Thijs van den Berg | Searcharxiv

arXiv2026

Mixture-Preserving, Arbitrage-Free Interpolation for Volatility-Surface Models

Given risk-neutral densities of a tradeable forward, fitted as $N$-component mixtures at a finite set of expiration pillars, we look for a continuous-time interpolation that is (i) \emph{mixture-preserving}, remaining a mixture of the same kernel (generically with more components than either pillar), and (ii) \emph{arbitrage-free} across expiries. The second requirement is the \emph{peacock} (convex-order) property, equivalently a non-negative Dupire local volatility; for full-support kernels (Gaussian, lognormal) it gives a unique continuous local-volatility diffusion (Lowther). We construct such an interpolation in a fixed $2N$-component family, freezing both pillars' components and moving only their weights. Applied to mixture term-structure models, it lifts Brigo--Mercurio to time-varying weights and reaches the free-per-strike-width generality of SANOS at additive cost.

q-fin.CP↗

arXiv2026

Fast, Reliable, and Error-Bounded Option Pricing with Pretrained Neural Networks: A GJR--GARCH Study

Many models in quantitative finance have no closed-form option prices and rely on slow, noisy Monte Carlo simulation; neural surrogates restore speed but offer no error guarantees. We present a general recipe for surrogates that are fast, with bounded and verifiable error, applicable to any simulation-based density model. A Mixture Density Network maps parameters and maturity to the terminal return density as a Gaussian mixture, so prices, implied volatilities, and Greeks follow in closed form as an arbitrage-free mixture of lognormals, with a CDF-matching loss aligned to pricing error. A distribution-free Monte Carlo noise floor, $\sqrt{1/(6N)}$, quantifies the best accuracy achievable at a given simulation budget and decomposes the out-of-sample error into four controllable terms. We demonstrate the method on GJR--GARCH, where the surrogate reaches an out-of-sample CDF error of $1.4\times10^{-4}$, within $10\%$ of the noise floor, and prices each option in a few microseconds on a single CPU core, or under a microsecond on a GPU.

q-fin.CP↗