A Portfolio’s Common Causal Conditional Risk-Neutral PDE

Alejandro Rodriguez Dominguez ()
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Alejandro Rodriguez Dominguez: Miralta Finance Bank S.A., Department of Quantitative Research

A chapter in Mathematical and Statistical Methods for Actuarial Sciences and Finance, 2024, pp 274-279 from Springer

Abstract: 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.

Keywords: causality; Gaussian copula; partial differential equations; portfolio management; risk-neutral measure (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-64273-9_45

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DOI: 10.1007/978-3-031-64273-9_45

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