Monte-Carlo Simulation Based Value-at-Risk for Non-Gaussian Seasonal Stochastic Volatility Model

Abstract

Commodity option has relatively low correlations with equities and bonds and is a good diversification asset to a portfolio compared with traditional assets. However, commodity has seasonal patterns compared with other assets. In this article, we combine stochastic volatility model with seasonal patterns and do risk measurement such as calculating options' value-at-risk (VaR). We also study non-Gaussian stochastic volatility model in student \(t\) distribution and skew-student-$t$ distribution instead of usual Gaussian distribution which take skewness and fat tails into consideration with tail losses and extreme events typical of commodity markets. Our results demonstrate that non-Gaussian distributed seasonal stochastic volatility model can better estimate VaR and has higher probability that extreme cases may happen. This research suggests that our model can serve as a powerful tool for investors seeking to manage risks more effectively in volatile commodity markets, highlighting the importance of considering both seasonal influences and distributional characteristics in financial modeling.