Crude Oil Options Stochastic Volatility Jump or Co-Jump: Evidence from Price Paths Stimulation

Pricing options in energy markets is particularly challenging because of sharp price swings, nonlinear dynamics, and heavy-tailed distributions observed in commodity returns. This study develops a numerical framework for valuing crude oil options by applying the stochastic volatility with correlated jumps model, which captures both volatility clustering and sudden price shocks. The associated partial integro-differential equation is reformulated into a system of forward–backward stochastic differential equations (FBSDEs), which we solve using a deep learning–based algorithm. We benchmark the proposed method against classical numerical techniques, including Monte Carlo simulation. Using real market data for West Texas Intermediate crude oil prices and options, we demonstrate that the deep learning–FBSDE approach provides greater accuracy and stability while reducing computational inefficiency. Our findings highlight the promise of this approach for advancing option valuation, hedging, and risk management in energy and commodity finance.