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arXiv · 2401.00949

A Portfolio's Common Causal Conditional Risk-neutral PDE

Alejandro Rodriguez Dominguez
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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.

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Alejandro Rodriguez Dominguez. 2024-01-31. A Portfolio's Common Causal Conditional Risk-neutral PDE. https://doi.org/10.1007/978-3-031-64273-9_45

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