Research On Weather Derivative Pricing Under Regime Switching

Weather derivatives are a risk management tool to hedge general weather risks.As weather derivatives are financial contracts written on weather index variables(such as temperature,humidity,wind,etc.),which cannot be traded,we cannot directly use traditional arbitrage free financial derivatives pricing method to price them,and need to explore new methods according to the characteristics of weather dynamics and weather derivatives market.This paper deals with partial differential equation(PDE)based pricing approaches for weather derivatives under regime switching.Firstly,we present two price partial differential equations of two typical two-state regime-switching temperature models,one of which is governed by two mean-reverting processes,the other is governed by a mean-reverting process and a Brownian motion.Then,to avoid causing spurious oscillations,the PDEs are discretized by a fully implicit finite difference method with one-sided up-wind differences.We obtain the unconditional stability of difference schemes by von Neumann analysis.Finally,we verify the convergence of the one-sided finite difference scheme for partial differential equations under regime switching through numerical experiments,and compare the solutions of regime-switching models,the Ornstein-Uhlenbeck model and Monte Carlo simulations.It is shown that the PDE solutions are basically consistent with the monte Carlo simulation solutions under regime-switching.And the PDE pricing method is practical and competitive,and can be utilized to price the temperature weather derivatives in real weather derivative markets with regime switching in weather risk management.