COS–TT–CHF: A Tensor-Train Characteristic-Function COS Method for Multi-Asset Option Pricing

Battle Count: 50

The paper addresses a core computational challenge in derivatives trading: pricing multi-asset European options (baskets, min/max) efficiently in high dimensions. The method enables fast strike-grid evaluation and component Greeks (Delta, Vega), which are essential for hedging and risk management in multi-asset portfolios. The tested dimensions (up to d=30) and model families (GBM, VG, NIG, Heston) cover regimes relevant to equity derivatives, index options, and structured products. However, the method is limited to European payoffs and does not yet address early-exercise or path-dependent contracts common in trading desks.

The method requires expertise in multiple advanced areas: Fourier/COS spectral methods, tensor-train decomposition and TT-cross algorithms, characteristic-function models (GBM, VG, NIG, Heston), multi-dimensional quadrature, payoff-specific contractions (basket projection, rectangle probabilities, tail integrals), and Greek computation via differentiated characteristic functions. The workflow involves careful tuning of frequency windows, quadrature nodes, COS orders, TT rank caps, and truncation intervals. Numerical diagnostics (mass, parity, held-out checks) are essential for validation. The proprietary code is not available, adding to practical implementation difficulty.

The implementation code is proprietary and not publicly released. However, the paper provides detailed mathematical formulations, algorithmic workflow steps, numerical parameters, market specifications, reference-pricing procedures, and diagnostics. All benchmark conventions are stated explicitly. The mathematical construction is self-contained, enabling independent reimplementation, but exact numerical reproduction of reported timings and ranks would require the same hardware and software environment.