Weather Derivatives

1. Weather Derivatives Michaël Moreno michael@weatherderivs.com *Speedwell is a member of the WRMA *Speedwell is regulated by the SFA

2. Speedwell Weather • Specialised in the weather risk measure of companies with optimized structuration of « insurance contract » • Software (simulations of temperature,…)

3. 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

4. Ex : Insurance against drought Put spread on rainy days

5. Les risques couverts • Energy companies • Tourism (april, may, june, …) • Agriculture… • Energy company (hydroelec.) • Agriculture • Winter station – summer station… • Energy company (windmill) • Some Sport competitions

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

7. 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 65°F  18.3°C). • Max{65 - Xi, 0} • Summertime : CDD (Cooling Degree Days - number of degrees above 65°F) • Max{Xi - 65, 0} • Where

8. Call (spread), put (spread)

9. Collar

10. Ex : HDD call Strikes Where CD is the money value for each DD.

11. « Actuarial » Analysis Historical HDD (Baltimore January)

12. HDD distribution

13. 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(X;0;1) is the cumulative standard normal distribution evaluated in X.

14. CTD Reference : 85°F

15. Parametric fit geometric

16. 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)

17. 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 ?

18. Temperature modelisation

19. Saisonnality

20. Temperature volatility

21. 2 processes • Mean reverting • AR(p)

22. Volatility structure Periodic volatility

23. Mean Reverting

24. Residues

25. Residues volatility

26. AR(p) Process

27. Final Autocorrelation

28. Orly

29. Marseille

30. Which process? AR betterly fits the data (chi² test)

31. They were wrong !!!

32. 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@weatherderivs.com