A Portfolio's Common Causal Conditional Risk-neutral PDE
arXiv:2401.00949 · doi:10.1007/978-3-031-64273-9_45
Abstract
Portfolio's optimal drivers for diversification are common causes of the constituents' correlations. A closed-form formula for the conditional probability of the portfolio given its optimal common drivers is presented, with each pair constituent-common driver joint distribution modelled by Gaussian copulas. A conditional risk-neutral PDE is obtained for this conditional probability as a system of copulas' PDEs, allowing for dynamical risk management of a portfolio as shown in the experiments. Implied conditional portfolio volatilities and implied weights are new risk metrics that can be dynamically monitored from the PDEs or obtained from their solution.
6 pages, 4 figures, Mathematical and Statistical Methods for Actuarial Sciences and Finance - MAF2024