Weather Derivatives Trading and Structuring The Forecast component Michael Moreno Speedwell Weather Derivatives Ltd

Michael Moreno - www.weatherderivs.com Plan Part I: Current Pricing Methods Part II: Forecast Categories Part III: Practical samples of forecast used in Weather Market Part IV: Forecast and RM 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Michael Moreno - www.weatherderivs.com Deals lengths The most traded contracts 1 day (from 7am to 5pm) or 2 to 3 days (event type insurance) 1 week (Mon-Fri. Energy sectors) 1 Month 5 Months X Years Maximum heard about: 10 years 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Weather Derivatives Pricing Methods There are 4 main methods Burn Analysis Actuarial/Index Method Black Daily simulation 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Michael Moreno - www.weatherderivs.com Burn Analysis 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Actuarial/Index Method 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Michael Moreno - www.weatherderivs.com Black Black’s 76 model on Futures => Lognormal distribution => Vol Smile => Standard Derivatives Methods OK for listed contract on positive values Not interesting elsewhere 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Temperature daily simulation AR => Short Memory + Homoskedasticity GARCH => Short Memory + Heteroskedasticity ARFIMA => Long Memory + Homoskedasticity FBM => Long Memory + Homoskedasticity ARFIMA-FIGARCH => Long Memory + Heteroskedasticity Time Series Bootsrapp 29-Jan-2004 Michael Moreno - www.weatherderivs.com

ARFIMA-FIGARCH model (proposed at WRMA 2003 by Moreno M.) Seasonality Trend ARFIMA-FIGARCH Seasonal volatility 29-Jan-2004 Michael Moreno - www.weatherderivs.com

ARFIMA-FIGARCH definition We consider first the ARFIMA process: Where, as in the ARMA model,  is the unconditional mean of yt while the autoregressive operator and the moving average operator are polynomials of order a and m, respectively, in the lag operator L, and the innovations t are white noises with the variance σ2. 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Michael Moreno - www.weatherderivs.com FIGARCH noise Given the conditional variance We suppose that Long term memory Cf Baillie, Bollerslev and Mikkelsen 96 or Chung 03 for full specification 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Distributions of London winter HDD Histo Sim Average 1700.79 1704.54 St Dev 128.52 119.26 Skewness 0.42 -0.01 Kurtosis 3.63 3.13 Minimum 1474.39 1375.13 Maximum 2118.64 2118.92 With similar detrending methods The slight differences come mainly from the year 1963 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Rainfall daily simulation Cf Moreno M 2 step process, the first step models the events “it Rains/it does not rain” (heterogeneous cyclic binary Markov Chain) the second the magnitude of rainfall 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Those methods have a few problems (Black 76 is specific) Sensitive to the number of data Sensitive to detrending methods Sensitive to data filling method Sensitive to the algorithm used to adjust the values after a change at the weather station Sensitive to El Nino/La Nina (US) ... 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Most importantly in their basic form they are “forecast blind” Let’s go back to the root of the weather derivatives market: the Energy Company Assume one of your friends is an electricity trader. What is important for him are the next 7 days. He can hedge his price risk through electricity future contracts but what about the volume risk? The volume volatility depends strongly on the temperature/rain conditions and the forecast is a critical information. Now let’s say he comes to buy a weather hedge for the next 7 days. Would you take the risk not to consider the weather forecast? 29-Jan-2004 Michael Moreno - www.weatherderivs.com

So can forecast be ignored? Yes 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Michael Moreno - www.weatherderivs.com Plan Part I: Current Pricing Methods Part II: Forecast Categories Part III: Practical samples of forecast used in Weather Market Part IV: Forecast and RM 29-Jan-2004 Michael Moreno - www.weatherderivs.com

What are the forecasts categories? Previsions used by the weather market can be split into 3 categories Short Term 0 to 10-14 days Medium Term ~1/2 Month to 6 Month-1 Year Long Term > 1 year 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Michael Moreno - www.weatherderivs.com Forecast Samples Source: AWS/WeatherNet www.myweatherbug.com 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Deterministic Forecast Look at the Temperature, wind and then Rain Forecasts Source: www.customweather.com 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Deterministic Forecast => Scenario Pricing technique 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Integrating the forecast in the pricing model Integrating the forecast in pricing model is “relatively easy” if it is deterministic or if it is made of ensembles. You can use “pruning” and conditional distribution/estimation. For Medium to Long Term forecast you may need to use other types of techniques based on weighted schemes (especially for El Nino/La Nina) and other techniques (external parameterization). 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Michael Moreno - www.weatherderivs.com Plan Part I: Current Pricing Methods Part II: Forecast Categories Part III: Practical samples of forecast used in Weather Market Part IV: Forecast and RM 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Michael Moreno - www.weatherderivs.com Prevision RTE C'est le Centre National d'Exploitation du Système (CNES) qui ajuste, à tout moment, les volumes de production aux besoins en électricité des consommateurs. La demande d'électricité varie tout au long de la journée et des saisons. Elle est représentée par une courbe de charge, dont le CNES élabore la prévision chaque jour. Il s'assure que les programmes de production prévus par les différents fournisseurs d'électricité permettent de satisfaire la consommation totale. Le diagramme présente les variations, par points quart-horaires, de la consommation française d'électricité de la journée en cours, ainsi que les prévisions estimées la veille. Les éventuels écarts résultent principalement de l'évolution des conditions météorologiques par rapport aux données prévues (température et luminosité). RTE ne pourra être tenu responsable de l'usage qui pourrait être fait des données mises à disposition, ni en cas de prévisions qui se révèleraient imprécises. Sources: http://www.rte-france.com/jsp/fr/courbes/courbes.jsp www.meteo.fr (Meteo France) 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Historical swap levels LONDON HDD December Forward  380 Before the period started: swap level below Then swap level above like the partial index 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Historical swap levels LONDON HDD January Forward  400 Before the period started: swap level below Then swap level has 2 peaks and does not follow the partial index evolution which is well above the mean 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Human resources planning The Power Curve of a Wind Turbine The power curve of a wind turbine is a graph that indicates how large the electrical power output will be for the turbine at different wind speeds. The graph shows a power curve for a typical Danish 600 kW wind turbine. You will organize plant maintenance when there will be no wind! 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Weather Related Flight Delays 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Short term forecast solutions WD or Real Option? Short term weather forecast oriented companies (e.g. supermarkets) buys forecasts and not WD Some companies organize teams depending on forecast Small Builders will paint/build roof when it does not rain Icy road prevention Flight delays … Traders will try to sell forecast protection It is a governance dilemma 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Michael Moreno - www.weatherderivs.com Medium term forecasts Mainly El Nino La Nina Forecasts In January of 1998, the El Niño is fully underway. Look, though, at how the unusually cold water at depth in the western Pacific has expanded towards the East. Our forecast model predicts that this anomaly will spread across to the coast of South America by the latter part of 1998, initiating the cold-water event known as "La Niña". When El Nino will happen, you need to take it account… And when it has happened you need to take it into account in your trend and distribution modelling potentially using analogous data 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Medium Term => Scenario Pricing 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Michael Moreno - www.weatherderivs.com El Nino/La Nina There is a big risk in following any El Nino/La Nina forecast There is an even bigger risk in not following it Traders/Structurers will try to diversify it by finding cross-correlated products Pricing methods must integrate some sort of weighted or scenario schemes The major issues are coming from correlation matrix estimation for portfolio management 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Michael Moreno - www.weatherderivs.com Long term forecasts Long term forecasts are usually coming from external variables like Human intervention (increase/decrease of population, pollution) Sun Solar flare activity 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Long Term contracts difficulties Credit Risk Issues And model risks There is a demand! There is no “real” Offer! 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Example: Companies with Gvt contract/strong legislation Some companies sign long term contract/agreements with government: Builders Road Maintenance companies Railways Water companies … 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Michael Moreno - www.weatherderivs.com Example with Gritting UK standard contract is 30 years for a fixed price indexed to the RPI Do you want to take the weather risk? Are you that sure of your estimation of the global warming trend? 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Example with water companies Drought issues => financial penalties and possibly licence withdrawal 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Michael Moreno - www.weatherderivs.com An “Exotic” Example Are you willing to sell a swap on Sunshine for next 10 years to a farmer without considering the vapour trail effects of airplanes? 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Michael Moreno - www.weatherderivs.com Plan Part I: Current Pricing Methods Part II: Forecast Categories Part III: Practical samples of forecast used in Weather Market Part IV: Forecast and RM 29-Jan-2004 Michael Moreno - www.weatherderivs.com

The forecast “completeness” issue in RM When using forecast in RM, you may not have all the forecasts for all the stations in your book This creates a forecast “incompleteness” and cannot be solved easily 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Forecast incompleteness example You have 1 deal on a compound index based on the same weather stations - Rain > 2mm - Temp < -1C You have the Rain forecast but not the Temperature forecast (or vice-versa or not for the same number of days) How do you price that deal/portfolio given that when it rains in December, the temperature average is usually warmer than normal? 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Greeks and RM implications Using forecast information in pricing models means that Greeks will be forward Greek You must think like for the bond market with a Spot Date that is a few days away The weather forecast volatility can be seen as the volga (vvol) 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Michael Moreno - www.weatherderivs.com Forecast and Copula In order to manage WD portfolio, copula remains the favourite simulation engine. But, the integration of Forecasts modifies the marginal distributions and the dependencies And therefore creates another “dependency modelling risk” 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Forecast Scenario and RM The easiest forecast to integrate into portfolio analysis and for which the effect is the least “unpredictable” are Scenario and Ensembles NB: deterministic forecast removes the vvol and will lower the risks. 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Michael Moreno - www.weatherderivs.com Conclusion Short/Medium Term Forecast gives the choice between a “real option” or a Weather Derivative Medium range forecast will often “force” you to diversify your portfolio Long term forecast/trends necessary for long term management (5 years plan) are quite hard to estimate and would reward trader with huge risk premiums => counterparty may no longer be willing to purchase protection Energy company traders more and more “trade the forecast” 29-Jan-2004 Michael Moreno - www.weatherderivs.com

ART “future” weather product Parametric Reinsurance 29-Jan-2004 Michael Moreno - www.weatherderivs.com

Michael Moreno - www.weatherderivs.com References J.C. Augros, M. Moreno, Book “Les dérivés financiers et d’assurance”, Ed Economica, 2002. R. Baillie, T. Bollerslev, H.O. Mikkelsen, “Fractionally integrated generalized autoregressive condition heteroskedasticity”, Journal of Econometrics, 1996, vol 74, pp 3-30. F.J. Breidt, N. Crato, P. de Lima, “The detection and estimation of long memory in stochastic volatility”, Journal of econometrics, 1998, vol 83, pp325-348 D.C. Brody, J. Syroka, M. Zervos, “Dynamical pricing of weather derivatives”, Quantitative Finance volume 2 (2002) pp 189-198, Institute of physics publishing R. Caballero et al, “Stochastic modelling of daily temperature time series for use in weather derivative pricing”, Department of the Geophysical Sciences, University of Chicago, 2003. J. Carle, S. Fourneaux, Ralph Holz, D. Marteau et M. Moreno, “La gestion du risque climatique”, Economica 2004. Ching-Fan Chung, “Estimating the FIGARCH Model”, Institute of Economics, Academia Sinica, 2003. M. Moreno, "Riding the Temp", published in FOW - special supplement for Weather Derivatives M. Moreno, O. Roustant, “Temperature simulation process”, Book “La Réassurance”, Ed Economica, Marsh 2003. Spectron Ltd for swap levels 29-Jan-2004 Michael Moreno - www.weatherderivs.com