Quantitative Finance

The moment-based Latent representation of correlated lognormal sums (Nagy, 2026, *The Exact Latent Distribution of Correlated Lognormal Sums*) relies on scaled moments $c_k = m_k/k!$ that grow as $e^{\sigma_{\max}^2 k^2/2}$.

We derive the ATM implied volatility skew power law $\psi(T) \sim C \cdot T^{H-1/2}$ from the rough Bergomi (rBergomi) model through a machine-verified chain of 125 theorems.

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.

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.

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

We propose Bayesian Live Risk (BLR), a framework in which the spectral representation of portfolio loss is treated as a posterior state updated in real time.

We construct a low-rank arbitrage-aware volatility surface with $O(rm)$ parameters and closed-form COS reuse for pricing and Greeks. Total implied variance is expressed as a finite cosine series in log-moneyness, $w(k, T) = c(T) + \sum_j u_j(T)\cos(\omega_j k)$, with $r = 6$–$12$ modes per maturity.

We derive a closed-form European option pricing formula valid for all spot prices \( S_0 \in \mathbb{R} \), including negative values. The formula replaces the logarithmic transform of Black-Scholes with the inverse hyperbolic sine, yielding a three-term call price \( C = S_+ \Phi(d_+) - S_- \Phi(d_-) - K e^{-rT} \Phi(d) \).