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Closed forms where Monte Carlo used to rule
Exact Quantitative Finance
Can core objects of quantitative finance — VaR, ES, rough volatility, tail risk — be computed exactly instead of simulated?
Progress
90%Fenton representation under review
Current approach
Latent representation of correlated lognormal sums (Fenton distribution); spectral importance sampling for tail risk.
Status notes
Fenton distribution representation published with Zenodo DOI. VaR/ES deterministic computation and ES backtesting complete. Rough volatility ongoing.
Direct contributions
3 papers
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
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
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