Weather Derivative Pricing and Risk Management: Volatility and Value at Risk

Abstract

Weather derivatives are financial contracts that allow entities to hedge themselves against the adverse impacts of fluctuations in the weather. The pricing of such contracts is based on a combination of actuarial and arbitrage methods. Risk management of portfolios of weather derivatives centres on the estimation of two distributions: the expiry distribution and the short term risk distribution. These distributions can be used to calculate the expiry VaR and the VaR, respectively. The expiry distribution can be estimated relatively easily using the actuarial methods used to price contracts and manage portfolios. The short term risk distribution, however, is much more difficult to estimate since it depends on market dynamics and the statistics of changes in probabilistic meteorological forecasts. Nevertheless, we show that, under certain reasonable assumptions, the short term risk distribution for a large class of standard contracts takes a particularly simple form. It depends on a single volatility that can be derived without having to perform any statistical analysis of past forecasts. In addition we show that the framework we develop for calculating the short term risk distribution leads to a simple method for the actuarial valuation of options during the contract period.

Keywords: weather derivatives, weather risk, risk management, value at risk, VaR, expiry value at risk, expiry VaR, seasonal value at risk, seasonal VaR, weather volatility, short term risk

JEL Classification: G12, G13