Paper: arXiv 2610.16732
Authors: Magnus Wiese, Hans Buehler, Blanka Horvath
Abstract
We present a statically and dynamically arbitrage-free European option market model with smooth interpolation between option prices, based on the SANOS framework, and prove that its dynamics admit a unique strong solution. In spirit, it is a stochastic model for local volatility when the latter is used as a representation of a European option price surface, not as a pricing model. We illustrate the strength of our approach on S&P Index Option data from January 2022 to August 2025. We show that the model’s initial state fits within bid/ask for more than 95% of relevant market option prices. We then train the model dynamics under $\mathbb{P}$ and $\mathbb{Q}$ and show that the model is indeed free of arbitrage while fitting the dynamics of the market well. We also propose a range of BHW-tests to test for absence of arbitrage.
Complexity vs Empirical Score
- Math Complexity: 9.0/10
- Empirical Rigor: 8.0/10
- Quadrant: Holy Grail — high math complexity, high empirical rigor
Why this score: This paper presents a highly mathematical and theoretically sound framework for arbitrage-free option market modeling. It is backed by strong empirical validation on real market data, demonstrating both fit and dynamic arbitrage-freeness. The approach is novel in its explicit construction of risk-neutral dynamics for a comprehensive option surface model.
Research Flowchart
flowchart TD
A[Research Goal: Develop Arbitrage-Free Option Market Model] --> B{Key Methodology: GROMM based on SANOS Framework};
B --> C[Data/Inputs: S&P Index Option Data (Jan 2022 - Aug 2025)];
C --> D{Computational Processes: <br>1. Static Arbitrage-Free Interpolation <br>2. Dynamic Model Training (P & Q) <br>3. BHW-Tests for Arbitrage Absence};
D --> E[Outcome 1: Statically & Dynamically Arbitrage-Free Model with Smooth Interpolation];
E --> F[Outcome 2: Initial State Fits >95% Market Bid/Ask Spreads];
F --> G[Outcome 3: Model Dynamics Fit Market Well];