New Trends in Energy Derivatives

Document Sample
New Trends in Energy Derivatives Powered By Docstoc
					New Trends in Energy
    Derivatives



   Alexander Eydeland
     Morgan Stanley
Increased interest in commodity-linked
products: the investors point of view
• spectacular returns in the last few years
• diversification
  – historically commodity returns are weakly correlated
    with equity or fixed income products and can be used
    as a separate asset class
  – protection against inflation caused by economic
    growth
  – commodities are correlated with non-economic
    drivers: weather, environmental issues, supply
    constraints, etc.
Increased interest in commodity-linked
products: the issuer point of view

• Frequently the products can be split into
  several components that can be used as a
  long-term hedge of existing commodity
  market risks - a useful feature particularly
  when the markets are illiquid
Examples: Commodity-linked bonds

• At redemption, holder is paid par if the GSCI has fallen.
  If the the GSCI price has risen, holder receives par (1 +
  a percentage gain in the GSCI)

• At redemption, holder receives
  85% of par + par * (2 * percentage rise in gold price)
  For example, if gold grows from $400 to $440 then the
  holder of a $1000 par bond gets $1000(.85) + $1000 *
  2(.1) = $1050
Examples: Commodity-linked bonds

• At redemption, holder receives par. In addition, holder
  receives semi-annual coupon. Those payments are .82
  (percentage gain in the NYMEX WTI). Say the NYMEX
  WTI goes from $50/bbl to $55/bbl, coupon payment on a
  $1000 par bond would be .82 (.1) (1000) or $82. Next
  coupon payment would be determined off a new base
  price of $55.
Hybrid Products


• Depend on several market/non-market drivers

• We interested in hybrid products which are
  exposed to at least one commodity

• Pricing requires analysis of correlation structure
  (in addition to volatility)
Hybrid Products: Examples
• Price/Price – spark spread options, crack spread options

• Price/Volume – load following deals

• Price/Temperature products

• Basket products – Rainbow options, Himalayan options

• Interest rates/FX/Equity contingent commodity products
  – swaps, swaptions

• Credit/Commodity products – cds linked to commodity
  price
Spark Spread Options
• Tolling deals
   – call on power with strike price dependent on the cost of fuels,
     emission and variable costs = option on spread between power
     prices and prices of fuels and emission
   – basket of correlated commodity products (three or four products
     in the basket)
   – objectives:
      • power operator will guarantee stable cash flows stream (option
        premium) typically from an institution with higher credit rating
      • power plant operator may also use these options to hedge against
        adverse power and fuel market movements
      • marketers use these options to financially replicate power plant
        operation without taking on operational and other risks associated
        with running the plant
Tolling Deals: Examples
• Unit Contingent Toll with Callback on High Gas
   – Standard Toll: Buyer has the right to call for power. When the
     right is exercised the buyer pays the cost:
      Number MWh x Price of 1MMBtu of NG x Heat Rate + costs

   – Callback: Seller has the right not to deliver power during not
     more than 10% of all hours of the year (if a specified unit is
     forced out)


• Tolling Deal with Limited Number of Start-ups during the
  year - complex path-dependent option

• Tolling deals with fuel substitution option
Challenges: Correlation Structure
• Correlation has a complex term structure: seasonality,
  dependence on time to maturity
• “Correlation smile”: in Black-Scholes-type models used
  to price complex spread options correlation parameters
  may depend on underlying prices
• Example: Correlation vs Power_price/NG_price
Price/Volume Products
• Swing options
• Load following contracts
   – receiving fixed payments
   – paying costs of serving the load: Price x Load
• Challenges:
   – Potentially strong non-linearity (if the correlation is high)
   – Complex correlation structure
   – Inability to hedge all risks, particularly, risks associated with load
     fluctuations and load shape dynamics
   – Need new approaches to valuation
Basket Products
• Options on basket price
   – basket components may include crude, NG, equity indices,
     bonds, etc.
• Rainbow or Best-of basket products
   – pays the best annual return of the basket components
• Himalayan option
   – every year pays the return of the best performing basket
     component and then this component is removed from the basket
• Challenges:
   – Finding distribution of basket prices
   – How to construct the volatility structure of the basket from the
     volatility structures of the individual components?
Commodity-contingent interest rate/equity
products
• Commodity-contingent interest rate swap
   – floating leg - LIBOR
   – “fixed” leg - fixed rate multiplied by the number of days
     (expressed as a fraction of the payment period) during which
     crude or other commodity prices are above a certain level
• Commodity-contingent interest rate swaption (typically,
  Bermudan style)
• Bermudan-style commodity-contingent guaranteed
  minimum coupon knock-out option
   – Pays coupon dependent on the commodity price levels at the
     payment time
   – Disappears after the total coupon reaches a specified level
   – If at the end of the deal the total value of paid coupons is less
     than the specified value the last coupon pays the difference
Modeling challenges
   • Test: terminal distributions of returns dP P at any
                                                T   T
     time T is normal - justification for the use of geometric
     Brownian motion (GBM) as a modeling process

   • SP500: distribution of returns is close to normal
Modeling Challenges

Power, NG and crude prices: normality must be rejected;
  distribution has fat tails
Modeling Challenges

 Crude: Fat tails of the distribution
Modeling Challenges

 Distribution Parameters (A. Werner, Risk Management
 in the Electricity Market, 2003)



                 Annual.      Skewness   Kurtosis
                 Volatility

     Nord Pool   182%         1.468      26.34


     NP 6.p.m.   238%         2.079      76.82


     DAX         23%          0.004      3.33
Stochastic Volatility (Heston, 1993)

Volatility is a random variable

            dPt
                  dt  v(t ) dW1                  price process
             Pt

     dv  t      v  t   dt   v(t ) dW2   volatility process


             E  dW1 dW2    dt
Stochastic volatility process generates more
realistic price distributions
Tails of CDF for terminal distributions generated by
  stochastic volatility process and by GBM
New Developments

• Levy Stable Processes (for review see Boyarchenko
  and Levendorskii, 2002 )


• Levy Processes with Stochastic Volatility: CGMY
  model (Carr, Geman, Madan, Yor, 2003)

• Regime-switching models
Historic Power Prices vs. GBM paths
Hybrid Power Price Model
Power is a function of principal drivers


     1. Demand




     2. Fuel Prices
     3. Outages
Hybrid Power Price Model
(Eydeland, Wolyniec, 2001)

         PT  1s gen ( DT ; T ,UT , T  2   , ET ,VOM T , 3CT )

Model uses fundamental and market data
• sgen - function determined by technical characteristics of
  all power plants (efficiency, operational constraints, etc.)
• D - demand
• U - fuel(s) used
• Ω - outages
Hybrid Model generates realistic paths


Actual prices vs. Modeled prices
Hybrid Model: Analytical Approximation
(Mahoney, 2004)

 • Fuel Price
                    G  e g
                 (t) - seasonal factor

 • Market Heat Rate
                    P
                 H            H  eh
                    G

 • Power Price
                     P  e   g h
   Hybrid Model (Mahoney, 2004)



               dg   g  g  g  dt   g dWg            - fuel

            d     t    dt    dW               - temperature

        dh   h ( Lh  M h   h)dt   h dwh  jh dqh    - Heat Rate

E  dWg dW    gdt       E  dWg dWh    gh dt      E  dW dWh    h dt

               qh - Poisson process with intensity h
                             h   h   h 
                             jh ~ N   h , h 
                                             2
                                                           - jump magnitude
      At t0 the value of the power plant at a future time T is
         computed as a conditional expectation
                                                                                          
                                                                                               
                                                         T  gT  hT            T  gT
                   V (t0 , g , h, )  Et0 , g ,h, e                    H 0e

      Using characteristic function
                                                                           A  g  B h C   D , 
f  , ; t0 , g , h,    Et0 , g ,h , e
                                                   i gT i hT
                                                                    e
      the value of the plant can be represented as
             

            
            
                 dgT dhT (e T  gT hT  H 0 e T  gT )  Pr( gT , hT | g , h, ) 
                               

                              
                              
                                   dgT dhT (e T  gT hT  H 0 e T  gT ) 
                                              
                                   (2 )2
                                      1
                                                
                                              
                                                   e  i gT ihT e A( ) gT  B ( ) hT C ( ) T  D ( , ) d d
          Correlation Risk
• Correlation structure is complex
• Term structure: dependence on time to
  expiration, time interval between two
  contracts; seasonality
• Sensitivity to correlation is high
• How to manage correlation risk?
Difficulties in managing correlation risk


• correlation is not traded
• historical data is poor
• data is nonstationary, markets are
  evolving
What are the alternatives?

• Structural models
• Correlation independent bounds;
  super/sub-replication
Managing other risks

• Credit risk - credit derivatives
• Operational risk - insurance
• Demographic, economic growth risks -
  contractual clauses
• All this increases the cost of risk
  management; these costs should be taken
  into consideration at the valuation stage
References
• Boyarchenko, Svetlana and Sergei Levendorskii, Non-Gaussian
  Merton-Black-Scholes Theory, World Scientific, 2002

• Eydeland, Alexander and Krzysztof Wolyniec, Energy and
  Power Risk Management: New Developments in Modeling,
  Pricing and Hedging, Wiley, 2002

• Carr, Peter and Helyette Geman, Dilip Madan, Marc Yor,
  Stochastic Volatility for Levy Processes, Mathematical Finance,
  Vol. 13, No. 3 (2003)
•
• Heston, Steven, A Closed-Form Solution for Options with
  Stochastic Volatility, Review of Financial Studies, Vol. 6, No. 2
  (1993)

• Mahoney, Daniel, A New Spot Model for Power Prices, Preprint,
  2004
                                                                      Disclosures
The information herein has been prepared solely for informational purposes and is not an offer to buy or sell or a solicitation of an offer to buy or sell any security or instrument or to participate in any trading
strategy. Any such offer would be made only after a prospective participant had completed its own independent investigation of the securities, instruments or transactions and received all information it
required to make its own investment decision, including, where applicable, a review of any offering circular or memorandum describing such security or instrument, which would contain material information
not contained herein and to which prospective participants are referred. No representation or warranty can be given with respect to the accuracy or completeness of the information herein, or that any future
offer of securities, instruments or transactions will conform to the terms hereof. Morgan Stanley and its affiliates disclaim any and all liability relating to this information. Morgan Stanley, its affiliates and
others associated with it may have positions in, and may effect transactions in, securities and instruments of issuers mentioned herein and may also perform or seek to perform investment banking services for
the issuers of such securities and instruments.

The information herein may contain general, summary discussions of certain tax, regulatory, accounting and/or legal issues relevant to the proposed transaction. Any such discussion is necessarily generic and
may not be applicable to, or complete for, any particular recipient's specific facts and circumstances. Morgan Stanley is not offering and does not purport to offer tax, regulatory, accounting or legal advice
and this information should not be relied upon as such. Prior to entering into any proposed transaction, recipients should determine, in consultation with their own legal, tax, regulatory and accounting
advisors, the economic risks and merits, as well as the legal, tax, regulatory and accounting characteristics and consequences, of the transaction.

Notwithstanding any other express or implied agreement, arrangement, or understanding to the contrary, Morgan Stanley and each recipient hereof are deemed to agree that both Morgan Stanley and such
recipient (and their respective employees, representatives, and other agents) may disclose to any and all persons, without limitation of any kind, the U.S. federal income tax treatment of the securities,
instruments or transactions described herein and any fact relating to the structure of the securities, instruments or transactions that may be relevant to understanding such tax treatment, and all materials of any
kind (including opinions or other tax analyses) that are provided to such person relating to such tax treatment and tax structure, except to the extent confidentiality is reasonably necessary to comply with
securities laws (including, where applicable, confidentiality regarding the identity of an issuer of securities or its affiliates, agents and advisors).

The projections or other estimates in these materials (if any), including estimates of returns or performance, are forward-looking statements based upon certain assumptions and are preliminary in nature. Any
assumptions used in any such projection or estimate that were provided by a recipient are noted herein. Actual results are difficult to predict and may depend upon events outside the issuer’s or Morgan
Stanley’s control. Actual events may differ from those assumed and changes to any assumptions may have a material impact on any projections or estimates. Other events not taken into account may occur
and may significantly affect the analysis. Certain assumptions may have been made for modeling purposes only to simplify the presentation and/or calculation of any projections or estimates, and Morgan
Stanley does not represent that any such assumptions will reflect actual future events. Accordingly, there can be no assurance that estimated returns or projections will be realized or that actual returns or
performance results will not be materially different than those estimated herein. Any such estimated returns and projections should be viewed as hypothetical. Recipients should conduct their own analysis,
using such assumptions as they deem appropriate, and should fully consider other available information in making a decision regarding these securities, instruments or transactions. Past performance is not
necessarily indicative of future results. Price and availability are subject to change without notice.
T he offer or sale of securities, instruments or transactions may be restricted by law. Additionally, transfers of any such securities, instruments or transactions may be limited by law or the terms thereof.
Unless specifically noted herein, neither Morgan Stanley nor any issuer of securities or instruments has taken or will take any action in any jurisdiction that would permit a public offering of securities or
instruments, or possession or distribution of any offering material in relation thereto, in any country or jurisdiction where action for such purpose is required. Recipients are required to inform themselves of
and comply with any legal or contractual restrictions on their purchase, holding, sale, exercise of rights or performance of obligations under any transaction. Morgan Stanley does not undertake or have any
responsibility to notify you of any changes to the attached information.

With respect to any recipient in the U.K., the information herein has been issued by Morgan Stanley & Co. International Limited, regulated by the U.K. Financial Services Authority. THIS
CO MMUNICATION IS DIRECTED IN THE UK TO THO SE PERSO NS WHO ARE MARKET CO UNTERPARTIES O R INTERMEDIATE CUSTO MERS (AS DEFINED IN THE UK
FINANCIAL SERVICES AUTHORITY’S RULES).

ADDITIO NAL INFO RMATIO N IS AVAILABLE UPON REQ UEST.

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:10
posted:5/30/2012
language:English
pages:33