Pricing Temperature Derivatives under a Time-Changed Levy Model

Abstract

The objective of the paper is to price weather contracts using temperature as the underlying process when the later follows a mean-reverting dynamics driven by a time-changed Brownian motion coupled to a Gamma Levy subordinator and time-dependent deterministic volatility. This type of model captures the complexity of the temperature dynamic providing a more accurate valuation of their associate weather contracts. An approximated price is obtained by a Fourier expansion of its characteristic function combined with a selection of the equivalent martingale measure following the Esscher transform proposed in Gerber and Shiu (1994).