Temperature Index Option Pricing Based on Caputo-Type Uncertain Fractional Differential Equation

To accurately characterize the memory and uncertainty of the temperature system, this study focuses on temperature model based on Caputo-type uncertain fractional differential equation and pricing of temperature index option, and constructs seasonal Caputo-type uncertain fractional mean-reverting differential equation. The solution of fractional differential equation is given by Mittag-Leffler function and α-path. This study employs the least squares estimation method to estimate the parameters of the temperature model and test the uncertainty hypothesis. Then, pricing formula for the Heating Degree Day (HDD) European call option with a profit cap will be given. Finally, corresponding numerical simulation is designed and obtain the price of the HDD European call option as 15.5007, then the impact of each parameter on the option price is discussed.