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Wolfgang Karl Härdle; Brenda López Cabrera; Ostap Okhrin; Weining Wang (2011)
Publisher: Humboldt-Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät
Types: Book
Subjects: Stochastischer Prozess, N53, G19, Finanzderivat, Q59, localising temperature residuals, local model selection, G22, Weather derivatives, 330 Wirtschaft, Wetter, N23, Elementarschadenversicherung, G29, Risiko, Weather derivatives, localising temperature residuals, seasonality, local model selection, HB, seasonality, Optionspreistheorie, Theorie
jel: jel:G22, jel:Q59, jel:N53, jel:G19, jel:N23, jel:G29
ddc: ddc:330
On the temperature derivative market, modelling temperature volatility is an important issue for pricing and hedging. In order to apply the pricing tools of financial mathematics, one needs to isolate a Gaussian risk factor. A conventional model for temperature dynamics is a stochastic model with seasonality and intertemporal autocorrelation. Empirical work based on seasonality and autocorrelation correction reveals that the obtained residuals are heteroscedastic with a periodic pattern. The object of this research is to estimate this heteroscedastic function so that, after scale normalisation, a pure standardised Gaussian variable appears. Earlier works investigated temperature risk in different locations and showed that neither parametric component functions nor a local linear smoother with constant smoothing parameter are flexible enough to generally describe the variance process well. Therefore, we consider a local adaptive modelling approach to find, at each time point, an optimal smoothing parameter to locally estimate the seasonality and volatility. Our approach provides a more flexible and accurate fitting procedure for localised temperature risk by achieving nearly normal risk factors. We also employ our model to forecast the temperature in different cities and compare it to a model developed in Campbell and Diebold (2005).