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《Wavelet Analysis and Weather Derivatives Pricing》.pdf
Wavelet Analysis and Weather Derivatives Pricing
Achilleas Zapranis1, Antonis Alexandridis2
Abstract. In this paper, we use wavelet analysis to localize in Paris, France, a mean-reverting
Ornstein-Uhlenbeck process with seasonality in the level and volatility. Wavelet analysis is an
extension of the Fourier transform, which is very well suited to the analysis of non-stationary
signals. We use wavelet analysis to identify the seasonality component in the temperature
process as well as in the volatility of the temperature anomalies (residuals). Our model is
validated on more than 100 years of data collected from Paris, one of the European cities
traded at Chicago Mercantile Exchange. We also study the effect of replacing the original
AR(1) process with ARMA, ARFIMA and ARFIMA-FIGARCH models, and the impact of
the temperature outliers on the normality of the temperature anomalies.
Keywords : Weather Derivatives, W avelet Analysi s, Temper ature Dyn amic Mod-
eling, AR , ARMA , ARFIMA , FIGARCH , CAT Option s, Di screte Pricing Model s.
JEL Classification : C5 1, G 13, Q54
1 Corresponding Author: Assistant Professor, Department of Accounting and Finance, University of
Macedonia, 156 Egnatia St., 54006 Thessaloniki, Greece (email: zapranis@uom.gr).
2 PhD Candidate, Department of Accounting and Finance, University of Macedonia, 156 Egnatia St.,
54006 Thessaloniki, Greece (email: aalex @uom.gr).
1
1. Introduction
Since their inception in 1996, weather derivatives have known a substantial growth. The
first parties to arrange for, and issue weather derivatives in 1996, were energy companies,
which after the deregulation of energy markets were exposed to weather risk. In September
1999, the Chicago Mercantile Exchange (CME) launched the first exchange trad
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