DYSANOS Generative Dynamic Smooth Arbitrage-free Non-parametric Option Surfaces

DYSANOS is the first generative market model for smooth SANOS option surfaces for all strikes and expiries which are free of static arbitrage. The model is designed to generate entire paths of daily spot and option prices for years in the future. The paper presents a robust and useful if somewhat simplistic baseline in the form of an AR(1) model, discusses model setup, data pipeline, and training, and investigates numerical presence of dynamic arbitrage. Model performance is illustrated on Option Metrics' IvyDB S&P Index data from 2020 to 2025 and compared to a pure implied-vol PCA model.

The paper introduces a ML-SANOS decoder, a coordinate transformation of the SANOS model such that the state parameters ht live in a low-dimensional space Rnh for nh 20. The call prices remain smooth and statically arbitrage free. This ML-SANOS is a natural decoder of a driving state process into an option surface of the form ht → C(ht; T, K). It is shown how ML-SANOS can be trained directly to suitably pre-processed option market data, yielding a trained ht for each day. The pre-processing step means that DYSANOS, via SANOS, is fitted to real market bid/ask prices.

For generative dynamics, the paper shows that most of the variance of daily changes to the joint space of spot and hidden state can be explained by essentially five parameters, in line with general PCA analysis of the implied vol surface. A simple baseline version of a generative state space model is presented based on a simple auto-regressive low-dimensional factor model which has in spirit the form dh̃t+1 = κ(m − h̃t)dt + wαt′(ω) + 1 − w2 AYt(ω) dut dt, where m ∈ Rnh is the long-term mean, κ ∈ Rnh ×nh is the mean-reversion speed and dut ∈ Rnα,nh are the main PCA factors driving dh̃t. The matrix A is the Cholesky decomposition of the historic covariance of the factor loadings α ∈ Rnt,nα. Moreover, Yt(ω) ∈ Rnα is normal and αt(ω) ∈ Rnα is sampled from historic factor loadings (αt)t∈T. The bandwidth parameter w can be used to mix between purely historical sampling with w = 1 and fully continuous state sampling w = 0. The actual model presented has an additional state h̃0 without mean-reversion which represents log-spot; it is also simulated using a more robust representation for large time steps. The authors do not claim that this approach provides the most realistic dynamics; rather, they see this implementation as baseline to beat with more modern time series models.

Regarding absence of dynamic arbitrage, every decoded SANOS surface is free of static arbitrage by construction. However, this cross-sectional property does not by itself imply the absence of dynamic arbitrage. Encoding dynamic no-arbitrage is particularly challenging for generated discrete data, since conditional means are typically estimated from noisy samples, making violations difficult to assess reliably. The paper focuses on assessing how static no-arbitrage propagates through the dynamically evolving call surfaces. A number of statistical tests are defined in Section 3.4 to detect the presence of actionable arbitrage in the generated data. DYSANOS is compared with a naive AR(1) PCA model applied directly to implied volatilities. While DYSANOS, as expected, exhibits no arbitrage when traded options are held to expiry, evidence of dynamic arbitrage is nevertheless found when options are traded from one period to the next.

The paper also presents a conditional spot importance sampling method. The surface-first structure allows sampling more frequently from the tails of spot without changing either the marginal law or any realized path of the surface state. The method increases the frequency with which spot reaches far strikes, but all reported physical-law probabilities and moments use the full mixture weight D. No marginal correction is applied in isolation, and the surface path is never resampled or altered by the proposal.

Empirical diagnostics show that the baseline captures the direction and most of the magnitude of the first-order level, skew, term, and leverage effects, but understates them. The baseline reproduces the dominant surface-change direction closely, but concentrates too much variance in it and is less accurate for secondary directions. The Gaussian baseline matches the first moment but not volatility clustering and crisis tails.

In testing for arbitrage in generated data, for returns to expiry, DYSANOS produces no candidates in the test, as expected. The PCA-IV benchmark contains complete-support arbitrage at zero cost and after one- and ten-basis-point costs. For period returns, the larger universe resolves every selected state–time center. DYSANOS has the higher occurrence in every row, and both generators retain candidates at ten basis points. An exact-state conditional resampling of the two strongest DYSANOS weekly raw period-return candidates at ten basis points rejects one of the two strongest DYSANOS candidates and leaves the other unresolved at the stated sampling precision. It does not establish non-negative P&L on the complete conditional support, but, considering the evidence, is a strong indicator that DYSANOS does admit dynamic arbitrage.

The conclusion states that DYSANOS is the first generative option market model built from smooth, strictly statically arbitrage-free SANOS surfaces. The approach does not rely on approximate static constraints; each smooth option surface is strictly arbitrage free and allows pricing of any option on GPU. The surface-first AR(1) captures first-order level, skew, term, and leverage effects, while the empirical diagnostics identify volatility clustering, crisis tails, and higher eigensurfaces as natural targets for future work. The paper provides a baseline model to generate long paths of daily spot and option prices. Each option surface is free of static arbitrage. Moreover, any option can be priced on each path given the ML-SANOS parameters for the respective sample and time step. Contrary to previous results, agents can therefore choose which options to trade at each time step. Numerical indication is found that in this situation, DYSANOS admits dynamic arbitrage along its paths.

Improvements to AI Systems Based on This Paper:

1. Arbitrage-Free Generative Market Modeling

• Implement a neural decoder (ML-SANOS) that maps low-dimensional latent states to smooth, strictly static-arbitrage-free option surfaces across all strikes and expiries.

• The improved AI system can generate entire multi-year paths of daily spot prices and full option surfaces without violating cross-sectional no-arbitrage constraints, enabling realistic synthetic market data for stress testing, backtesting, and simulation.

2. Dynamic Arbitrage Detection and Quantification

• Integrate the paper’s statistical tests (Section 3.4) for detecting actionable dynamic arbitrage in generated data, including cost-adjusted and conditional-support checks.

• The improved system can automatically flag whether a generative model admits dynamic arbitrage when options are traded across periods, allowing users to reject or adjust models that produce exploitable inconsistencies.

3. Low-Dimensional State-Space Representation with Mean Reversion

• Use the AR(1)-style factor model with mean reversion (κ, m) and PCA-driven noise (A, α, Y) to capture first-order level, skew, term, and leverage effects in option surfaces.

• The improved system can generate realistic daily changes in spot and surface states with reduced dimensionality (20 latent variables), making it computationally efficient for large-scale Monte Carlo simulations on GPUs.

4. Conditional Importance Sampling for Tail Events

• Adopt the surface-first conditional spot importance sampling method to oversample extreme spot movements without altering marginal laws or surface paths.

• The improved system can efficiently estimate rare-event probabilities (e.g., deep out-of-the-money option payoffs, crash scenarios) with higher precision, while preserving unbiased physical-law moments via mixture weights.

5. Benchmarking and Diagnostics for Generative Models

• Use the paper’s empirical diagnostics (first-order effects, variance concentration, volatility clustering, crisis tails) to evaluate and compare generative models.

• The improved system can automatically diagnose model weaknesses—such as understated skew or over-concentrated variance—and guide iterative improvements toward more realistic dynamics.

6. Cost-Aware Arbitrage Testing in Generated Data

• Incorporate transaction cost thresholds (e.g., 1 and 10 basis points) into arbitrage detection, as done in the paper.

• The improved system can determine whether apparent arbitrage opportunities remain profitable after realistic trading costs, providing a practical measure of model realism for trading applications.

7. Pathwise Option Pricing and Trading Simulation

• Leverage the ML-SANOS decoder to price any option (arbitrary strike/expiry) at each time step along generated paths.

• The improved system enables agent-based simulations where trading decisions (which options to buy/sell) are made dynamically at each step, supporting realistic portfolio optimization and risk management research.

8. Hybrid Historical-Continuous Noise Sampling

• Implement the bandwidth parameter w to mix historical factor loadings with continuous Gaussian noise, balancing realism and smoothness in generated dynamics.

• The improved system can tune w to match desired volatility clustering or crisis behavior, offering flexibility for different simulation purposes (e.g., stress testing vs. steady-state generation).

9. Model Comparison and Selection Framework

• Use the paper’s comparison against a pure implied-vol PCA model to establish a baseline for evaluating new generative approaches.

• The improved system can automatically benchmark novel time-series models (e.g., transformers, normalizing flows) against this baseline, quantifying improvements in no-arbitrage preservation, moment matching, and arbitrage occurrence rates.

10. GPU-Accelerated Synthetic Data Generation

• Exploit the smooth, parametric SANOS representation to price options on GPU without grid interpolation.

• The improved system can generate millions of realistic market paths in parallel, enabling large-scale reinforcement learning, option pricing, and risk analytics that require massive synthetic datasets.

This article presents with DYSANOS the first generative market model for smooth SANOS option surfaces for all strikes and expiries which are free of static arbitrage. Our model is designed to generate entire paths of daily spot and option prices for years in the future. We present a robust and useful if somewhat simplistic baseline hidden state generative model in the form of an AR(1) model. We discuss model setup, data pipeline, and training and investigate numerical resence of dynamic arbitrage. We illustrate model performance on Option Metrics' IvyDB S&P Index data from 2020 to 2025 and compare it to a pure implied-vol PCA model.