Risk-Neutral Compression and the Geometry of Latent Market Stress

This paper develops the risk-neutral pricing and compression layer for the Perron latent market-stress state derived in the preceding market-theory paper. It shows that equivalent pricing changes the projection of claims onto public information, but not the underlying directed Volterra geometry, rough exponents, screened contagion operator, spectral radius, or Perron mode. The main mathematical object is the priced structural loading of a claim under the risk-neutral measure; public option surfaces, premium comparisons, variance claims, and visible hedges observe only compressed or projected versions of that loading. The paper proves the resulting Hilbert-space compression theorem, visibility classification, option-surface transfer results, signed physical/risk-neutral premium bridge, convexity-compression bound, and visible-hedging residual theorem. Empirically, it matches an SPX/NDX OptionMetrics panel to the Oxford-Man realized-volatility construction and finds evidence consistent with the compression mechanism: implied-volatility level, total-variance level, and signed downside total-variance skew align with the rebuilt Perron stress direction in full-sample and rolling-window designs. The Gaussian source-family verification needed for the local option-factor specialization is delegated to a companion technical note, while the main paper keeps the focus on the standalone risk-neutral compression theorem, its option and premium implications, and the SPX/NDX diagnostic evidence.