Weather derivatives and stochastic modelling of temperature. (English) Zbl 1229.91298
The authors propose a new model for the dynamics of temperature which forms the basis for pricing weather derivatives. The model generalizes previous continuous-time autoregressive models, more exactly, stochastic volatility effects are allowed. It is established that the volatility of futures prices on the cumulative average temperature is given by the temperature volatility, modified by a Samuelson effect inherited from the autoregressive structure of the temperature dynamics. The risk premium in derivative prices is parametrized by a time-dependent market price of risk. In addition, a market price of volatility risk is included. In mathematical terms, the pricing measure is obtained by a combination of a Girsanov and Esscher transform.
Reviewer: Yuliya S. Mishura (Kyïv)
MSC:
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
Keywords:
temperature dynamics; weather derivatives; futures contracts; cumulative average temperature; stochastic volatility; Ornstein-Uhlenbeck processReferences:
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