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Quantitative Finance
Exact pricing, risk, and distributions
Closed-form results and machine-verified theorems for financial mathematics — rough volatility, expected shortfall, spectral importance sampling, and exact distribution theory.
3 papers
Quantitative Finance
Working Paper
DOI
Spectral Importance Sampling: Optimal Rare-Event Simulation via Eigenvalue-Conditioned Measure Change
We develop a variance reduction framework for simulating rare events in correlated portfolios by exploiting the eigenvalue decomposition of the correlation matrix. The central observation is that the eigenvalue modes $Z_k$ — projections of the asset vector onto the eigenvectors of the correlation matrix — are mutually independent.
Quantitative Finance
Working Paper
Lean
DOI
Deterministic Portfolio VaR Without Monte Carlo: The Eigen-COS Method
We present the Eigen-COS method, a deterministic algorithm that computes exact Value-at-Risk, closed-form Expected Shortfall, and the full CDF/PDF for weighted sums of correlated lognormal assets — without Monte Carlo simulation.
Quantitative Finance
Working Paper
Lean
DOI
Contaminated by Construction: Separating Simulation Noise from Model Risk in ES Backtests
Expected Shortfall backtesting under Basel III/IV suffers from an unmeasured structural weakness: Monte Carlo estimation of ES injects computational noise into the Acerbi-Székely (2014) test statistic, but the magnitude of this contamination has not