Basket Option Pricing Under Stochastic Volatility via Eigenvalue-Conditional Heston Mixing

The eigenvalue-conditional mixing framework (Nagy, 2026a, 2026c) prices basket options under geometric Brownian motion by decomposing the correlation matrix, conditioning on dominant factors, and mixing per-scenario Black-Scholes prices. We prove that the Mixture Collapse theorem enabling this approach is distribution-agnostic (Lean-verified: MixtureCollapse.lean), depending only on linearity of finite sums and the law of iterated expectations. This motivates extending the framework to stochastic volatility: replace per-scenario Black-Scholes with per-scenario Heston (1993) pricing, where the conditional characteristic function is known analytically. We derive the eigenvalue-conditional Heston pricing formula, show that the conditional basket characteristic function approximately factorizes as a product of single-asset Heston CFs (with residual error bounded by the first omitted eigenvalue \(\lambda_{K+1}\)), and establish error bounds decomposing into three components: correlation conditioning error, single-asset Heston CF truncation error, and Gauss-Hermite quadrature error. We conjecture a conditional variance reduction result extending Proposition 1 of Nagy (2026c) to stochastic volatility and provide heuristic arguments. Numerical experiments on 2--50 asset baskets under the multi-asset Heston model are designed to benchmark this approach against Monte Carlo simulation; we describe the full experimental protocol with eight test configurations spanning diverse Heston regimes. To our knowledge, this is the first deterministic (non-Monte-Carlo) basket option pricing method under multi-asset stochastic volatility that exploits the spectral structure of cross-asset correlation.