Magnus Wiese, Hans Buehler, Blanka N. Horvath · 2026 · arXiv (Cornell University)
DOI: 10.48550/arxiv.2610.16732 · cited by 0 works (OpenAlex) · open-access PDF
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.
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Topics: Valuation of options, Econometrics, Call option, Economics, Implied volatility, Arbitrage
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