A Portfolio's Common Causal Conditional Risk-neutral PDE
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911271993999360 |
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| author | Dominguez, Alejandro Rodriguez |
| author_facet | Dominguez, Alejandro Rodriguez |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_00949 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Portfolio's Common Causal Conditional Risk-neutral PDE Dominguez, Alejandro Rodriguez Portfolio Management Mathematical Finance 35A35, 93C20, 91G70, 91G60, 91G10, 91G30, 58J65 G.1.8; G.3; J.4 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. |
| title | A Portfolio's Common Causal Conditional Risk-neutral PDE |
| topic | Portfolio Management Mathematical Finance 35A35, 93C20, 91G70, 91G60, 91G10, 91G30, 58J65 G.1.8; G.3; J.4 |
| url | https://arxiv.org/abs/2401.00949 |