{"title":"A Portfolio's Common Causal Conditional Risk-neutral PDE","authors":"Alejandro Rodriguez Dominguez","doi":"arxiv-2401.00949","DOIUrl":null,"url":null,"abstract":"Portfolio's optimal drivers for diversification are common causes of the\nconstituents' correlations. A closed-form formula for the conditional\nprobability of the portfolio given its optimal common drivers is presented,\nwith each pair constituent-common driver joint distribution modelled by\nGaussian copulas. A conditional risk-neutral PDE is obtained for this\nconditional probability as a system of copulas' PDEs, allowing for dynamical\nrisk management of a portfolio as shown in the experiments. Implied conditional\nportfolio volatilities and implied weights are new risk metrics that can be\ndynamically monitored from the PDEs or obtained from their solution.","PeriodicalId":501045,"journal":{"name":"arXiv - QuantFin - Portfolio Management","volume":"28 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - QuantFin - Portfolio Management","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2401.00949","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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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