Full grid solution for multi-asset options pricing with tensor networks

Battle Count: 57

Highly relevant for quantitative finance practitioners dealing with multi-asset derivatives. Provides deterministic full-grid pricing and Greeks computation that eliminates Monte Carlo noise, enables instant re-pricing via interpolation, and supports dense cross-sensitivities for hedging. Directly applicable to options desks, risk management, and model validation. However, limited to Black-Scholes dynamics (no stochastic vol/jumps) and currently demonstrated only up to 5 assets. The ability to run on commodity hardware (laptop) makes it accessible for smaller trading desks.

Requires deep understanding of tensor network theory (TT, QTT, MPO), numerical PDE methods (finite differences, implicit schemes), and specialized algorithms (ALS, MALS, TT-Cross). The QTT constructions for operators, payoffs, and boundary conditions are non-trivial. However, the paper provides complete pseudocode, time complexity analyses, and detailed appendix derivations. Implementation in Python is feasible but performance-critical operations (ALS sweeps, TT-Cross) would benefit from optimized tensor libraries. The adaptive domain selection and rank tuning add practical complexity.

The paper provides detailed algorithms with pseudocode (Algorithm 1, Algorithm 2), specifies hardware (MacBook Pro M3 Pro, 18GB RAM), software (Python 3.11), and all market parameters (spot prices, strikes, volatilities, correlations, maturity, interest rate). Time complexity derivations are provided in appendices. However, no GitHub repository or code link is provided, and the QTT library used is not explicitly named. The adaptive two-stage domain selection procedure is described but not fully parameterized.