Pricing Temperature Derivatives under a Time-Changed Levy Model

TL;DR

This paper develops a novel pricing model for weather derivatives using a mean-reverting temperature process driven by a time-changed Levy model with Gamma subordinator, enhancing valuation accuracy.

Contribution

It introduces a new temperature derivative pricing framework employing a time-changed Levy process with Fourier-based approximation and Esscher transform for measure selection.

Findings

Provides an explicit Fourier-based pricing method.

Captures temperature dynamics more accurately.

Offers a practical approach for weather derivative valuation.

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).