Modelling and valuation of temperature-based weather derivatives under the benchmark approach.

Weather derivatives have emerged as valuable instruments for diversifying and hedging portfolios against climate-related risks. Nevertheless, despite their growing popularity, pricing remains challenging due to market incompleteness. This study explores the benchmark approach as an alternative pricing method that, relying on the growth optimal portfolio, allows to price any contingent claims without the need for measure transformations. In fact, when the GOP acts as benchmark or numeraire it makes any benchmarked derivative price process a martingale, directly yielding the real world probability measure. The research focuses on assessing this approach in pricing derivatives linked to daily average temperature indices of the Chicago Airport meteorological station, considering both historical and Gaussian residuals. A discrete time model is developed to capture temperature characteristics, addressing trends and seasonality. Results from the historical fair price indicate that when the GOP can be assumed independent of the underlying variable, the fair price is a special case of the generalized actuarial pricing. However, this approach seems not suitable for pricing Chicago heating degree days (HDD) futures. Additionally, analysis of Gaussian distribution reveals deviations from normality, challenging starting assumptions. The role of market price of risk and independence between the numeraire and the underlying variables are also discussed, paving the way for future research in weather derivative pricing and valuation.