Commodity and Energy Markets
|
|
- Dale McKinney
- 6 years ago
- Views:
Transcription
1 Lecture 3 - Spread Options p. 1/19 Commodity and Energy Markets (Princeton RTG summer school in financial mathematics) Lecture 3 - Spread Option Pricing Michael Coulon and Glen Swindle June 17th - 28th, 2013 mcoulon@princeton.edu
2 Lecture 3 - Spread Options p. 2/19 Commodity Spread Options A general spread option payoff (at time T ) has the form: (ax T by T K) + where X T and Y T are different commodity prices (spot or forward): Input / Output (e.g., dark if X T is electricity, Y T is coal) Input / Output (e.g., crack if X T is refined product, Y T is crude) Calendar (e.g., X T is Dec13 forward,y T is Jun13 forward) Locational (e.g.,x T is Henry Hub gas, Y T is NorthEast gas) Spread options are of utmost importance, due to their strong link with physical assets (hence hedging and valuation tools). Examples above: Coal power plant, Oil refinery, Gas storage facility, Pipeline Optimal (unconstrained) operation mimics a string of spread options.
3 Lecture 3 - Spread Options p. 3/19 Classical Spread Option Pricing Margrabe (1978) derived a well-known closed-form formula for spread options when K = 0 (ie, exchange options ) and assets follow GBMs: ds (1) t = rs (1) t dt+σ 1 S (1) t dw (1) t ds (2) t = rs (2) t dt+σ 2 S (2) t dw (2) t dw (1) t dw (2) t = ρdt Then via a clever use of change of numeraire: V t = e r(t t) E Q t [ ( ) ] + S (1) T S(2) T = S (2) t E Q t ( S (1) T S (2) T 1 ) + we obtain (where σ 2 = σ 2 1 +σ 2 2 2ρσ 1 σ 2 ): V t = S (1) t Φ(d + ) S (2) t Φ(d ), and d ± = ( ) log S (1) t /S (2) t ± 1 2 σ2 (T t) σ. T t
4 Lecture 3 - Spread Options p. 4/19 Power Plants / Tolling Deals Goal: Power plant value approximated as string of spread options Plant Value exp( rt j )E Q[ ( PTj h g G Tj e g A Tj K ) ] + j J Main challenge: Capturing multi-commodity dependence structure (and link with demand), while retaining mathematical tractability. How can we attempt to model these relationships? Reduced-Form: Correlated Lognormals, etc. (including Margrabe and its extensions; see e.g. Carmona & Durrleman ( 03) ) Full Fundamental: Via production cost optimization problem. Structurally: Embedded into a model for spot power: Power = f(gas, Coal, Carbon,...). What are some of the problems with using Margrabe in this case?
5 Lecture 3 - Spread Options p. 5/19 Electricity Markets Many differences when compared with other commodity markets: Non-storability of electricity Hourly matching of supply & demand required for market clearing Wide price variation across different locations within a grid Clear links to costs of production and demand patterns Dependence on local conditions and market structure Recently deregulated, but rules can still matter (eg, bidding). These lead to many effects which we would like to capture: Highly complicated periodicities / seasonality Sudden price spikes! (jumps followed by rapid recoveries) High volatility, skew and kurtosis Mean reversion - at multiple time scales Complex forward curve movements (many factors needed) Correlation / cointegration with fuel prices
6 Lecture 3 - Spread Options p. 6/19 Electricity Price Spikes! Dramatic spikes in peak hours early Aug 2011 during Texas heatwave: 9:;.<"=<>?."3@,5;78" %!!!" $'!!" $!!!" #'!!" #!!!" '!!".A.?B<>?>BC"D=:B"=<>?.".A.?B<>?>BC"2./012","A:02" #!!" +!" *!" )!" (!" '!" &!" %!" $!" #!" -./012"34!!!"5678"!" *,#,##" *,$,##" *,%,##" *,&,##" *,',##" *,(,##" *,),##" *,*,##" *,+,##" *,#!,##"!"
7 Lecture 3 - Spread Options p. 7/19 What about negative prices? Let s look at West Texas zonal prices, instead of the main North Hub: (Transmission constraints, lots of volatile wind power, and subsidies!) (##$ '##$ "##$ %##$ &##$ #$!&##$!%##$!"##$ -./!#,$ 012!#,$ 3*4!#,$ )56!#,$ 057!#,$ 89:!#,$ ;.9!#,$ )*+!&#$ 3*2!&#$ 012!&#$ )5+!&#$ )56!&#$ <.1!&#$ =>?!&#$
8 Lecture 3 - Spread Options p. 8/19 What about negative prices? Zooming in on a nine-day period: some very unusual dynamics! ("#$,$-./0$12$3405$647.0$89:;40$<=89$&%$!$>./$)?$&##,@$$ (%#$ (&#$ (##$ '#$ "#$ %#$ &#$ #$!&#$ ($ &$ )$ %$ *$ "$ +$ '$,$!%#$!"#$
9 Energy Price Correlations Example of power to gas relationship from ERCOT (Texas): #('!!"!!## /"'01$23!$*+,-.$%&'()$3#$4)5&1$467$5"86&"0$!"#$ '!"!!# #(&$!"!!##./012#345# &$"!!# #(&!!"!!## 6789:7;#57<# &!"!!# #(%$!"!!## %$"!!# #(%!!"!!## %!"!!# #($!"!!## $"!!# #()####!"!!# %*%*!+# '*%*!+# $*%*!+# +*%*!+#,*%*!+# %%*%*!+# %*%*!-# '*%*!-# $*%*!-# +*%*!-#,*%*!-# %%*%*!-# %*%*!,# '*%*!,# $*%*!,# +*%*!,#,*%*!,# %%*%*!,# %*%*%!# '*%*%!# $*%*%!# +*%*%!#,*%*%!# %%*%*%!# *+,-.$%&'()$$!"#$%&'()$ Lecture 3 - Spread Options p. 9/19
10 Observed Demand (Load) Demand is easily observable and follows fairly predictable seasonal patterns with short-term weather-driven fluctuations. (ERCOT daily avg data below) (!" '!" &!" %!" $!" #!"!" )*+,!'" )-.,!'" )*+,!(" )-.,!(" )*+,!/" )-.,!/" )*+,!0" )-.,!0" )*+,!1" )-.,!1" )*+,#!" )-.,#!" )*+,##" )-.,##" Lecture 3 - Spread Options p. 10/19
11 Lecture 3 - Spread Options p. 11/19 Structural Models for Power Hybrid / structural models provide a convenient compromise between reduced-form, and full fundamental: Identify Key Factors - Demand, Fuel Prices, Outages, etc. Choose function P t = B(t,D t,g t,...) to map to spot power. Exploit available forward looking market data. (e.g., fuel forward prices, regulatory changes, renewables) Examples from literature include: Spot price as a function of... DemandD t : Barlow (2002) Capacity ξ t : Burger et al. (2004), Cartea et al. (2007) Fuel prices G t : Pirrong, Jermakyan (2005), Aid et al. (2009,11) Big Challenge: Need for multiple fuels in many cases, and complex dependencies! Daily auction data provides a natural starting point.
12 Lecture 3 - Spread Options p. 12/19 The bid stack function Day-ahead generator bids arranged by price to form the bid stack Spot price P t is highest bid needed to match inelastic demandd t Merit order (of production costs) drives dynamics of the stack 600 PJM sample bid stacks st Feb st Mar 2003 oil price ($) gas 100 nuclear coal quantity (MW)
13 Lecture 3 - Spread Options p. 13/19 Historical PJM Bid Dynamics Historically, Lower part of the PJM stack driven by coal (eg, 40% of ξ point). Upper part of the PJM stack driven by gas (eg, 70% of ξ point). However, recent evidence for a significant merit order change occurring (due to shale gas discoveries, dropping US gas prices to under $2). $(" $!" )(" )!" #(" #!" '(" '!" (" 0123"45"$!6"718-9"1-"592:;" $!6"1-"592:;" :123"7<8:=" '%!" '$!" '#!" '!!" &!" %!" $!" #!" '%!" '$!" '#!" '!!" &!" %!" $!" #!" 012"32".!4"567+8"6+"2819:".!4"6+"2819:" +18";12"5<79=" '&" '%" '$" '#" '!" &" %" $" #"!" '*+,-*!!" '*+,-*!'" '*+,-*!#" '*+,-*!)" '*+,-*!$" '*+,-*!(" '*+,-*!%" '*+,-*!." '*+,-*!&" '*+,-*!/" '*+,-*'!" '*+,-*''"!"!" '()*+(!!" '()*+(!'" '()*+(!#" '()*+(!," '()*+(!$" '()*+(!-" '()*+(!%" '()*+(!." '()*+(!&" '()*+(!/" '()*+('!" '()*+(''"!"
14 Lecture 3 - Spread Options p. 14/19 An alternative perspective Can look at bid stack as a histogram of bids Merit order is often visible through clusters of bids nuc coal PJM sample bid histogram natural gas + a few higher bids in tail bid amount (MW) bid price ($)
15 Lecture 3 - Spread Options p. 15/19 Distribution-based Bid Stack Model Coulon / Howison (09) - Stochastic Behaviour of the Electricity Bid Stack... Fuel typesi = 1,...,n with weights (relative capacities) w 1,...,w n Bid distributionsf 1 (x),...,f N (x) (proportion of bids belowx). Require 0 < D t / ξ < 1. (demand D t cannot exceed max capacity ξ) The bid stack function is then the quantile function of the distribution of bids. Then choose two-parameter distributions for bids such as Gaussian, etc. Set parameters (m i,s i ) to be linear in fuel price for each technology. Finally, pick typical processes (eg, exp OU) for factors C t, G t,d t, ξ t. The spot power price P t solves: N w i F i (P t ) = i=1 N ( ) Pt m i w i Φ i=1 s i = D t ξ t Key idea: Clusters of bids of each fuel type moving together (with fuel price).
16 Lecture 3 - Spread Options p. 16/19 Next challenge: closed-form! Multi-fuel case: no explicit expressions even for spot or forward. Alternative: allow slightly less flexibility in the stack but with the benefit of closed-form expressions for forwards, options and even spark or dark spread options. (e.g., payoff V T = (P T HG T ) + ) (Carmona / Coulon / Schwarz ( 13), Electricity Price Modeling and...) Key assumption: within each fuel type, heat rate differences lead to exponential bid stacks. (multiplicative in fuel price) Assume coal and gas generators only, with capacity ξ c and ξ g. Then aggregation of coal bids produces the sub bid stack : b c (D) = C t e k c+m c D, for 0 D ξ c and similarly for gas: b g (D) = G t e k g+m g D, for 0 D ξ g
17 Lecture 3 - Spread Options p. 17/19 Case of exponential sub bid stacks The total market bid stack (as a function of demand) is given by: B(x) = (b 1 c +b 1 g ) 1 (D), for 0 D ξ = ξ c + ξ g Hence, the result is piecewise exponential, although the precise form depends on ordering of start and endpoints of coal and gas stacks. Possible Expressions for P t Criteria Marginal Fuel Type b c (D) = C t e k c+m c D b c (D) < b g (0) Coal (no gas used) b g (D) = G t e k g+m g D b g (D) < b c (0) Gas (no coal used) b c (D ξ g ) = C t e k c+m c (D ξ g ) b g (D ξ c ) = G t e k g+m g (D ξ c ) b g ( ξ g ) < b c (D ξ g ) Coal (all gas used) b c ( ξ c ) < b g (D ξ c ) Gas (all coal used) b cg (D) = C α c t G α g t e β+γd otherwise Both (overlapping) α c = m g, α g = 1 α c, β = k cm g +k g m c, γ = m cm g, m c +m g m c +m g m c +m g
18 Lecture 3 - Spread Options p. 18/19 Exponential Stacks - Power vs Fuel Depicting power price P t as a function ofg t (or similarly C t ) leads to three different demand regimes, with three cases each (note: ξ c > ξ g below): Low Demand Medium Demand High Demand P4 High Demand: D > ξ c (i.e.,d > max( ξ c, ξ g )) Power Price P1 P5 P3 Medium Demand: ξ g < D < ξ c P2 Low Demand: D < ξ g (i.e.,d < min( ξ c, ξ g )) 0 Gas Price P1 to P5 on plot match rows 1 to 5 of previous table. Quadrilateral in middle represents region of coal and gas price overlap (ie, both generators at margin).
19 Lecture 3 - Spread Options p. 19/19 Exponential Bid Stack Model Topic to be continued in next lecture...
Lecture 13. Commodity Modeling. Alexander Eydeland. Morgan Stanley
Lecture 13 Commodity Modeling Alexander Eydeland Morgan Stanley 1 Commodity Modeling The views represented herein are the author s own views and do not necessarily represent the views of Morgan Stanley
More informationA STRUCTURAL MODEL FOR ELECTRICITY PRICES
A STRUCTURAL MODEL FOR ELECTRICITY PRICES RENE CARMONA, MICHAEL COULON, AND DANIEL SCHWARZ Abstract. In this paper we propose a new and highly tractable structural approach to spot price modeling and derivative
More informationManaging Risk of a Power Generation Portfolio
Managing Risk of a Power Generation Portfolio 1 Portfolio Management Project Background Market Characteristics Financial Risks System requirements System design Benefits 2 Overview Background! TransAlta
More informationModeling spark spread option and power plant evaluation
Computational Finance and its Applications III 169 Modeling spark spread option and power plant evaluation Z. Li Global Commoditie s, Bank of Amer ic a, New York, USA Abstract Spark spread is an important
More information(A note) on co-integration in commodity markets
(A note) on co-integration in commodity markets Fred Espen Benth Centre of Mathematics for Applications (CMA) University of Oslo, Norway In collaboration with Steen Koekebakker (Agder) Energy & Finance
More informationEvaluating Electricity Generation, Energy Options, and Complex Networks
Evaluating Electricity Generation, Energy Options, and Complex Networks John Birge The University of Chicago Graduate School of Business and Quantstar 1 Outline Derivatives Real options and electricity
More informationStochastic Finance 2010 Summer School Ulm Lecture 1: Energy Derivatives
Stochastic Finance 2010 Summer School Ulm Lecture 1: Energy Derivatives Professor Dr. Rüdiger Kiesel 21. September 2010 1 / 62 1 Energy Markets Spot Market Futures Market 2 Typical models Schwartz Model
More informationDeterminants of the Forward Premium in Electricity Markets
Determinants of the Forward Premium in Electricity Markets Álvaro Cartea, José S. Penalva, Eduardo Schwartz Universidad Carlos III, Universidad Carlos III, UCLA June, 2011 Electricity: a Special Kind of
More informationIMPA Commodities Course: Introduction
IMPA Commodities Course: Introduction Sebastian Jaimungal sebastian.jaimungal@utoronto.ca Department of Statistics and Mathematical Finance Program, University of Toronto, Toronto, Canada http://www.utstat.utoronto.ca/sjaimung
More informationVOLATILITY EFFECTS AND VIRTUAL ASSETS: HOW TO PRICE AND HEDGE AN ENERGY PORTFOLIO
VOLATILITY EFFECTS AND VIRTUAL ASSETS: HOW TO PRICE AND HEDGE AN ENERGY PORTFOLIO GME Workshop on FINANCIAL MARKETS IMPACT ON ENERGY PRICES Responsabile Pricing and Structuring Edison Trading Rome, 4 December
More informationA Structural Model for Carbon Cap-and-Trade Schemes
A Structural Model for Carbon Cap-and-Trade Schemes Sam Howison and Daniel Schwarz University of Oxford, Oxford-Man Institute The New Commodity Markets Oxford-Man Institute, 15 June 2011 Introduction The
More informationResource Planning with Uncertainty for NorthWestern Energy
Resource Planning with Uncertainty for NorthWestern Energy Selection of Optimal Resource Plan for 213 Resource Procurement Plan August 28, 213 Gary Dorris, Ph.D. Ascend Analytics, LLC gdorris@ascendanalytics.com
More informationLinz Kickoff workshop. September 8-12,
Linz Kickoff workshop September 8-12, 2008. 1 Power and Gas Markets Challenges for Pricing and Managing Derivatives Peter Leoni, Electrabel Linz Kickoff workshop September 8-12, 2008. 2 Outline Power Markets:
More informationA Structural Model for Interconnected Electricity Markets
A Structural Model for Interconnected Electricity Markets Toronto, 2013 Michael M. Kustermann Chair for Energy Trading and Finance University of Duisburg-Essen Seite 2/25 A Structural Model for Interconnected
More informationModeling the Spot Price of Electricity in Deregulated Energy Markets
in Deregulated Energy Markets Andrea Roncoroni ESSEC Business School roncoroni@essec.fr September 22, 2005 Financial Modelling Workshop, University of Ulm Outline Empirical Analysis of Electricity Spot
More informationEnergy Price Processes
Energy Processes Used for Derivatives Pricing & Risk Management In this first of three articles, we will describe the most commonly used process, Geometric Brownian Motion, and in the second and third
More informationIMPA Commodities Course : Forward Price Models
IMPA Commodities Course : Forward Price Models Sebastian Jaimungal sebastian.jaimungal@utoronto.ca Department of Statistics and Mathematical Finance Program, University of Toronto, Toronto, Canada http://www.utstat.utoronto.ca/sjaimung
More informationGas storage: overview and static valuation
In this first article of the new gas storage segment of the Masterclass series, John Breslin, Les Clewlow, Tobias Elbert, Calvin Kwok and Chris Strickland provide an illustration of how the four most common
More informationMSc in Financial Engineering
Department of Economics, Mathematics and Statistics MSc in Financial Engineering On Numerical Methods for the Pricing of Commodity Spread Options Damien Deville September 11, 2009 Supervisor: Dr. Steve
More informationThe Price of Power. Craig Pirrong Martin Jermakyan
The Price of Power Craig Pirrong Martin Jermakyan January 7, 2007 1 The deregulation of the electricity industry has resulted in the development of a market for electricity. Electricity derivatives, including
More informationINTRODUCTION - Price volatility is a measure of the dispersion in prices observed over a time period. - Price volatility in the electricity market is
Day-ahead market price volatility analysis in deregulated electricity markets. M.Benini, A. Venturini P. Pelacchi, Member, IEEE, M. Marracci CESI - T&D Network Milan, Italy Electric Systems and Automation
More informationGeneralized Multi-Factor Commodity Spot Price Modeling through Dynamic Cournot Resource Extraction Models
Generalized Multi-Factor Commodity Spot Price Modeling through Dynamic Cournot Resource Extraction Models Bilkan Erkmen (joint work with Michael Coulon) Workshop on Stochastic Games, Equilibrium, and Applications
More informationVolatility, risk, and risk-premium in German and Continental power markets
Volatility, risk, and risk-premium in German and Continental power markets Stefan Judisch Supply & Trading GmbH RWE Supply & Trading PAGE 0 Agenda 1. What are the market fundamentals telling us? 2. What
More information5. Vorlesung Energiewirtschaft II: Risk Management and Electricity Trade
5. Vorlesung Energiewirtschaft II: Risk Management and Electricity Trade Georg Zachmann V 5.3-1 - Agenda of Today's Lecture 1) Organizational Issues 2) Summary of Last Weeks Findings 3) Market Efficiency
More informationConstellation Energy Comments on Proposed OTC Reforms
Constellation Energy Comments on Proposed OTC Reforms Constellation Energy Key Facts Constellation Energy is a Fortune 500 company (#125 on the 2009 list). Over 26,500 MW 2008 peak load served to retail
More informationThe Black-Scholes Model
The Black-Scholes Model Liuren Wu Options Markets Liuren Wu ( c ) The Black-Merton-Scholes Model colorhmoptions Markets 1 / 18 The Black-Merton-Scholes-Merton (BMS) model Black and Scholes (1973) and Merton
More informationVolatility, risk, and risk-premium in German and Continental power markets. Stefan Judisch Supply & Trading GmbH 3 rd April 2014
Volatility, risk, and risk-premium in German and Continental power markets Stefan Judisch Supply & Trading GmbH 3 rd April 2014 RWE Supply & Trading 01/04/2014 PAGE 0 Agenda 1. What are the market fundamentals
More informationThe Black-Scholes Model
The Black-Scholes Model Liuren Wu Options Markets (Hull chapter: 12, 13, 14) Liuren Wu ( c ) The Black-Scholes Model colorhmoptions Markets 1 / 17 The Black-Scholes-Merton (BSM) model Black and Scholes
More informationCommercial Operations. Steve Muscato Chief Commercial Officer
Commercial Operations Steve Muscato Chief Commercial Officer PORTFOLIO OPTIMIZATION ERCOT MARKET KEY TAKEAWAYS POWER PORTFOLIO AS A SERIES OF OPTIONS Vistra converts unit parameters and fuel logistics
More informationCalifornia ISO October 1, 2002 Market Design Elements
California October 1, 2002 Market Design Elements California Board of Governors Meeting April 25, 2002 Presented by Keith Casey Manager of Market Analysis and Mitigation Department of Market Analysis 1
More informationValuation of Transmission Assets and Projects. Transmission Investment: Opportunities in Asset Sales, Recapitalization and Enhancements
Valuation of Transmission Assets and Projects Assef Zobian Cambridge Energy Solutions Alex Rudkevich Tabors Caramanis and Associates Transmission Investment: Opportunities in Asset Sales, Recapitalization
More informationClearing Manager. Financial Transmission Rights. Prudential Security Assessment Methodology. 18 September with September 2015 variation
Clearing Manager Financial Transmission Rights Prudential Security Assessment Methodology with September 2015 variation 18 September 2015 To apply from 9 October 2015 Author: Warwick Small Document owner:
More informationStochastic modeling of electricity prices
Stochastic modeling of electricity prices a survey Fred Espen Benth Centre of Mathematics for Applications (CMA) University of Oslo, Norway In collaboration with Ole E. Barndorff-Nielsen and Almut Veraart
More informationEx post payoffs of a tolling agreement for natural-gas-fired generation in Texas
Ex post payoffs of a tolling agreement for natural-gas-fired generation in Texas The 5th IAEE Asian Conference, University of Western Australia, Spring, 2016 Yun LIU, Ph.D. Candidate Department of Economics,
More informationIndex. Cambridge University Press Valuation and Risk Management in Energy Markets Glen Swindle. Index.
Actuarial risk, 257, 376, 414 Amaranth, 3 Argus, 19, 226 Bachelier model, 209 Backwardation, see Forward curves, Backwardation Banks Energy trading activities, 433 Risk metrics requirements, 413 Basis,
More informationNYISO s Compliance Filing to Order 745: Demand Response. Wholesale Energy Markets
NYISO s Compliance Filing to Order 745: Demand Response Compensation in Organized Wholesale Energy Markets (Docket RM10-17-000) Donna Pratt NYISO Manager, Demand Response Products Market Issues Working
More informationModelling Energy Forward Curves
Modelling Energy Forward Curves Svetlana Borovkova Free University of Amsterdam (VU Amsterdam) Typeset by FoilTEX 1 Energy markets Pre-198s: regulated energy markets 198s: deregulation of oil and natural
More informationTwo and Three factor models for Spread Options Pricing
Two and Three factor models for Spread Options Pricing COMMIDITIES 2007, Birkbeck College, University of London January 17-19, 2007 Sebastian Jaimungal, Associate Director, Mathematical Finance Program,
More informationSimulation of delta hedging of an option with volume uncertainty. Marc LE DU, Clémence ALASSEUR EDF R&D - OSIRIS
Simulation of delta hedging of an option with volume uncertainty Marc LE DU, Clémence ALASSEUR EDF R&D - OSIRIS Agenda 1. Introduction : volume uncertainty 2. Test description: a simple option 3. Results
More informationSeasonal Factors and Outlier Effects in Returns on Electricity Spot Prices in Australia s National Electricity Market.
Seasonal Factors and Outlier Effects in Returns on Electricity Spot Prices in Australia s National Electricity Market. Stuart Thomas School of Economics, Finance and Marketing, RMIT University, Melbourne,
More informationUtility Indifference Pricing and Dynamic Programming Algorithm
Chapter 8 Utility Indifference ricing and Dynamic rogramming Algorithm In the Black-Scholes framework, we can perfectly replicate an option s payoff. However, it may not be true beyond the Black-Scholes
More informationCharting Functionality
Charting Functionality Author Version Date Gary Huish 1.0 25-Oct-2107 Charting Functionality... 1 Charting Principles... 3 Data model... 3 Data cleaning... 3 Data extraction... 4 Chart Images extraction...
More informationAdditional Notes: Introduction to Commodities and Reduced-Form Price Models
Additional Notes: Introduction to Commodities and Reduced-Form Price Models Michael Coulon June 013 1 Commodity Markets Introduction Commodity markets are increasingly important markets in the financial
More informationMemorandum. This memorandum does not require Board action. EXECUTIVE SUMMARY
California Independent System Operator Corporation Memorandum To: ISO Board of Governors From: Eric Hildebrandt, Executive Director, Market Monitoring Date: November 7, 2018 Re: Department of Market Monitoring
More informationThis memo provides highlights of market performance in October and November.
California Independent System Operator Corporation Memorandum To: ISO Board of Governors From: Eric Hildebrandt, Executive Director, Market Monitoring Date: December 5, 2018 Re: Department of Market Monitoring
More informationPart I: Correlation Risk and Common Methods
Part I: Correlation Risk and Common Methods Glen Swindle August 6, 213 c Glen Swindle: All rights reserved 1 / 66 Outline Origins of Correlation Risk in Energy Trading Basic Concepts and Notation Temporal
More informationP VaR0.01 (X) > 2 VaR 0.01 (X). (10 p) Problem 4
KTH Mathematics Examination in SF2980 Risk Management, December 13, 2012, 8:00 13:00. Examiner : Filip indskog, tel. 790 7217, e-mail: lindskog@kth.se Allowed technical aids and literature : a calculator,
More informationSupply, Demand, and Risk Premiums in Electricity Markets
Supply, Demand, and Risk Premiums in Electricity Markets Kris Jacobs Yu Li Craig Pirrong University of Houston November 8, 217 Abstract We model the impact of supply and demand on risk premiums in electricity
More information1 Volatility Definition and Estimation
1 Volatility Definition and Estimation 1.1 WHAT IS VOLATILITY? It is useful to start with an explanation of what volatility is, at least for the purpose of clarifying the scope of this book. Volatility
More informationSTATEMENT ON SSE S APPROACH TO HEDGING 14 November 2018
STATEMENT ON SSE S APPROACH TO HEDGING 14 November 2018 INTRODUCTION SSE is working towards its vision of being a leading energy company in a low carbon world by focusing on core businesses of regulated
More informationFrom default probabilities to credit spreads: Credit risk models do explain market prices
From default probabilities to credit spreads: Credit risk models do explain market prices Presented by Michel M Dacorogna (Joint work with Stefan Denzler, Alexander McNeil and Ulrich A. Müller) The 2007
More informationCalibration Lecture 4: LSV and Model Uncertainty
Calibration Lecture 4: LSV and Model Uncertainty March 2017 Recap: Heston model Recall the Heston stochastic volatility model ds t = rs t dt + Y t S t dw 1 t, dy t = κ(θ Y t ) dt + ξ Y t dw 2 t, where
More informationMarket Design for Emission Trading Schemes
Market Design for Emission Trading Schemes Juri Hinz 1 1 parts are based on joint work with R. Carmona, M. Fehr, A. Pourchet QF Conference, 23/02/09 Singapore Greenhouse gas effect SIX MAIN GREENHOUSE
More informationForecast of Louisiana Unemployment Insurance Claims. September 2014
Forecast of Louisiana Unemployment Insurance Claims September 2014 Executive Summary This document summarizes the forecasts of initial and continued unemployment insurance (UI) claims for the period September
More informationThe valuation of clean spread options: linking electricity, emissions and fuels
The valuation of clean spread options: linking electricity, emissions and fuels Article (Unspecified) Carmona, René, Coulon, Michael and Schwarz, Daniel (212) The valuation of clean spread options: linking
More informationMonthly Broker Webinar. November 12, 2014
Monthly Broker Webinar November 12, 2014 Monthly Broker Webinar Winter Weather Outlook Commodities Market Update Strategic Recommendations Winter Weather Outlook Beau Gjerdingen, Senior Meteorologist 3
More informationFE610 Stochastic Calculus for Financial Engineers. Stevens Institute of Technology
FE610 Stochastic Calculus for Financial Engineers Lecture 13. The Black-Scholes PDE Steve Yang Stevens Institute of Technology 04/25/2013 Outline 1 The Black-Scholes PDE 2 PDEs in Asset Pricing 3 Exotic
More informationWHITE PAPER. Financial Transmission Rights (FTR)/ Congestion Revenue Rights (CRR) Analysis Get ahead with ABB Ability PROMOD
WHITE PAPER Financial Transmission Rights (FTR)/ Congestion Revenue Rights (CRR) Analysis Get ahead with ABB Ability PROMOD 2 W H I T E PA P E R F T R / C R R A N A LY S I S Market participants and system
More informationInstalled Capacity (ICAP) Market
Installed Capacity (ICAP) Market Amanda Carney Associate Market Design Specialist, Capacity Market Design, NYISO New York Market Orientation Course (NYMOC) October 16-19, 2018 Rensselaer, NY 1 ICAP Market
More informationThe University of Chicago, Booth School of Business Business 41202, Spring Quarter 2012, Mr. Ruey S. Tsay. Solutions to Final Exam
The University of Chicago, Booth School of Business Business 41202, Spring Quarter 2012, Mr. Ruey S. Tsay Solutions to Final Exam Problem A: (40 points) Answer briefly the following questions. 1. Consider
More informationCustomers. State Regulated. FERC Regulated. Competitive PSERC ISO LSE
PSERC Shmuel Oren oren@ieor.berkeley.edu IEOR Det., University of California at Berkeley and Power Systems Engineering Research Center (PSerc) (Based on joint work with Yumi Oum and Shijie Deng) Centre
More informationNRG Energy, Inc.: Transforming The Business of Wholesale Power Generation
NRG Energy, Inc.: Transforming The Business of Wholesale Power Generation Lehman Brothers 2006 CEO Energy/Power Conference New York, New York September 5-8, 2006 Safe Harbor Statement This Investor Presentation
More informationCrashcourse Interest Rate Models
Crashcourse Interest Rate Models Stefan Gerhold August 30, 2006 Interest Rate Models Model the evolution of the yield curve Can be used for forecasting the future yield curve or for pricing interest rate
More informationOn Asymptotic Power Utility-Based Pricing and Hedging
On Asymptotic Power Utility-Based Pricing and Hedging Johannes Muhle-Karbe ETH Zürich Joint work with Jan Kallsen and Richard Vierthauer LUH Kolloquium, 21.11.2013, Hannover Outline Introduction Asymptotic
More informationPricing and hedging with rough-heston models
Pricing and hedging with rough-heston models Omar El Euch, Mathieu Rosenbaum Ecole Polytechnique 1 January 216 El Euch, Rosenbaum Pricing and hedging with rough-heston models 1 Table of contents Introduction
More informationPricing and Risk Management of guarantees in unit-linked life insurance
Pricing and Risk Management of guarantees in unit-linked life insurance Xavier Chenut Secura Belgian Re xavier.chenut@secura-re.com SÉPIA, PARIS, DECEMBER 12, 2007 Pricing and Risk Management of guarantees
More informationMONTHLY MARKET REPORT. January 2017
MONTHLY MARKET REPORT January 217 Table of Contents 1. Market Prices... 1 1.1 Introduction... 1 1.2 Hourly Ontario Energy Price (HOEP)... 1 1.3 Ontario 5-Minute Market Clearing Price (MCP)... 3 1.4 Operating
More informationHotelling Under Pressure. Soren Anderson (Michigan State) Ryan Kellogg (Michigan) Stephen Salant (Maryland)
Hotelling Under Pressure Soren Anderson (Michigan State) Ryan Kellogg (Michigan) Stephen Salant (Maryland) October 2015 Hotelling has conceptually underpinned most of the resource extraction literature
More informationThe basics of energy trading. Edgar Wilton
The basics of energy trading Edgar Wilton Overview I. Liberalized electricity markets II. OTC and exchange trading III. Pricing analysis IV. Risk management V. Trading strategies 2 About me MSc in Risk
More informationBusiness Statistics 41000: Probability 3
Business Statistics 41000: Probability 3 Drew D. Creal University of Chicago, Booth School of Business February 7 and 8, 2014 1 Class information Drew D. Creal Email: dcreal@chicagobooth.edu Office: 404
More informationEffectiveness of CPPI Strategies under Discrete Time Trading
Effectiveness of CPPI Strategies under Discrete Time Trading S. Balder, M. Brandl 1, Antje Mahayni 2 1 Department of Banking and Finance, University of Bonn 2 Department of Accounting and Finance, Mercator
More informationThe stochastic calculus
Gdansk A schedule of the lecture Stochastic differential equations Ito calculus, Ito process Ornstein - Uhlenbeck (OU) process Heston model Stopping time for OU process Stochastic differential equations
More informationThe Yield Envelope: Price Ranges for Fixed Income Products
The Yield Envelope: Price Ranges for Fixed Income Products by David Epstein (LINK:www.maths.ox.ac.uk/users/epstein) Mathematical Institute (LINK:www.maths.ox.ac.uk) Oxford Paul Wilmott (LINK:www.oxfordfinancial.co.uk/pw)
More informationGaussian Errors. Chris Rogers
Gaussian Errors Chris Rogers Among the models proposed for the spot rate of interest, Gaussian models are probably the most widely used; they have the great virtue that many of the prices of bonds and
More informationSanjeev Chowdhri - Senior Product Manager, Analytics Lu Liu - Analytics Consultant SunGard Energy Solutions
Mr. Chowdhri is responsible for guiding the evolution of the risk management capabilities for SunGard s energy trading and risk software suite for Europe, and leads a team of analysts and designers in
More informationICAP Demand Curve. Zachary T. Smith Supervisor, ICAP Market Operations, NYISO. Intermediate ICAP Course. November 7-8, 2017 Rensselaer, NY 12144
ICAP Demand Curve Zachary T. Smith Supervisor, ICAP Market Operations, NYISO Intermediate ICAP Course November 7-8, 2017 Rensselaer, NY 12144 1 Objectives Upon the completion of this module, trainees should
More informationPractical example of an Economic Scenario Generator
Practical example of an Economic Scenario Generator Martin Schenk Actuarial & Insurance Solutions SAV 7 March 2014 Agenda Introduction Deterministic vs. stochastic approach Mathematical model Application
More informationManaging Systematic Mortality Risk in Life Annuities: An Application of Longevity Derivatives
Managing Systematic Mortality Risk in Life Annuities: An Application of Longevity Derivatives Simon Man Chung Fung, Katja Ignatieva and Michael Sherris School of Risk & Actuarial Studies University of
More informationCounterparty Credit Risk Simulation
Counterparty Credit Risk Simulation Alex Yang FinPricing http://www.finpricing.com Summary Counterparty Credit Risk Definition Counterparty Credit Risk Measures Monte Carlo Simulation Interest Rate Curve
More informationThis report summarizes key market conditions, developments, and trends for November 2001.
California Independent System Operator Memorandum To: ISO Board of Governors From: Anjali Sheffrin, Director of Market Analysis CC: ISO Officers, ISO Board Assistants Date: February 1, 22 Re: Market Analysis
More informationModeling Emission Trading Schemes
Modeling Emission Trading Schemes Max Fehr Joint work with H.J. Lüthi, R. Carmona, J. Hinz, A. Porchet, P. Barrieu, U. Cetin Centre for the Analysis of Time Series September 25, 2009 EU ETS: Emission trading
More informationA Two-Factor Model for the Electricity Forward Market
A Two-Factor Model for the Electricity Forward Market Ruediger Kiesel (University of Ulm) Gero Schindlmayr (EnBW Trading GmbH) Reik H. Boerger (University of Ulm, Speaker) December 8, 2005 1 A Two-Factor
More informationThe University of Chicago, Booth School of Business Business 41202, Spring Quarter 2009, Mr. Ruey S. Tsay. Solutions to Final Exam
The University of Chicago, Booth School of Business Business 41202, Spring Quarter 2009, Mr. Ruey S. Tsay Solutions to Final Exam Problem A: (42 pts) Answer briefly the following questions. 1. Questions
More informationOn the pricing of emission allowances
On the pricing of emission allowances Umut Çetin Department of Statistics London School of Economics Umut Çetin (LSE) Pricing carbon 1 / 30 Kyoto protocol The Kyoto protocol opened for signature at the
More informationImplications of Spot Price Models on the Valuation of Gas Storages
Implications of Spot Price Models on the Valuation of Gas Storages LEF, Energy & Finance Dr. Sven-Olaf Stoll EnBW Trading GmbH Essen, 4th July 2012 Energie braucht Impulse Agenda Gas storage Valuation
More informationDynamic Replication of Non-Maturing Assets and Liabilities
Dynamic Replication of Non-Maturing Assets and Liabilities Michael Schürle Institute for Operations Research and Computational Finance, University of St. Gallen, Bodanstr. 6, CH-9000 St. Gallen, Switzerland
More informationEskom 2018/19 Revenue Application
Eskom 2018/19 Revenue Application Nersa Public Hearings Klerksdorp 13 November 2017 Where we are coming from This revenue application is being made for the year 2018/19, after the Energy Regulator maintained
More informationValue-at-Risk Based Portfolio Management in Electric Power Sector
Value-at-Risk Based Portfolio Management in Electric Power Sector Ran SHI, Jin ZHONG Department of Electrical and Electronic Engineering University of Hong Kong, HKSAR, China ABSTRACT In the deregulated
More informationModelling the electricity markets
Modelling the electricity markets Fred Espen Benth Centre of Mathematics for Applications (CMA) University of Oslo, Norway Collaborators: J. Kallsen and T. Meyer-Brandis Stochastics in Turbulence and Finance
More informationCVAR-Constrained Multi-Period Power Portfolio Optimization. Cigdem Z. Gurgur Emily K. Newes Coliseum Blvd. East Westminster CO 80021, USA
CVAR-Constrained Multi-Period Power Portfolio Optimization Cigdem Z. Gurgur Emily K. Newes Indiana - Purdue University Doermer School of Business Platts Analytics 10225 Westmoor Drive 2101 Coliseum Blvd.
More informationELECTRICITY FUTURES MARKETS IN AUSTRALIA. Sami Aoude, Lurion DeMello & Stefan Trück Faculty of Business and Economics Macquarie University Sydney
ELECTRICITY FUTURES MARKETS IN AUSTRALIA AN ANALYSIS OF RISK PREMIUMS DURING THE DELIVERY PERIOD Sami Aoude, Lurion DeMello & Stefan Trück Faculty of Business and Economics Macquarie University Sydney
More informationMulti-Period Trading via Convex Optimization
Multi-Period Trading via Convex Optimization Stephen Boyd Enzo Busseti Steven Diamond Ronald Kahn Kwangmoo Koh Peter Nystrup Jan Speth Stanford University & Blackrock City University of Hong Kong September
More informationValuation of Power Plants and Abatement Costs in Carbon Markets
Valuation of Power Plants and Abatement Costs in Carbon Markets d-fine GmbH Kellogg College University of Oxford A thesis submitted in partial fulfillment of the MSc in Mathematical Finance April 19, 2011
More informationONTARIO ENERGY REPORT Q3 2018
ONTARIO ENERGY REPORT Q3 JULY SEPTEMBER OIL AND NATURAL GAS Regular Gasoline and Diesel Provincial Retail Prices ($/L) Regular Gasoline $1.3 Diesel $1.9 Source: Ministry of Energy, Northern Development
More informationThe Black-Scholes Model
IEOR E4706: Foundations of Financial Engineering c 2016 by Martin Haugh The Black-Scholes Model In these notes we will use Itô s Lemma and a replicating argument to derive the famous Black-Scholes formula
More information1. What is Implied Volatility?
Numerical Methods FEQA MSc Lectures, Spring Term 2 Data Modelling Module Lecture 2 Implied Volatility Professor Carol Alexander Spring Term 2 1 1. What is Implied Volatility? Implied volatility is: the
More informationBooth School of Business, University of Chicago Business 41202, Spring Quarter 2014, Mr. Ruey S. Tsay. Solutions to Midterm
Booth School of Business, University of Chicago Business 41202, Spring Quarter 2014, Mr. Ruey S. Tsay Solutions to Midterm Problem A: (30 pts) Answer briefly the following questions. Each question has
More informationAn hour-ahead prediction model for heavy-tailed spot prices. Jae Ho Kim, Warren B. Powell
Accepted Manuscript An hour-ahead prediction model for heavy-tailed spot prices Jae Ho Kim, Warren B. Powell PII: S0140-9883(11)00129-0 DOI: doi: 10.1016/j.eneco.2011.06.007 Reference: ENEECO 2126 To appear
More informationhydro thermal portfolio management
hydro thermal portfolio management presentation @ Schloss Leopoldskron 8 Sep 004 contents. thesis initiation. context 3. problem definition 4. main milestones of the thesis 5. milestones presentation 6.
More informationBarrier options. In options only come into being if S t reaches B for some 0 t T, at which point they become an ordinary option.
Barrier options A typical barrier option contract changes if the asset hits a specified level, the barrier. Barrier options are therefore path-dependent. Out options expire worthless if S t reaches the
More information