The Three-Dimensional Decomposition of Volatility Memory
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| Format: | Preprint |
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2025
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| _version_ | 1866914177256259584 |
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| author | Wang, Ziyao Trindade, A. Alexandre Rachev, Svetlozar T. |
| author_facet | Wang, Ziyao Trindade, A. Alexandre Rachev, Svetlozar T. |
| contents | This paper develops a three-dimensional decomposition of volatility memory into orthogonal components of level, shape, and tempo. The framework unifies regime-switching, fractional-integration, and business-time approaches within a single canonical representation that identifies how each dimension governs persistence strength, long-memory form, and temporal speed. We establish conditions for existence, uniqueness, and ergodicity of this decomposition and show that all GARCH-type processes arise as special cases. Empirically, applications to SPY and EURUSD (2005--2024) reveal that volatility memory is state-dependent: regime and tempo gates dominate in equities, while fractional-memory gates prevail in foreign exchange. The unified tri-gate model jointly captures these effects. By formalizing volatility dynamics through a level--shape--tempo structure, the paper provides a coherent link between information flow, market activity, and the evolving memory of financial volatility. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_02166 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Three-Dimensional Decomposition of Volatility Memory Wang, Ziyao Trindade, A. Alexandre Rachev, Svetlozar T. Mathematical Finance This paper develops a three-dimensional decomposition of volatility memory into orthogonal components of level, shape, and tempo. The framework unifies regime-switching, fractional-integration, and business-time approaches within a single canonical representation that identifies how each dimension governs persistence strength, long-memory form, and temporal speed. We establish conditions for existence, uniqueness, and ergodicity of this decomposition and show that all GARCH-type processes arise as special cases. Empirically, applications to SPY and EURUSD (2005--2024) reveal that volatility memory is state-dependent: regime and tempo gates dominate in equities, while fractional-memory gates prevail in foreign exchange. The unified tri-gate model jointly captures these effects. By formalizing volatility dynamics through a level--shape--tempo structure, the paper provides a coherent link between information flow, market activity, and the evolving memory of financial volatility. |
| title | The Three-Dimensional Decomposition of Volatility Memory |
| topic | Mathematical Finance |
| url | https://arxiv.org/abs/2512.02166 |