Pricing Weather Derivatives with Deep Neural Networks in an Equilibrium Trading Model

Abstract

Each year, changes in weather patterns have a large impact on economies around the world. They can drastically alter revenues for businesses tied to the environment, put heavy strain on insurance companies, and shift a country's GDP by a wide margin. The threat of climate change over the coming century only serves to make these risks more severe, and both weather-dependent corporations and the companies that insure them have sought ways to hedge against these climate risks. This is usually accomplished through insurance and reinsurance, but the inefficient pricing of climate risk likely makes these options needlessly expensive, and a more promising option may be to hedge this risk in capital markets. Ideally this would be accomplished through exchange-traded weather derivatives, defined as financial products which derive their value from physical weather events and are traded on an open market, but these only exist in a few cities for a few types of weather processes. This means that we would like to find a method by which over-the-counter weather derivatives can be efficiently priced. This project aims to extend an existing model and implement an existing method for correctly pricing them. This model is an equilibrium model based on the dynamics of the climate process as well as the involved agents' financial dependence on the climate. This involves taking real climate data, finding an accurate way to model it as a stochastic differential equation, and simulating how market agents interact based on this information and their own interests. The chosen model results in a backwards stochastic differential equation for which we implement an existing numerical solver which relies on deep neural networks, and from which the price of climate risk emerges as a solution. We find numerical results for optimal utility and derivative price for a variety of potential trading environments and provide algorithms which generalize this process to any stochastic climate process in any location. These algorithms would ideally be utilized in future research that could determine if these derivatives could be feasible and cost-effective alternatives to reinsurance.