Numerical valuation of European options under two-asset infinite-activity exponential Lévy models

Battle Count: 57

The paper addresses accurate pricing of multi-asset European derivatives under realistic jump-diffusion models, which is fundamental for quantitative trading desks dealing with exotic options, energy derivatives, and multi-asset structured products. The NTS framework encompasses NIG and VG models widely used in practice. However, the paper is primarily a numerical methods contribution rather than a trading strategy paper. Direct applicability is in derivative pricing and risk management rather than signal generation or execution.

High complexity due to: (1) 2D non-local integral discretization with three-region partition and tailored quadrature weights; (2) FFT-based evaluation of summation term requiring circulant matrix construction and interpolation between grids; (3) Semi-Lagrangian method with characteristic tracing and interpolation; (4) Operator splitting with fixed-point iteration for integral term; (5) BiCGSTAB iterative solver with ILU preconditioning; (6) Non-uniform grid construction with sinh transformation; (7) Cell averaging for non-smooth payoffs; (8) Higher-order extrapolation for fixed-point initialization. Requires expertise in numerical PDEs, FFT, iterative solvers, and stochastic processes.

The paper provides a complete algorithm (Algorithm 1), detailed parameter sets (Tables 1-2), explicit choices for all numerical parameters (grid sizes, tolerances, interpolation methods), and theoretical convergence results. However, no code repository is provided. Parameter sets are sourced from literature (Hilber et al. 2013, Rydberg 1997) and estimated from Yahoo Finance data. The methodology is fully specified but implementation requires significant numerical expertise.