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New Trends in Energy Derivatives: 

New Trends in Energy Derivatives Alexander Eydeland Morgan Stanley

Increased interest in commodity-linked products: the investors point of view: 

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: 

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: 

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: 

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: 

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: 

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: 

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: 

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: 

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: 

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: 

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/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: 

Modeling challenges Test: terminal distributions of returns at any 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: 

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

Modeling Challenges: 

Modeling Challenges Crude: Fat tails of the distribution

Modeling Challenges: 

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

Stochastic Volatility (Heston, 1993): 

Stochastic Volatility (Heston, 1993) Volatility is a random variable price process volatility process

Stochastic volatility process generates more realistic price distributions: 

Stochastic volatility process generates more realistic price distributions Tails of CDF for terminal distributions generated by stochastic volatility process and by GBM

New Developments: 

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: 

Historic Power Prices vs. GBM paths

Hybrid Power Price Model Power is a function of principal drivers: 

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): 

Hybrid Power Price Model (Eydeland, Wolyniec, 2001) 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 generates realistic paths Actual prices vs. Modeled prices

Hybrid Model: Analytical Approximation (Mahoney, 2004) : 

Hybrid Model: Analytical Approximation (Mahoney, 2004) Fuel Price  (t) - seasonal factor Market Heat Rate Power Price

Hybrid Model (Mahoney, 2004) : 

Hybrid Model (Mahoney, 2004)


At t0 the value of the power plant at a future time T is computed as a conditional expectation Using characteristic function the value of the plant can be represented as

Correlation Risk: 

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: 

Difficulties in managing correlation risk correlation is not traded historical data is poor data is nonstationary, markets are evolving

What are the alternatives?: 

What are the alternatives? Structural models Correlation independent bounds; super/sub-replication

Managing other risks: 

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

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