Weather Derivatives Michaël Moreno *Speedwell is a member of the WRMA *Speedwell is regulated by the SFA

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

It is not an insurance against natural disasters Weather Derivatives : An insurance against the climate Even if the deal can be profiled so that it prevents from bad revenues dues to extreme weather conditions

Ex : Insurance against drought Put spread on rainy days

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

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

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 - X i, 0} Summertime : CDD (Cooling Degree Days - number of degrees above 65°F) Max{X i - 65, 0} Where

Call (spread), put (spread)

Collar

Ex : HDD call Where C D is the money value for each DD. Strikes

« Actuarial » Analysis Historical HDD (Baltimore January)

HDD distribution

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.

CTD Reference : 85°F

Parametric fit geometric

Problems 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) Sometimes few data (it depends on the country Brazil, thermometer problem (you have to believe on cleaning data methods),…)

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 ?

Temperature modelisation

Saisonnality

Temperature volatility

2 processes Mean reverting AR(p)

Volatility structure Periodic volatility

Mean Reverting

Residues

Residues volatility

AR(p) Process

Final Autocorrelation

Orly

Marseille

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

They were wrong !!!

Conclusion 1.« Actuarial » analysis is not really adapted 2.Processes must take into account daily volatility and skewness 3.We have developped a non parametric AR process with seasonnal distributions and daily volatility