A Perron-Frobenius comonotonic approximation for sums of lognormals

Battle Count: 68

The paper is relevant to quantitative risk management rather than direct trading strategy development. It provides an efficient analytical tool for computing tail risk measures (VaR, CTE, ESF) of portfolios composed of lognormal assets, which is directly applicable to risk assessment in trading books, option portfolios, and structured products. The method is particularly useful in high-volatility regimes where accurate tail risk quantification is critical for position sizing and capital allocation decisions.

The PF approximation is computationally straightforward: it requires computing the Perron-Frobenius eigenvector of the covariance matrix Sigma (standard eigenvalue computation) and the matrix inverse Sigma^{-1}. Once the eigenvector is obtained, the conditioning variable Lambda and all risk measures follow from closed-form expressions. No iterative optimization or simulation is needed for the approximation itself. The main computational cost is the eigendecomposition, which is O(n^3) for an n-dimensional problem.

The paper provides complete analytical formulas for the PF approximation, clear parameter settings (n=20, mu=0.075, sigma in {0.05,0.15,0.15,0.25,0.35}, alpha_i=1), and Monte Carlo benchmark methodology (500,000 paths with antithetic variates). However, no code repository is provided. The mathematical derivations are self-contained and reproducible from the paper alone.