions to broaden its footprint. Recovering, recycling and reusing hydrocarbons, plastics, and chemicals, has been a very hot area for investors the last couple of years. Several mergers and acquisitions in the space have made Vertex Energy a potential target. Heckmann (HEK) acquired Thermal Fluids in 2011, followed by Clean Harbor’s (CLH) acquisition of Safety-Kleen a few months ago. Heritage-Crystal Clean (HCCI), an industry comparable trades at over 20x 2013 EPS estimates. Vertex Energy has flown under the radar even while producing a more impressive growth curve then its larger peers. While the peer group trades at 20x 2013 analyst estimates, Vertex trades at 5x 2013 estimates, and that's the opportunity. Listen to CEO Ben Cowart as he tells the story.
Steve Corneli, NRG Energy, Inc. - Speaker at the marcus evans Generation Summit 2012 held in San Antonio, TX, delivered his presentation entitled Clean Energy Trends – Costs, Policies and Initiatives
Uma cidade sustentável é, por definição, “compacta, completa e conectada”. A cidade inteligente nasce deste conceito de sustentabilidade urbana e assenta numa gestão dinâmica e em tempo real de todos as condições e dos fluxos que a cidade gera, dando prioridade à resiliência da cidade, à eficiência na utilização de recursos e à utilização de recursos renováveis, distribuindo os benefícios de forma equitativa.
A eficiência energético-ambiental do meio edificado, a descentralização da transformação de recursos renováveis que introduzem o conceito de “utilizador-produtor”, as “redes inteligentes e bi-direccionais” e a capacidade de “armazenamento descentralizado de recursos” à escala urbana, a disponibilização de toda a informação em tempo real sobre os fluxos e a gestão dinâmica das condicionantes climáticas que afectam o bem estar da cidade, estão entre os temas abordados.
O Workshop é dirigido a todos os decisores que influenciam a qualidade de construção do meio edificado.
A inscrição para o Workshop é gratuita sendo pre-inscrição individual e obrigatoria.
Mais informações: Tel: 918 613 023 - e-mail: mail@construcaosustentavel.pt
BP Solar: Drivers for Commercial Solar ProjectsMDV-SEIA
Bill Poulin, Director of Commercial Projects at BP Solar, discusses the facts and the philosophy behind BP Solar's large-scale commercial projects.
This presentation was given December 4, 2009 at the Solar Energy Focus Conference: Fall 2009 hosted by the Maryland, DC, Virginia Solar Energy Industries Association (MDV-SEIA) in Gaithersburg, MD.
To learn more please visit:
www.mdvseia.camp7.org
Similar to Modeling and Hedging the Risk in Retail Load Contracts (20)
LA HUG - Video Testimonials with Chynna Morgan - June 2024Lital Barkan
Have you ever heard that user-generated content or video testimonials can take your brand to the next level? We will explore how you can effectively use video testimonials to leverage and boost your sales, content strategy, and increase your CRM data.🤯
We will dig deeper into:
1. How to capture video testimonials that convert from your audience 🎥
2. How to leverage your testimonials to boost your sales 💲
3. How you can capture more CRM data to understand your audience better through video testimonials. 📊
Company Valuation webinar series - Tuesday, 4 June 2024FelixPerez547899
This session provided an update as to the latest valuation data in the UK and then delved into a discussion on the upcoming election and the impacts on valuation. We finished, as always with a Q&A
VAT Registration Outlined In UAE: Benefits and Requirementsuae taxgpt
Vat Registration is a legal obligation for businesses meeting the threshold requirement, helping companies avoid fines and ramifications. Contact now!
https://viralsocialtrends.com/vat-registration-outlined-in-uae/
At Techbox Square, in Singapore, we're not just creative web designers and developers, we're the driving force behind your brand identity. Contact us today.
Putting the SPARK into Virtual Training.pptxCynthia Clay
This 60-minute webinar, sponsored by Adobe, was delivered for the Training Mag Network. It explored the five elements of SPARK: Storytelling, Purpose, Action, Relationships, and Kudos. Knowing how to tell a well-structured story is key to building long-term memory. Stating a clear purpose that doesn't take away from the discovery learning process is critical. Ensuring that people move from theory to practical application is imperative. Creating strong social learning is the key to commitment and engagement. Validating and affirming participants' comments is the way to create a positive learning environment.
3.0 Project 2_ Developing My Brand Identity Kit.pptxtanyjahb
A personal brand exploration presentation summarizes an individual's unique qualities and goals, covering strengths, values, passions, and target audience. It helps individuals understand what makes them stand out, their desired image, and how they aim to achieve it.
Recruiting in the Digital Age: A Social Media MasterclassLuanWise
In this masterclass, presented at the Global HR Summit on 5th June 2024, Luan Wise explored the essential features of social media platforms that support talent acquisition, including LinkedIn, Facebook, Instagram, X (formerly Twitter) and TikTok.
What is the TDS Return Filing Due Date for FY 2024-25.pdfseoforlegalpillers
It is crucial for the taxpayers to understand about the TDS Return Filing Due Date, so that they can fulfill your TDS obligations efficiently. Taxpayers can avoid penalties by sticking to the deadlines and by accurate filing of TDS. Timely filing of TDS will make sure about the availability of tax credits. You can also seek the professional guidance of experts like Legal Pillers for timely filing of the TDS Return.
The world of search engine optimization (SEO) is buzzing with discussions after Google confirmed that around 2,500 leaked internal documents related to its Search feature are indeed authentic. The revelation has sparked significant concerns within the SEO community. The leaked documents were initially reported by SEO experts Rand Fishkin and Mike King, igniting widespread analysis and discourse. For More Info:- https://news.arihantwebtech.com/search-disrupted-googles-leaked-documents-rock-the-seo-world/
RMD24 | Retail media: hoe zet je dit in als je geen AH of Unilever bent? Heid...BBPMedia1
Grote partijen zijn al een tijdje onderweg met retail media. Ondertussen worden in dit domein ook de kansen zichtbaar voor andere spelers in de markt. Maar met die kansen ontstaan ook vragen: Zelf retail media worden of erop adverteren? In welke fase van de funnel past het en hoe integreer je het in een mediaplan? Wat is nu precies het verschil met marketplaces en Programmatic ads? In dit half uur beslechten we de dilemma's en krijg je antwoorden op wanneer het voor jou tijd is om de volgende stap te zetten.
B2B payments are rapidly changing. Find out the 5 key questions you need to be asking yourself to be sure you are mastering B2B payments today. Learn more at www.BlueSnap.com.
Modeling and Hedging the Risk in Retail Load Contracts
1. Modeling and Hedging the Risk in Retail
Load Contracts
Eric Meerdink, Director of Structuring & Analytics
May 3, 2011
Hess Energy · 2010 All Rights Reserved
1
3. Hess: Who We are Today
A Totally Integrated Energy Company
RETAIL MARKETING
ENERGY TRADING
Selling motor fuels and
REFINING Hess Energy Trading
convenience products at
EXPLORATION Processing the Company, a joint
retail stores
Discovering oil crude oil into venture buying and
and gas finished products selling energy financial
instruments
ENERGY
MARKETING
Marketing petroleum
SUPPLY, TRADING & products, natural gas
PRODUCTION & TRANSPORTATION TERMINALS and electricity to
DEVELOPMENT Buying, selling and Storing products and commercial,
Getting crude oil out of transporting crude oil and distributing fuels to our industrial and utility
the ground finished products customers customers
Hess Energy · 2010 All Rights Reserved
3
4. One of the Largest Energy Suppliers on the East Coast
Hess Energy · 2010 All Rights Reserved
4
5. Hess Energy: Robust Product Suite
Electricity Natural Gas Fuel Oil Green Suite
Marketing to Marketing to Delivery to Commercial Reducing electric
Commercial & Commercial & & Industrial customers usage during times of
Industrial customers Industrial customers peak demand
Distributor sales from
4,500 MWs/hr (RTC ) Wholesale to LDCs Hess terminals Support renewable
(enough electricity to energy sources, such
power 4 million 1.5 BCF/day 110K BPD as wind, solar, biomass
average homes) and hydropower
#2 electric marketer on Balance your carbon
the east coast impact from oil and
natural gas with carbon
offsets
Hess Energy · 2010 All Rights Reserved
5
6. Volumetric Risk in Retail Load Contracts
Hess Energy · 2010 All Rights Reserved
6
7. What is a Full Requirements Load Following Contract
• Full Requirements Load Following: A fixed price agreement to serve all
the electricity load of a customer, and provide all products required to
supply the electric load, for a pre-determined interval of time, without
restrictions on volume. Typically served at a fixed rate per MWH.
• Also called Full Plant Requirements Contract.
• Typical key products to be supplied:
○ Load Following Energy
○ Capacity
○ Transmission
○ Ancillaries
○ RECs
Hess Energy · 2010 All Rights Reserved
7
8. Volumetric or Swing Risk
• Volumetric or swing risk is defined as a cash flow risk caused by
deviations in delivered volumes compared to expected volumes. The
primary cause of these volumetric deviations is weather and economic
conditions.
• Not enough that delivered volumes deviate from expected volumes.
○ These deviations in delivered volumes must be positively correlated with
market prices.
○ The full requirements load following contract is delta hedged at some
expected volume.
• Under these conditions the resulting expected cash flow position is
negative and non-linear with respect to changes in market prices.
• Swing risk is similar to the gamma position of an option, as it is a second
order price risk.
Hess Energy · 2010 All Rights Reserved
8
9. Figure 1. Correlation Between Price and Load
12-Month Rolling Average of Load and Price in PSE&G Zone
5,500 $90.00
$80.00
5,400
$70.00
5,300
$60.00
5,200
$50.00
$/MWH
MW
$40.00
5,100
MW
$30.00
$/MWH
5,000
$20.00
4,900
$10.00
4,800 $0.00
May-06 Sep-06 Jan-07 May-07 Sep-07 Jan-08 May-08 Sep-08 Jan-09 May-09 Sep-09 Jan-10 May-10 Sep-10
Month/Yr
Hess Energy · 2010 All Rights Reserved
9
10. Figure 2: Retail Sale and Long Hedge
$
Long Hedge
+
$/MWH
Net: Swing Risk
“Gamma”
-
Short Sale
Short Retail Sale
Hess Energy · 2010 All Rights Reserved
10
11. Figure 3. Change in Cash Flow when Power is Delta Hedged
A B C
Load greater
Load less than Load equals than expected
expected load expected load load
Price less than
1
expected price - 0 +
2 Price equals
expected price 0 0 0
Price greater
3 than expected
price
+ 0 - Swing Risk
- - - - - -
Long Hedged Short
Position Position
Hess Energy · 2010 All Rights Reserved
11
12. Expected Cost to Serve Load
and Swing Risk
Hess Energy · 2010 All Rights Reserved
12
13. Expected Cost to Serve Load
• Model assumptions:
○ Pi = Actual price in hour i (random variable)
○ Li = Actual load in hour i (random variable)
○ Covi = Covariance between P and L in hour i Cov(Pi,Li).
○ i = hours in the month i = 1,…,N
○ Averages will be denoted with a bar over the variable
○ Expectations will be taken at time t given information available up to and
including time t. Referenced by a subscript t.
N
1
Pt =
N
∑P
i =1
t
i
= Forward Value of Power
N
1
Lt =
N
∑L
i =1
i
t = Forward Value of Expected Load
Hess Energy · 2010 All Rights Reserved
13
14. Expected Cost to Serve Load
N
• Cost to serve load: Cost = ∑P L
i =1
i i
N i i
• Expected cost to serve load : Et ( Cost ) = Et P L
i =1
∑
• Taking expectations and solving we get:
Expected block Expected load Expected covariance
cost of power. shaping cost. between price and load.
∑(L )
N N
(1 Et ( Cost ) = N ⋅ Pt ⋅ Lt +
)
i =1
i
t − L Pti +
t ∑Cov ( P , L )
i =1
i i
( 2) Et ( Cost ) = (1 + SFt ) Pt N Lt
SF = Shaping Factor. Ratio of the sum of the
expected load shaping cost and expected covariance
cost to the expected block cost.
Hess Energy · 2010 All Rights Reserved
14
15. Hedging the Expected Cost
• Start with the expected cost function, equation (1) and take a Taylor series
expansion with respect to prices and loads.
N
∂Cti ∂Cti i
(3) ∆Costt = ∑( )
i =1
Lit ∆Pti + ∆Lit ( )
Pti + i ∆Pt + i ∆Lt +
∂Pt
i
∂Lt
• Where refers to higher order terms. Neglecting these terms we can write
the change in expected cost as:
∂Pti ∂Cti ∂Pti N i ∂Cti ∂Lit
∑( )
N
= N ⋅ Lt +
Lit − Lt + i
∂Pt ∂Pt ∂Pt
∆Pt + Pt + i
∂Lt
∑
∂L
∆Lt
(3)
i =1 i =1 t
Price Hedge Load Hedge
The delta on a load following After delta hedging the price risk
contract does not equal 1.0 we are left with the first order load risk
or Gamma risk.
Hess Energy · 2010 All Rights Reserved
15
16. Fair Value of a Load Following Contract
• A fair price or fair value contract has an expected value of zero.
• Fair value contracts require the inclusion of the expected value of the
covariance between price and load, not just the expected hourly shaping
cost. Excluding this cost component biases the distribution to the left.
• But inclusion of the expected covariance in the contract price does not
guarantee that the swing risk has been minimized or removed. It only
guarantees that the contract is priced fairly.
• We are still left with the negative tail risk from large positively correlated
price and load movements – Cash Flow at Risk.
Hess Energy · 2010 All Rights Reserved
16
17. Figure 4. P&L Distribution: Swing Risk vs. Swing Cost
Excluding the expected covariance produces a distribution
with a negative expected value.
0.04
0.03
Mean
Density
0.02
Negative Skew:
0.01
Swing Risk
0.00
-60 -50 -40 -30 -20 -10 0 10 20 30
Cash Flow
Swing Cost
Hess Energy · 2010 All Rights Reserved 17
17
19. Figure 5. Short Gamma Hedge
− Γ( P )
How do we create this hedge?
+ Hedge
Change in P&L
Monthly
Average
Price $/mwh
gamma
-
Γ( P )
Hess Energy · 2010 All Rights Reserved
19
20. Figure 6. Creating a Gamma Position from Options
Use vanilla calls and puts to construct the gamma position.
− Γ( P )
+
− Γ( P )
ˆ
Change in P&L
Monthly
Average
Price $/mwh
-
Hess Energy · 2010 All Rights Reserved
20
21. Solving for the Estimated Gamma Function
• Select a series of strikes, Ki , and quantities, θi, to create a portfolio of
puts and calls.
• To estimate the gamma function we need to choose the amount of
options for each strike, θi , so as to minimize the distance between the
estimated gamma function and the true gamma function.
• Estimated gamma function equals:
N M
− Γ( P ) =
ˆ
∑Max( P − K , 0) ×θ + ∑Max( K
i =1
i i
i =1
i − P,0 ) ×θi
• Choose the optimal quantities by minimizing the sum of the squared
errors between the true and estimated gamma function over a set of Q
prices. 2
∑ [Γ( P ) − Γ( P )]
Q
min ˆ j j
θ
j =1
Hess Energy · 2010 All Rights Reserved
21
22. Theoretical Model
• It has been shown that a static hedge of plain vanilla options and
forwards can be used to replicate any European derivative (Carr and
Chou 2002, Carr and Madan 2001).
• Any twice continuously differentiable payoff function, f (S ), of the
terminal price S can be written as:
F0 ∞
f ( S ) = f ( F0 ) + f ′( F0 )( S − F0 ) + ∫ f ′′( K )( K − S ) dK ++
∫ f ′′( K )( S − K ) + dK
0 F0
Initial Delta
Gamma Hedge: “Swing Risk”
P&L Position
• Our payoff function is the terminal profit. It can be decomposed into a
static position in the day 1 P&L, initially costless forward contracts,
and a continuum of out-of-the-money options. F0 is the initial forward
price.
Hess Energy · 2010 All Rights Reserved
22
23. Theoretical Model, Cont.
• The initial value of the payoff must be the cost of the replicating
portfolio.
F0 ∞
V0 ( F0 ) = f ( F0 ) e −rT
+ ∫ f ′′( K ) P ( K , T ) dK + ∫ f ′′( K ) C ( K , T ) dK
0 F0
• Where P(K,T) and C(K,T) are the initial values of out-of-the-money
puts and calls respectively.
• Interpretation of term within the integral: Second derivative of the
payoff function representing the quantity of options bought or sold.
○ R = Fixed revenue rate
○ SF = Shaping Factor
○ L(S) = MWH, function of S (spot price of power)
f ( S ) = ( R − (1 + SF ) S ) L( S )
f ′′( K ) = 2 (1 + SF ) ∂L
∂S
Hess Energy · 2010 All Rights Reserved
23
24. Estimating the Gamma Function
• Need to estimate the relationship between load and price.
• Use historic data to estimate the following regression equation.
11 11
Load t = α + β lmpt + ∑λ D + ∑φ D lmp
i =1
i i
i =1
i i t
• The data for this equation is average load (peak, off-peak) and average price
(peak, off-peak). LMP is the price, D is a monthly dummy variable, and DXLMP
is an interactive dummy variable with price.
• Next set up a portfolio of a short load sale and a long hedge using monthly
forwards. The fixed rate on the load sale equals the RTC cost of serving the
load ($/MWH).
• Use the relationship estimated in the regression equation to vary the average
monthly load with respect to a change in average monthly price. Use this to
estimate the gamma function.
Hess Energy · 2010 All Rights Reserved
24
25. Example Regression Output On-Peak PSE&G FP
A $1 change is prices equals a 7 MW change in average daily peak load.
For July the change equals 19 = 7 + 12.
Regression Statistics
Multiple R 87.27%
R Square 76.16%
Adjusted R Square 75.61% Adjusted R2 = 75 %.
Standard Error 417.5841127
Observations 445
ANOVA
df SS MS F Significance F
Regression 10 241771008.8 24177100.88 138.6488552 2.4513E-128
Residual 434 75679397.18 174376.4912
Total 444 317450406
Coefficients Standard Error t Stat P-value
Intercept 3,698.5486 64.27 57.55 0.00%
LMP 7.1820 0.83 8.64 0.00%
Mar_P -4.9284 1.02 -4.81 0.00%
Apr_P -6.7488 1.01 -6.68 0.00%
May_P -5.8316 0.96 -6.08 0.00% Statistically
Jun_P 6.4907 0.73 8.94 0.00%
Significant
Interactive dummy variables Jul_P 11.8957 0.73 16.30 0.00%
Aug_P 10.2282 0.77 13.28 0.00%
Sep_P 4.6888 0.84 5.61 0.00%
Oct_P -2.2002 0.92 -2.38 1.77%
Nov_P -3.5755 0.99 -3.62 0.03%
Hess Energy · 2010 All Rights Reserved
25
26. Figure 7: Example of a Gamma Function Estimate
Estimated gamma function for July 2010 PSE&G FP load.
The option cost equals $1.89/MWH per MWH served.
$20,000
$18,000
$16,000
$14,000
Change in P&L ($000)
$12,000
-Gamma
$10,000
Estimate
$8,000
$6,000
$4,000
$2,000
$0
$0.00 $20.00 $40.00 $60.00 $80.00 $100.00 $120.00 $140.00
-$2,000
Cost as of February 9, 2009. Market Price
Hess Energy · 2010 All Rights Reserved
26
27. Mitigating Swing Risk in Practice
“In theory there is no difference between theory and practice.
In practice there is” Yogi Berra
Hess Energy · 2010 All Rights Reserved
27
28. Minimizing Cash Flow at Risk
• In practice we cannot purchase options in such a way as to create the
smooth curves depicted earlier. Instead we need to find discrete strikes
so as to minimize the “swing risk”.
• Swing risk is here defined as Cash Flow at Risk (CF@R). CF@R is the
expected loss assuming that all contracts are taken to delivery. I am
defining CF@R as the difference between the mean of the distribution
and the 5th percentile.
• Since we cannot perfectly hedge the swing risk by purchasing a
continuum of options we need another objective risk minimization
strategy.
• Use as a strategy the minimization of the CF@R or an objective level for
the CF@R. An example would be to reduce the CF@R by 50%.
Hess Energy · 2010 All Rights Reserved
28
29. Reduce Cash Flow at Risk
0.06
Accountnig or Actuarial w ith Options
0.05
Accounting Model Hedged with
Options
0.04
Delta Hedged
Densit y
0.03
0.02
Swing Risk
Reduced
0.01
0.00
-50 -40 -30 -20 -10 0 10 20 30
CashXFlow
Hess Energy · 2010 All Rights Reserved
29
30. Methodology
• Use Monte Carlo simulation to model the load following contract and all
hedges.
• Model takes into account the relationship between price and load,
volatilities and correlations.
• Run the model to estimate the expected cost to serve the load and
establish the fair price of the contract.
• Layer in delta hedges to estimate the cash flow distribution and estimate
the CF@R.
• Determine the amount of risk to be minimized. This is a management
decision. Cut the CF@R by 50%.
• Determine the portfolio of available options in the market.
• Use an available optimization routine to determine the optimal option
portfolio that meets the required risk criteria.
Hess Energy · 2010 All Rights Reserved
30
31. Simulated Gamma Position
Example uses NJ BGS CIEP Load for July.
$400,000
Approximately 80 MWs average load on-peak.
$200,000
$0
($200,000)
($400,000)
Total P&L
($600,000)
($800,000)
($1,000,000)
($1,200,000)
($1,400,000)
($1,600,000)
$0 $50 $100 $150 $200 $250 $300 $350
Average On-Peak LMP
Hess Energy · 2010 All Rights Reserved
31
32. Cash Flow Distribution
NJ BGS CIEP Load for July
Swing Risk
Hess Energy · 2010 All Rights Reserved
32
33. Cash Flow Distribution with Swing Hedge
NJ BGS CIEP Load for July.
Objective was to reduce CF@R by 50%.
Swing Risk Removed
Hess Energy · 2010 All Rights Reserved
33
34. Efficient Frontier Analysis
The efficient frontier tells what the minimum option cost would be to
achieve a particular level of the 5th percentile.
$0
+/- 10% Strangle
($200,000)
($400,000)
5th Percentile
+/- 30% Strangle
($600,000)
($800,000)
($1,000,000)
($1,200,000)
$0 $200,000 $400,000 $600,000 $800,000 $1,000,000 $1,200,000
Option Cost
Hess Energy · 2010 All Rights Reserved
34
35. Contact
Eric Meerdink
Director of Structuring & Analytics
Hess Corporation
One Hess Plaza
Woodbridge, NJ 07095
Office: 732-750-6591
Cell: 732-425-4655
Email: emeerdink@hess.com
Hess Energy · 2010 All Rights Reserved
35
Editor's Notes
Let’s talk about how all of these milestones made us into the company we are today. Hess is a totally integrated energy company. You can see the breadth and depth of our offerings and expertise. Today I’m here to talk to you about the Energy Marketing side of the business and what we can do for you.
We are one of the largest suppliers on the east coast and can offer you service where you are in business.
A quick glimpse at the commodities we can provide for you – we offer electricity, natural gas, fuel oil and a number of green energy solutions for your business. We will share more about our products in subsequent slides. Up to the account manager what points to highlight, based on customer he/she is meeting with