Finite Element Solution of the Two-Dimensional Bates Model for Option Pricing Under Stochastic Volatility and Jumps

Battle Count: 85

The paper addresses option pricing under realistic market dynamics (stochastic volatility + jumps), which is directly relevant to derivatives trading desks. The Bates model captures skew, fat tails, and smile effects observed in equity and FX markets. The computational efficiency gains (up to 2 orders of magnitude faster than FEM) are practically relevant for real-time pricing and risk management. However, the paper is primarily a numerical methods contribution rather than a trading strategy paper, limiting its direct applicability to algorithmic trading systems.

The HOC-FD scheme requires careful construction of compact stencils (3x3) for first, second, and mixed derivatives with variable coefficients. The IMEX-Crank-Nicolson time stepping requires assembling and solving a sparse linear system at each time step. The jump integral requires Simpson quadrature with interpolation for off-grid values. The mixed derivative via sequential compact differentiation adds complexity. However, the structured grid and tensor-product approach simplify implementation compared to unstructured FEM. The verification template for constant coefficients aids debugging.

Simulation parameters are fully specified in Table 1 (K=110, T=1.0, r=0.03, kappa=1.8, theta=0.02, rho=-0.4, sigma=0.15, lambda=0.25, lognormal jump law). The mathematical formulation, stencils, and boundary conditions are explicitly given. However, no code repository or implementation details (programming language, solver libraries) are provided. Jump parameters mu_J and sigma_J are set per experiment but specific values are not fully enumerated.