Our goal today is to use our knowledge of stochastic calculus in a practical way to fit a meanreverting stochastic process to real world data under the physical probability measure. We will attempting to model the variation of the difference between daily average temperature (DAT) and our deterministic seasonal temperature model which takes into consideration temperature trend and seasonality. The detrended and deseasonalized temperature series is meanreverting and displays heteroskedasticity.

In this tutorial we use Ito calculus and specifically the Ito doeblin formula to justify the modified meanreverting OrnsteinUhlenbeck process (sometimes called an OU process) dynamics we eventually use to model this detrended and deseasonalized temperature series. We will then go through the estimatation of the key parameters within this modified meanreverting OrnsteinUhlenbeck process, including the speed of mean reversion.

Online written tutorial: https://quantpy.com.au/weatherderiva...

In this series we take a deep dive into a type of exotic financial products weather derivatives. Weather derivatives are financial instruments that can be used to reduce risk associated with adverse weather conditions like temperature, rainfall, frost, snow, and wind speeds.

Historical Data, Weather Observations for Sydney, Australia – Observatory Hill: http://www.bom.gov.au/climate/data/st...

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