Arbitrage-Free Multi-Maturity Risk-Neutral Marginals

Battle Count: 75

Highly relevant to quantitative trading and derivatives desks. The paper directly addresses the gap between arbitrage-free option prices (upstream) and usable risk-neutral marginals (downstream) required by MOT solvers, Bass calibration, scenario analysis, and tail-risk measurement. The construction is computationally efficient (O(n) per maturity, ~15ms per strike), guarantees no-arbitrage by construction, and provides closed-form densities, CDFs, quantiles, and Monte Carlo sampling. The JPMorgan affiliation and practical S&P 500 validation demonstrate production-readiness. Directly applicable to options pricing, hedging, risk management, and model calibration workflows at trading desks.

Moderate complexity. The single-maturity construction is straightforward: slope estimation via Lagrange finite differences, two-piece curvature with closed-form solution (Theorem 1), and power-law tails. The multi-maturity extension adds sequential processing, three-piece optimization (small per-interval QP), and global tail-slope selection (convex QP with m variables). The main implementation challenges are: (1) careful handling of boundary slope estimation (Algorithm 1 with bootstrap), (2) the three-piece optimization requiring a small solver per interval, (3) the global tail-slope QP, and (4) the optional PL3 density-anchored tail with its feasibility check and calendar filter. All components are well-specified with closed-form solutions or small convex programs, but the overall pipeline has many interacting pieces.

The paper provides complete algorithms (Algorithms 1-4), all proofs in the appendix, and detailed parameter specifications for SSVI benchmarks. The S&P 500 data is from OptionMetrics (commercial source). The construction is fully specified with closed-form solutions for the two-piece case and small convex QPs for multi-maturity tail selection. No code repository is mentioned, but the mathematical specification is sufficiently detailed for independent implementation.