Weather Derivatives Trading and Structuring The Forecast component

1
Weather Derivatives Trading and StructuringThe
Forecast component

• Michael Moreno
• Speedwell Weather Derivatives Ltd

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

3
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

4
Weather Derivatives Pricing Methods

• There are 4 main methods
• Burn Analysis
• Actuarial/Index Method
• Black
• Daily simulation

5
Burn Analysis
6
Actuarial/Index Method
7
Black

• Blacks 76 model on Futures
• gt Lognormal distribution
• gt Vol Smile
• gt Standard Derivatives Methods
• OK for listed contract on positive values
• Not interesting elsewhere

8
Temperature daily simulation
AR gt Short Memory Homoskedasticity GARCH gt
Short Memory Heteroskedasticity ARFIMA gt Long
Memory Homoskedasticity FBM gt Long Memory
Homoskedasticity ARFIMA-FIGARCH gt Long Memory
Heteroskedasticity Time Series Bootsrapp
9
ARFIMA-FIGARCH model (proposed at WRMA 2003 by
Moreno M.)
Seasonality
Trend
ARFIMA-FIGARCH
Seasonal volatility
10
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 s2.
11
FIGARCH noise
Given the conditional variance We suppose that
Long term memory
Cf Baillie, Bollerslev and Mikkelsen 96 or Chung
03 for full specification
12
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 mainlyfrom the year 1963
13
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

14
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)
• ...

15
Most importantly in their basic form they are
forecast blind

• Lets 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 lets say he comes to buy a weather hedge for
  the next 7 days. Would you take the risk not to
  consider the weather forecast?

16
So can forecast be ignored?

• No
• Yes

17
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

18
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 gt 1 year

19
Forecast Samples
Source AWS/WeatherNet www.myweatherbug.com
20
DeterministicForecast
Look at the Temperature, wind and then Rain
Forecasts Source www.customweather.com
21
Deterministic Forecast gt Scenario Pricing
technique
22
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).

23
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

24
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)

25
Historical swap levels LONDON HDD December
Forward ? 380 Before the period started swap
level below Then swap level above like the
partial index
26
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
27
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!
28
Weather Related Flight Delays
29
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

30
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
31
Medium Term gt Scenario Pricing
32
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

33
Long term forecasts

• Long term forecasts are usually coming from
  external variables like
• Human intervention (increase/decrease of
  population, pollution)
• Sun Solar flare activity

34
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!

35
Example Companies with Gvt contract/strong
legislation

• Some companies sign long term contract/agreements
  with government
• Builders
• Road Maintenance companies
• Railways
• Water companies

36
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?

37
Example with water companies

• Drought issues gt financial penalties and
  possibly licence withdrawal

38
An ExoticExample
Are you willing to sell a swap on Sunshine for
next 10 years to a farmer without
considering the vapour trail effects of airplanes?
39
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

40
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

41
Forecast incompleteness example

• You have 1 deal on a compound index based on the
  same weather stations
• - Rain gt 2mm
• - Temp lt -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?

42
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)

43
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

44
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.

45
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 gt counterparty may no longer be willing
  to purchase protection
• Energy company traders more and more trade the
  forecast

46
ART future weather product

• Parametric Reinsurance

47
References

• J.C. Augros, M. Moreno, Book Les dérivés
  financiers et dassurance, 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