Paper: arXiv 2603.10857

Authors: Charlie Che, Hanxuan Lin, Yudong Yang, Guofan Hu, Lei Fang

Abstract

We propose a model independent framework for generating SPX and VIX risk scenarios based on a joint optimal transport calibration of their market smiles. Starting from the entropic martingale optimal transport formulation of Guyon, we introduce a perturbation methodology that computes sensitivities of the calibrated coupling using a Fisher information linearization. This allows risk to be generated without performing a full recalibration after market shocks. We further introduce a dimension reduction method based on perturbed optimal transport that produces fast and stable risk estimates while preserving the structural properties of the calibrated model. The approach is combined with Skew Stickiness Ratio(SSR) dynamics to translate SPX shocks into perturbations of forward variance and VIX distributions. Numerical experiments show that the proposed method produces accurate risk estimates relative to full recalibration while being computationally much faster. A backtesting study also demonstrates improved hedging performance compared with stochastic local volatility models.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 8.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a rigorous mathematical framework extending Guyon’s entropic martingale optimal transport via Fisher information linearization and dimension reduction for SPX-VIX risk propagation. The methodology is backed by robust numerical validation and empirical backtesting that shows superior hedging performance compared to standard stochastic local volatility models.

Research Flowchart

  flowchart TD
    A["Research Goal: Fast, Model-Independent<br>SPX-VIX Risk & Sensitivity Scenarios"] --> B["Inputs: SPX & VIX Market Smiles,<br>SSR Dynamics, SPX Market Shocks"]
    B --> C["Entropic Martingale Optimal Transport<br>Joint Model Calibration"]
    C --> D["Linearized Perturbation Methodology<br>via Fisher Information Matrix"]
    D --> E["Dimension Reduction Method<br>for Fast Sensitivity Computation"]
    E --> F["Outcomes: Fast & Stable Risk Estimates,<br>Superior Hedging vs SLV Models"]

Cited References (65)

  1. Sinkhorn Distances: Lightspeed Computation of Optimal Transport (2013)
  2. Building arbitrage-free implied volatility: Sinkhorn algorithm and variants (2019) — link
  3. Joint modelling and calibration of SPX and VIX by optimal transport (2021)
  4. Dispersion-Constrained Martingale Schr "o dinger Bridges and the Exact Joint S&P 500/ VIX Smile Calibration Puzzle (2024)
  5. Calibration of local stochastic volatility models by optimal transport (2022)
  6. Rough Volatility (2023)
  7. From (martingale) Schrödinger bridges to stochastic volatility models (2019)
  8. Iterative Bregman Projections for Regularized Transportation Problems (2015)
and 57 more
  1. Information Geometry and Its Applications (2016)
  2. A General Framework for Joint S&P 500–VIX Smile Calibration (2021)
  3. Entropic approximation for multi-dimensional martingale optimal transport (2018) — link
  4. Building arbitrage-free implied volatility: Sinkhorn’s algorithm and variants (2019) — link
  5. Optimal Transport: Old and New (2009)
  6. Optimal transport for model calibration (2021)
  7. Model-Free Hedging: A Martingale Optimal Transport Viewpoint (2017)
  8. From (Martingale) Schr" o dinger bridges to a new class of Stochastic Volatility Models (2019) — link
  9. Model-independent bounds for option prices: A mass transport approach (2013) — link
  10. Introduction to Entropic Optimal Transport (2022)
  11. Optimal transportation under controlled stochastic dynamics (2013)
  12. Random fields and diffusion processes (2006)
  13. Joint Calibration to SPX and VIX Options with Signature-Based Models — → 2301.13235
  14. the Quintic Orstein–Uhlenbeck Volatility Model that Jointly Calibrates SPX & VIX Smiles (2023)
  15. Joint Modeling and Calibration of SPX and VIX by Optimal Transport (2022) — link
  16. Stochastic Volatility Modeling (2016)
  17. A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options (1993) — link
  18. The Volatility Surface: A Practitioner’s Guide (2006)
  19. Replication of financial derivatives under extreme market models given marginals — → 2307.00807
  20. On the probability of large deviations of random variables (1957)
  21. A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem (2000)
  22. A Convexity Theory for Interacting Gases and Equilibrium Crystals (1994)
  23. Robust pricing and hedging of options on multiple assets and its numerics (2021)
  24. A B enamou- B renier formulation of martingale optimal transport (2019)
  25. Calibration of local‐stochastic volatility models by optimal transport (2021) — link
  26. Smile Dynamics IV (2009)
  27. Joint Modeling and Calibration of SPX and VIX by Optimal Transport (2022) — link
  28. Calibration of local-stochastic volatility models by optimal transport (2022)
  29. Joint Modelling and Calibration of SPX and VIX by Optimal Transport (2021) — link
  30. The joint S&P 500/ VIX Smile Calibration Puzzle Solved (2020)
  31. Dispersion-Constrained Martingale Schr" o dinger Bridges and the Exact Joint S&P 500/ VIX Smile Calibration Puzzle (2024)
  32. Dispersion-Constrained Martingale Schr" o dinger Bridges: Joint Entropic Calibration of Stochastic Volatility models to S&P 500 and /VIX Smiles (2022)
  33. Robust and Fast Bass local volatility — → 2411.04321
  34. Likelihood Training of Schrödinger Bridge using Forward-Backward SDEs Theory (2022) — link
  35. Polynomial Chaos Expansion Efficient Evaluation and Estimation of Computational Models (2022)
  36. Exact simulation scheme for the Ornstein-Uhlenbeck driven stochastic volatility model with the Karhunen-Lo$\backslash$eve expansions — → 2402.09243
  37. Bass Construction with Multi-Marginals: Lightspeed Computation in a New Local Volatility Model (2021)
  38. Automated option pricing: Numerical methods (2013)
  39. On the Martingale Schr" o dinger Bridge between Two Distributions — → 2401.05209
  40. Entropic Neural Optimal Transport via Diffusion Processes (2022) — link
  41. Neural Operator: Learning Maps Between Function Spaces (2022)
  42. PDOT: a Practical Primal-Dual Algorithm and a GPU-Based Solver for Optimal Transport (2024) — link
  43. A survey of the Schr" o dinger problem and some of its connections with optimal transport (2013)
  44. The measure preserving martingale Sinkhorn algorithm — → 2310.13797
  45. Martingale \uppercase B enamou-\uppercase B renier: A probabilistic perspective (2013)
  46. Generalization of an inequality by talagrand and links with the logarithmic sobolev inequality (2000)
  47. Computational Optimal Transport (2019)
  48. Sinkhorn Distances: Lightspeed Computation of Optimal Transport (2013) — link
  49. On the complexity of approximating multimarginal optimal transport (2022)
  50. Computation of Robust Option Prices via Structured Multi-Marginal Martingale Optimal Transport — → 2406.09959
  51. Foundations of Modern Probability (2021) — link
  52. Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration (2017)
  53. Much faster algorithms for matrix scaling (2017)
  54. cuPDLP. jl: A GPU implementation of restarted primal-dual hybrid gradient for linear programming in Julia (2023) — link
  55. Convex Analysis (1970)
  56. Prices of State-Contingent Claims Implicit in Option Prices (1978)
  57. The Pricing of Options and Corporate Liabilities (1973)

7 of 65 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.