By Majdala Khater and C line Levy

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Table of Contents. Weather derivatives overviewWeather derivatives marketsWeather derivatives structurePricing weather derivatives. Weather Derivatives ?Usefulness. Most industries in the world are directly or indirectly affected by the unexpected weather eventsWeather risk affects a great n

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By Majdala Khater and C line Levy

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2. Table of Contents Weather derivatives overview Weather derivatives markets Weather derivatives structure Pricing weather derivatives

3. Weather Derivatives Usefulness Most industries in the world are directly or indirectly affected by the unexpected weather events Weather risk affects a great number of businesses all around the world In fact, a survey has proved that more than 200 major US companies suffered from huge losses due to unexpected weather change events Weather derivatives have been introduced to the financial market as a protection or insurance against potential losses due to weather changes Weather derivatives concern not only the energy market but also the tourism, the transportation and the agricultural industry.

4. Weather Derivatives what are they? Financial risk management tools used by companies and enterprises to hedge against the risk of weather changes they cover the high probability for unexpected events such as a dryer or freezer weather, while an insurance covers the high probability events such as hurricanes... Purpose: Stabilize revenues that may be affected by severe change in weather Control Pricing and Volume Risk Enhance financial portfolios Competitive advantage versus the simple insurance: No moral hazard

5. Weather Derivatives limitations Increasing interest in weather risk management but: volume of trade in weather derivatives have been growing slowly Lack of liquidity The weather derivatives market needs to be more developed and potential research opportunities are needed to be analysed Capital pricing model assumptions are not realistic for weather-linked financial instruments

6. Weather derivatives markets One of the most exposed sector: power industry 730,087 contracts traded worldwide from April 2006 to March 2007 Total value of contracts on temperature in OTC markets and CME: $18.9 billion Rain: $142 million Wind: $36 million

7. Volume of contracts traded worldwide

8. Exchange traded market At the beginning: swaps between companies like Enron & Koch Energy Two main markets: Chicago Mercantile Exchange (CME) London International Financial Futures and Options Exchange (LIFFE)

9. CME 10 cities in the US Reference temperature: 65F (18.33C) Heating Degree Days (HDD): October to April Cooling Degree Days (CDD): May to September Arithmetic mean between highest and lowest temperature Contract size: $100, a tick being 1F

10. Euronext - LIFFE London, Paris, Berlin London: contracts of 3,000 Paris and Berlin: 3,000 Tick of 0.01C ? 30 or 30 a tick

11. Nextweather Mto-France & Euronexxt National and regional (5 regions) Temperatures reported daily and quarterly

12. Weather derivative structure Most of weather derivatives traded are call or put options, swaps, collars Weather futures contract Provides or requires payments according to the level of a weather index No initial premium is required The payment of a HDD-Future (Heating Degree Days) contract is F-N*HDD F: future price (amount of money) N: contract size (affecting a financial value) For a CME temperature contract: N=$100/degree

13. Weather derivative structure call and put options The underlying assets of a call or a put option are either HDD or CDD (Cooling Degree Days) A dollar amount is associated with every degree In order to limit the maximum payout by the counterparties, the contracts are usually capped For a call option: Payoff= P($/DD)*Max(ST-X,0) For a put option: Payoff= P($/DD)*Max(X-ST,0) Example: Consider a CDD call option with a strike price of 1000CDDs paying 4000$ per degree day. Payoff= 4000 *Max (CDDt-1000, 0) CDDt is the cumulative cooling degree days over the life of the contract

14. Weather derivative structure swaps Combination of a call and put option having the same strike price and the same underlying location The simplest kinds: uncapped swaps The payoff is calculated: Payoff= [Min{P($/DD)*Max(ST-X,0), h}]-[Min{P($/DD)*Max(X-ST,0), h}] Example: An icemaker and a cinemas operator want to cover respectively against a fresh summer and warm summer. They put in place a swap in which the exercise price is 24 C. If the average temperature over the period agreed exceeds 24 C, the producer of ice pay to the operator of cinemas the provision in the contract;

15. Weather derivative structure collars Purchase an OTM put (call) with a particular strike price (K2) and sell in the same time an OTM call (put) with different strike price (K1). Payoff= [Min{P($/DD)*Max(ST-K1,0), h}]-[Min{P($/DD)*Max(K2-ST,0), h}] Example: A company who wish to protect itself against a hard winter will buy a HDD Cap having the following characteristics: Strike 500HDD with $2000 per HDD and a payoff capped to $2000000. Payoff Cap=Min (2000*Max (0,CumHDD-500),2 000000) P&L= Payoff Cap-premium for buying the cap

16. Weather derivative Pricing The no-arbitrage option pricing model is not practical pricing tool for weather derivatives: the underlynig weather indexes are not a tradable instruments The underlying weather indexes are not stationary: Hard to implement pricing techniques Historical data are characterized by high degree of autocorrelation: reduces the number of independent observations

17. Weather derivative Pricing Simple option pricing This model can be constructed using a probability distribution that will fit the historical data collected of monthly CDDs or HDDs The expected payoff of a CDD option can be calculated using the formula: Payoff (CDD) = M P(CDD)Q(CDD)d(CDD) The expected value of a weather derivative depends on : the strike price the probability distribution that describes the CDDs the number of dollar per CDD

18. Weather derivative Pricing Many complications encounter the pricing of weather derivatives: A simple distribution should not explain the historical data. Variability in weather trends Data given by the atmospheric community cant be used directly

19. Weather derivatives Pricing Black and Scholes The B&S model shows that, under certain assumptions, the price of options can be determined from the price of the underlying asset The asset can be traded continuously with no transaction costs The asset price follows geometric Brownian motion The asset is uninfluenced by the trading of the asset that is undertaken to hedge the option No riskless arbitrage Some of these assumptions do not probably fit the weather derivative because: The underlying instruments in weather derivatives is not tradable Its also impossible to create a risk-neutral portfolio

20. Weather derivatives Pricing the actuarial method The average final payment EM is calculated using the expected value of the function fp of the contract payoff under the measure of the probability chosen EM= ?R fp(x)g(x)dx The actuarial method is much more robust than the Burn analysis

21. Weather derivatives Pricing Burn Analysis Called simulation on historical data, the burn analysis answers the question: what would have been the average option payoff in the past n years There are 6 steps to be considered in a Burn analysis process: Collecting the historical data Converting them to degree day: either HDD or CDD Some corrections should be made to the data converted. Then, for every year in the past and for each weather pattern, we determine the payout of the option Find the average of these payout amounts Discount back to the settlement date. Burn analysis formula consists on estimating an average final payment based on historical data EM and risk hedge standard deviation sM. P=d(EM+?*sM)

22. Weather derivatives Pricing Pruning Analysis The Pruning technique consists of integrating into daily simulation models various weather forecasts The integration of climate forecast is slightly more difficult, because it requires the calculation of conditional probability distributions Solution: use of historical scenarios for each forecast

23. Conclusion The weather derivatives efficiently meet the specific needs of coverage: Climate uncertainty reamins high despite improved weather forecasts Existing pricing models described are not necessarily used by market makers Need for a standard pricing model

24. Sources La lettre mensuelle dEuronext Paris - Fvrier 2002 - N 41 - Bourse Information Introduction to Weather Derivatives de Geoffrey Considine, Ph.D, Weather Derivatives Group, Aquila Energy Weather Derivatives: Instruments and Pricing Issues Mark Garman', Carlos Blanco and Robert Erickson Quel avenir pour les drivs climatiques en Europe ? Phillipe Smadja et Andr Yves Ponts Evaluation des drivs climatiques, Michael Moreno Options, futures and other derivatives 6me edition, JOHN C. HULL La Gestion du Risque Climatique Didier Marteau, Jean CARLE, Stphane Fourneaux, Ralph Holz, Michael Moreno

25. Sources Websites La Grande Relve > Articles > N1070 - novembre 2006 >nergie et climat

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