weather derivatives trading and structuring the forecast component michael moreno speedwell weather...

Weather Derivatives Trading and StructuringThe Forecast component

Michael MorenoSpeedwell Weather Derivatives Ltd

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

2

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


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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


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Weather Derivatives Pricing Methods

There are 4 main methods

Burn Analysis Actuarial/Index Method Black Daily simulation


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Burn Analysis

Historical Payoff with Premium

Pay off + Premium (Non Det.)gfedcb

06/12/199907/12/199508/12/199109/12/198710/12/198311/12/197912/12/197513/12/197114/12/196715/12/1963

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0


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Actuarial/Index Method

HistogramKernelNormal

Density

2 2002 0001 8001 6001 4001 2001 000

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dxxfxPayoffP


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Black

Black’s 76 model on Futures

=> Lognormal distribution

=> Vol Smile

=> Standard Derivatives Methods

OK for listed contract on positive values

Not interesting elsewhere


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Temperature daily simulation

AR => Short Memory + HomoskedasticityGARCH => Short Memory + Heteroskedasticity

ARFIMA => Long Memory + HomoskedasticityFBM => Long Memory + Homoskedasticity

ARFIMA-FIGARCH => Long Memory + HeteroskedasticityTime Series Bootsrapp


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ARFIMA-FIGARCH model (proposed at WRMA 2003 by Moreno M.)

iiiii ymST

Seasonality Trend ARFIMA-FIGARCH

Seasonal volatility


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ARFIMA-FIGARCH definition

ttd LyLL 01

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.

a

j

jjLL

1

1

We consider first the ARFIMA process:

m

j

jjLL

1

1


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FIGARCH noise

1 ttt Varh Given the conditional variance

We suppose that

22 1]1[1 td

tt LLLhL

Cf Baillie, Bollerslev and Mikkelsen 96 or Chung 03 for full specification

Long term memory


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Distributions of London winter HDD

HistoSim

Densities

2,4002,2002,0001,8001,6001,4001,2001,000

0.003

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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 mainlyfrom the year 1963


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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


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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) ...


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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?


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So can forecast be ignored?

No

Yes


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Plan




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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


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Forecast Samples

Source: AWS/WeatherNetwww.myweatherbug.com


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DeterministicForecast

Look at the Temperature, wind and then Rain Forecasts

Source:www.customweather.com


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Deterministic Forecast => Scenario Pricing technique


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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).


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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


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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)


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Historical swap levels LONDON HDD December

London HDD December

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05-Nov-02 10-Nov-02 15-Nov-02 20-Nov-02 25-Nov-02 30-Nov-02 05-Dec-02 10-Dec-02 15-Dec-02

Date

HD

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MeanMaxMinCurrent Index

Weather Index Cone - LONDON HDD December 2002

28/12/200221/12/200214/12/200207/12/2002

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Forward 380Before the period started: swap level belowThen swap level above like the partial index


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Historical swap levels LONDON HDD January

London HDD January

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30-Dec-02 04-Jan-03 09-Jan-03 14-Jan-03 19-Jan-03 24-Jan-03

Date

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DMeanMaxMinCurrent Index

Weather Index Cone - LONDON HDD January 2003

31292725232119171513110907050301

580560540

520500480460

440420400380

360340320300

280260240220

200180160

14012010080

604020

Forward 400Before the period started: swap level belowThen swap level has 2 peaks and does not followthe partial index evolution which is well above the mean


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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!


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Weather Related Flight Delays


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Short term forecast solutionsWD 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


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Medium term forecasts

Mainly El NinoLa 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


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Medium Term => Scenario Pricing


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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


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Long term forecasts

Long term forecasts are usually coming from external variables like

Human intervention (increase/decrease of population, pollution)

Sun Solar flare activity


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Long Term contracts difficulties

Credit Risk Issues Credit Risk Issues Credit Risk Issues Credit Risk Issues Credit Risk Issues Credit Risk Issues Credit Risk Issues Credit Risk Issues Credit Risk Issues Credit Risk Issues Credit Risk Issues

And model risks

There is a demand!There is no “real” Offer!


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Example: Companies with Gvt contract/strong legislation

Some companies sign long term contract/agreements with government:

- Builders- Road Maintenance companies- Railways- Water companies- …


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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?


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Example with water companies

Drought issues => financial penalties and possibly licence withdrawal


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An “Exotic”Example

Are you willing to sell a swapon Sunshine for next 10 years to a farmerwithout consideringthe vapour trail effects of airplanes?


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Plan




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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


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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?


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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)


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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”


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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.


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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”


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ART “future” weather product

Parametric Reinsurance


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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

weather derivatives trading and structuring the forecast component michael moreno speedwell weather...

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