Futures Options Pricing in the Indian Commodity Market Using Univariate GARCH Models and Particle Swarm Optimization

Abstract

In the ever-changing commodity markets, accurate futures option pricing is critical for investors and traders for managing risks and making sound decisions. Traditional models like Black-76, often fall short in capturing the complex volatility patterns observed in these markets because of the constant volatility assumption. Furthermore, while the generalized autoregressive conditional heteroskedasticity (GARCH) model effectively captures time-varying volatility, its estimation of parameters using maximum likelihood estimation (MLE) with gradient based methods, is highly sensitive to initial parameter values and can suffer from issues like local minima, leading to poor estimates. To address these issues, this study combines Particle Swarm Optimization (PSO) algorithm with GARCH model to improve the parameter estimation process. PSO algorithm explores the parameter space dynamically, allowing for a better fitting to the underlying dynamics of market volatility. This paper uses several variants of GARCH models, such as GARCH, GJR-GARCH, and E-GARCH to account for different features of volatility behavior. Empirical analysis shows that the PSO-variant is better than the Black-76 model and MLE-variant for all GARCH models in terms of pricing accuracy. Among the PSO-variants, the PSO-GARCH model provides the best option pricing fit to the Indian commodity market. These findings highlight the practical significance of PSO-enhanced GARCH models in emerging markets, providing reliable and adaptable tools for precise option pricing and effective volatility estimation. © The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd. 2025.