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

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weather derivatives trading and structuring the forecast component

Weather Derivatives Trading and StructuringThe Forecast component

Michael Moreno

Speedwell Weather Derivatives Ltd

slide2
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

Michael Moreno - www.weatherderivs.com

deals lengths
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

Michael Moreno - www.weatherderivs.com

weather derivatives pricing methods
Weather Derivatives Pricing Methods

There are 4 main methods

  • Burn Analysis
  • Actuarial/Index Method
  • Black
  • Daily simulation

Michael Moreno - www.weatherderivs.com

burn analysis
Burn Analysis

Michael Moreno - www.weatherderivs.com

actuarial index method
Actuarial/Index Method

Michael Moreno - www.weatherderivs.com

black
Black
  • Black’s 76 model on Futures

=> Lognormal distribution

=> Vol Smile

=> Standard Derivatives Methods

OK for listed contract on positive values

Not interesting elsewhere

Michael Moreno - www.weatherderivs.com

temperature daily simulation
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

Michael Moreno - www.weatherderivs.com

arfima figarch model proposed at wrma 2003 by moreno m
ARFIMA-FIGARCH model (proposed at WRMA 2003 by Moreno M.)

Seasonality

Trend

ARFIMA-FIGARCH

Seasonal volatility

Michael Moreno - www.weatherderivs.com

arfima figarch definition
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 tare white noises with the variance σ2.

Michael Moreno - www.weatherderivs.com

figarch noise
FIGARCH noise

Given the conditional variance

We suppose that

Long term memory

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

Michael Moreno - www.weatherderivs.com

distributions of london winter hdd
Distributions of London winter HDD

With similar detrending methods

The slight differences come mainlyfrom the year 1963

Michael Moreno - www.weatherderivs.com

rainfall daily simulation
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

Michael Moreno - www.weatherderivs.com

those methods have a few problems black 76 is specific
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)
  • ...

Michael Moreno - www.weatherderivs.com

most importantly in their basic form they are forecast blind
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?

Michael Moreno - www.weatherderivs.com

so can forecast be ignored
So can forecast be ignored?
  • No
  • Yes

Michael Moreno - www.weatherderivs.com

slide17
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

Michael Moreno - www.weatherderivs.com

what are the forecasts categories
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

Michael Moreno - www.weatherderivs.com

forecast samples
Forecast Samples

Source: AWS/WeatherNet

www.myweatherbug.com

Michael Moreno - www.weatherderivs.com

deterministic forecast
DeterministicForecast

Look at the Temperature, wind and then Rain Forecasts

Source:

www.customweather.com

Michael Moreno - www.weatherderivs.com

deterministic forecast scenario pricing technique
Deterministic Forecast => Scenario Pricing technique

Michael Moreno - www.weatherderivs.com

integrating the forecast in the pricing model
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).

Michael Moreno - www.weatherderivs.com

slide23
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

Michael Moreno - www.weatherderivs.com

prevision rte
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)

Michael Moreno - www.weatherderivs.com

historical swap levels london hdd december
Historical swap levels LONDON HDD December

Forward  380

Before the period started: swap level below

Then swap level above like the partial index

Michael Moreno - www.weatherderivs.com

historical swap levels london hdd january
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

Michael Moreno - www.weatherderivs.com

human resources planning
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!

Michael Moreno - www.weatherderivs.com

weather related flight delays
Weather Related Flight Delays

Michael Moreno - www.weatherderivs.com

short term forecast solutions wd or real option
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

Michael Moreno - www.weatherderivs.com

medium term forecasts
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

Michael Moreno - www.weatherderivs.com

medium term scenario pricing
Medium Term => Scenario Pricing

Michael Moreno - www.weatherderivs.com

el nino la nina
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

Michael Moreno - www.weatherderivs.com

long term forecasts
Long term forecasts

Long term forecasts are usually coming from external variables like

  • Human intervention (increase/decrease of population, pollution)
  • Sun Solar flare activity

Michael Moreno - www.weatherderivs.com

long term contracts difficulties
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!

Michael Moreno - www.weatherderivs.com

example companies with gvt contract strong legislation
Example: Companies with Gvt contract/strong legislation

Some companies sign long term contract/agreements with government:

  • Builders
  • Road Maintenance companies
  • Railways
  • Water companies

Michael Moreno - www.weatherderivs.com

example with gritting
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?

Michael Moreno - www.weatherderivs.com

example with water companies
Example with water companies

Drought issues => financial penalties and possibly licence withdrawal

Michael Moreno - www.weatherderivs.com

an exotic example
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?

Michael Moreno - www.weatherderivs.com

slide39
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

Michael Moreno - www.weatherderivs.com

the forecast completeness issue in rm
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

Michael Moreno - www.weatherderivs.com

forecast incompleteness example
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?

Michael Moreno - www.weatherderivs.com

greeks and rm implications
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)

Michael Moreno - www.weatherderivs.com

forecast and copula
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”

Michael Moreno - www.weatherderivs.com

forecast scenario and rm
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.

Michael Moreno - www.weatherderivs.com

conclusion
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”

Michael Moreno - www.weatherderivs.com

art future weather product
ART “future” weather product

Parametric Reinsurance

Michael Moreno - www.weatherderivs.com

references
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

Michael Moreno - www.weatherderivs.com