Commodity options pricing under Wishart stochastic volatility model equipped with jump process: Model calibration by an optimized neural network

This paper presents the valuation of commodity options within the context of a Wishart stochastic volatility model that is equipped with a jump process. To achieve this, we propose a semi-analytical solution for pricing European options on commodity futures by introducing the characteristic function of the proposed model. The unique challenges posed by this model underscore the necessity for effective calibration techniques. To address this, we utilize an Artificial Neural Network (ANN) designed to improve the precision and efficiency of the calibration process. To optimize the presented ANN model, we use the flower pollination (FP) algorithm. Empirical studies suggest that the Wishart stochastic volatility model incorporating a jump factor enhances calibration accuracy compared to common models in the literature. Moreover, applying the FP-optimized ANN to calibration leads to a marked improvement in accuracy, as demonstrated by both in-sample and out-of-sample data.