Stochastic model genetic programming: Deriving pricing equations for rainfall weather derivatives

Rainfall derivatives are in their infancy since starting trading on the Chicago Mercantile Exchange (CME) in 2011. Being a relatively new class of financial instruments there is no generally recognised pricing framework used within the literature. In this paper, we propose a novel Genetic Programming (GP) algorithm for pricing contracts. Our novel algorithm, which is called Stochastic Model GP (SMGP), is able to generate and evolve stochastic equations of rainfall, which allows us to probabilistically transform rainfall predictions from the risky world to the risk-neutral world. In order to achieve this, SMGP's representation allows its individuals to comprise of two weighted parts, namely a seasonal component and an autoregressive component. To create the stochastic nature of an equation for each SMGP individual, we estimate the weights by using a probabilistic approach. We evaluate the models produced by SMGP in terms of rainfall predictive accuracy and in terms of pricing performance on 42 cities from Europe and the USA. We compare SMGP to 8 methods: its predecessor DGP, 5 well-known machine learning methods (M5 Rules, M5 Model trees, k-Nearest Neighbors, Support Vector Regression, Radial Basis Function), and two statistical methods, namely AutoRegressive Integrated Moving Average (ARIMA) and Monte Carlo Rainfall Prediction (MCRP). Results show that the proposed algorithm is able to statistically outperform all other algorithms.