# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Modelling the temperature time-dependent speed of mean reversion in the context of weather derivatives pricing. (English) Zbl 1142.91575
Summary: In the context of an Ornstein-Uhlenbeck temperature process, we use neural networks to examine the time dependence of the speed of the mean reversion parameter $\alpha$ of the process. We estimate non-parametrically with a neural network a model of the temperature process and then compute the derivative of the network output w.r.t. the network input, in order to obtain a series of daily values for $\alpha$. To our knowledge, this is the first time that this has been done, and it gives us a much better insight into the temperature dynamics and temperature derivative pricing. Our results indicate strong time dependence in the daily values of $\alpha$, and no seasonal patterns. This is important, since in all relevant studies performed thus far, $\alpha$ was assumed to be constant. Furthermore, the residuals of the neural network provide a better fit to the normal distribution when compared with the residuals of the classic linear models used in the context of temperature modelling (where $\alpha$ is constant). It follows that by setting the mean reversion parameter to be a function of time we improve the accuracy of the pricing of the temperature derivatives. Finally, we provide the pricing equations for temperature futures, when $\alpha$ is time dependent.

##### MSC:
 91B28 Finance etc. (MSC2000) 91B24 Price theory and market structure 60K35 Interacting random processes; statistical mechanics type models; percolation theory 92B20 General theory of neural networks (mathematical biology) 86A10 Meteorology and atmospheric physics
##### Keywords:
neural networks; weather derivatives pricing
Full Text: