Weather Derivatives

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Weather Derivatives

• Michaël Moreno
• michael_at_weatherderivs.com
• Speedwell is a member of the WRMA
• Speedwell is regulated by the SFA

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Speedwell Weather

• Specialised in the weather risk measure of
  companies with optimized structuration of
   insurance contract 
• Software (simulations of temperature,)

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Weather Derivatives An insurance against the
climate
It is not an insurance against natural disasters
Even if the deal can be profiled so that it
prevents from bad revenues dues to extreme
weather conditions
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Ex Insurance against drought
Put spread on rainy days
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Les risques couverts

• Energy companies
• Tourism (april, may, june, )
• Agriculture

• Energy company (hydroelec.)
• Agriculture
• Winter station summer station

• Energy company (windmill)
• Some Sport competitions

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Temperature contracts

• Reference Site
• Contract Pay off (call, put, swap,)
• Underlying (HDD, CDD, CTD, GDD,)
• Cover period
• Others (barrier, compound,)

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Underlying

• Weather derivatives usually have a 5 months
  lifetime
• for cold period November to March
• For hot period May to September
• Wintertime HDD (Heating Degree Days - number of
  degrees below 65F ? 18.3C).
• Max65 - Xi, 0
• Summertime CDD (Cooling Degree Days - number of
  degrees above 65F)
• MaxXi - 65, 0
• Where

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Call (spread), put (spread)
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Collar
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Ex HDD call
Strikes
Where CD is the money value for each DD.
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 Actuarial  Analysis
Historical HDD (Baltimore January)
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HDD distribution
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Closed formulae prices
Assuming normal distribution, the call up out
price is And the price of a binary call is
where ? ?
?
? ? are estimated mean standard
deviation of the HDD distribution N(X01) is
the cumulative standard normal distribution
evaluated in X.
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CTD
Reference 85F
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Parametric fit
geometric
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Problems
Sometimes few data (it depends on the country
Brazil, thermometer problem (you have to believe
on cleaning data methods),)

• Always hard to correct the history to forecast
  the future
• Tendancy
• Volatility
• Correlation with other towns

Distribution tails are not necessarily correctly
estimated (extreme risks are not correctly takenb
into account)
Mark to market mark to model are just
impossible (conditionnal probability with so few
data cannot be rightly estimated)
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A simple question

• Suppose that in London recorded temperature in
  July has never reached 37C
• CTD distribution is therefore Dirac weight in 0.
• Would you sell us such a contract for 0.00 ?

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Temperature modelisation
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Saisonnality
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Temperature volatility
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2 processes

• Mean reverting
• AR(p)

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Volatility structure
Periodic volatility
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Mean Reverting
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Residues
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Residues volatility
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AR(p) Process
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Final Autocorrelation
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Orly
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Marseille
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Which process?
AR betterly fits the data (chi² test)
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They were wrong !!!
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Conclusion

•  Actuarial  analysis is not really adapted
• Processes must take into account daily volatility
  and skewness
• We have developped a non parametric AR process
  with seasonnal distributions and daily volatility
• http//www.weatherderivs.com/
• michael_at_weatherderivs.com