Pricing Gamma Based Temperature Derivatives

Abstract

Farmers are impacted by temperature as high temperatures during the rainy season can lead to a substantial decrease in crop production. To safeguard farmers from this risk, temperature derivatives can be used, but they are frequently mispriced. This study aims to address this issue by developing a Stochastic Differential Equation (SDE) for temperature, with the assumption that it conforms to a gamma distribution. A synthesis technique that effectively manages the auto correlation within the data is employed to deduce the SDE. The resulting pricing formula is based on the anticipated value derived from the SDE. Notably, the formulated equation’s outcome is not linked to the expected temperature itself, but rather hinges on the gamma distribution parameters and the trigger temperature. This approach yields accurate forecasts for both price predictions and temperature projections. The model is found to predict temperature with R² = 91%, MSE = 0.14, and MAPE = 1.3%. When used to price call option, the prices decrease with increase in trigger value, which is more realistic. Thus, the model is more flexible.