Signature approach for pricing and hedging path-dependent options with frictions

Battle Count: 90

Highly relevant for derivatives desks and quantitative trading teams dealing with path-dependent options in markets with liquidity constraints. The framework directly addresses the practical problem of hedging exotic options when large trades move prices. The finding that market impact smooths optimal strategies (making low-order signature approximations accurate) is practically significant. The indifference pricing approach is directly applicable to option desk operations. However, the mathematical complexity and computational requirements may limit immediate industry adoption.

Very high complexity. Requires: (1) computation of path-signatures (iterated stochastic integrals) up to order M, (2) solving infinite-dimensional systems of ODEs (Riccati equations) on the extended tensor algebra, (3) implementing shuffle products and projections on tensor spaces, (4) handling time-dependent coefficients in signature linear combinations, (5) numerical integration of the Riccati system with projected shuffle products at each time step, (6) for non-signature payoffs, regression of payoffs against truncated signatures. The tensor algebra operations and infinite-dimensional ODE systems require specialized numerical libraries and careful truncation management.

The paper provides detailed mathematical formulations, explicit parameter settings for numerical experiments (S0=10, mu=0, sigma=2, T=0.2, eta=0.001, nu=0.001, lambda=0.01), and Algorithm 1 for signature regression. However, no code repository is provided. The infinite-dimensional Riccati system and signature computations require specialized numerical implementations. Sanity checks against known closed-form solutions (Almgren-Li, Bank-Soner-Voss) are included.