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Notebook","readme":"\u003cdiv align=\"center\"\u003e\n  \u003ca href=\"https://github.com/open-source-modelling\" target=\"_blank\"\u003e\n    \u003cpicture\u003e\n      \u003cimg src=\"images/OSM_logo.jpeg\" width=280 alt=\"Logo\"/\u003e\n    \u003c/picture\u003e\n  \u003c/a\u003e\n\u003c/div\u003e\n\n\u003ch1 align=\"center\" style=\"border-botom: none\"\u003e\n  \u003cb\u003e\n    🐍 Actuarial models in Python 🐍     \n  \u003c/b\u003e\n\u003c/h1\u003e\n\n\u003c/br\u003e\n\n\u003cp align=\"center\"\u003e\n  Collection of useful models that actuaries can use to speed up their tasks. \n\u003c/p\u003e\n\n\n## Algorithms available\n\n| Algorithm                | Source                              | Description                                                                   |\n| -------------------------| ----------------------------------- | ----------------------------------------------------------------------------- |\n| [Smith_Wilson]           | [Technical-documentation]           | Interpolation and extrapolation of missing interest rates.                    |\n| [Stationary_boot_calib]  | [Whitepaper-2004]                   | Automatic calibration of the stationary bootstrap algorithm.                  |\n| [Stationary_bootstrap]   | [Politis-Romano-1994]               | Resampling procedure for weakly dependent stationary observations.            |\n| [Calibration_of_alpha]   | [Technical-documentation]           | Calibration of the Smith \u0026 Wilson's alpha parameter.                          |\n| [Correlated Brownian]    | [Wiki Brownian motion]              | Simple function to generate correlated Brownian motion in multiple dimensions.|\n| [Nel_Si_Svansson]        | [BIS whitepaper]                    | Nelson-Siegel-Svansson model for approximating the yield curve.               |\n| [Black_Scholes]          | [Wiki Black\u0026Sholes]                 | Black\u0026Scholes model for pricing option contracts.                             |\n| [Vasicek one factor]     | [Wiki Vasicek]                      | Vasicek model for modelling the evolution of interest rates.                  |\n| [Vasicek two factor]     | [Wiki Vasicek]                      | Vasicek model for modelling the evolution of a pair of interest rates.        |\n| [1F Hull White]          | [Wiki Hull White]                   | One factor Hull White model of short rates.                                   |\n| [Dothan one factor]      | [Quant Exchange]                    | One factor Dothan model of short rates.                                       |\n\n[Quant Exchange]:https://quant.stackexchange.com/questions/16017/for-the-dothan-model-eqbt-infty\n[Dothan one factor]:https://github.com/open-source-modelling/insurance_python/tree/main/dothan_one_factor\n[Wiki Hull White]:https://en.wikipedia.org/wiki/Hull%E2%80%93White_model\n[1F Hull White]:https://github.com/open-source-modelling/insurance_python/tree/main/hull_white_one_factor\n[Smith_Wilson]: https://github.com/open-source-modelling/insurance_python/tree/main/smith_wilson\n[Technical-documentation]: https://www.eiopa.europa.eu/sites/default/files/risk_free_interest_rate/12092019-technical_documentation.pdf\n[Stationary_boot_calib]: https://github.com/open-source-modelling/insurance_python/tree/main/stationary_bootstrap_calibration\n[Whitepaper-2004]: http://public.econ.duke.edu/~ap172/Politis_White_2004.pdf\n[Stationary_bootstrap]: https://github.com/open-source-modelling/insurance_python/tree/main/stationary_bootstrap\n[Politis-Romano-1994]: https://www.jstor.org/stable/2290993\n[Calibration_of_alpha]: https://github.com/open-source-modelling/insurance_python/tree/main/bisection_alpha\n[Correlated Brownian]: https://github.com/open-source-modelling/insurance_python/tree/main/correlated_brownian_motion\n[Wiki Brownian motion]: https://en.wikipedia.org/wiki/Brownian_motion\n[Nel_Si_Svansson]: https://github.com/open-source-modelling/insurance_python/tree/main/nelson_siegel_svansson\n[BIS whitepaper]: https://www.bis.org/publ/bppdf/bispap25l.pdf\n[Black_Scholes]: https://github.com/open-source-modelling/insurance_python/tree/main/black_sholes\n[Wiki Black\u0026Sholes]: https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model\n[Vasicek one factor]: https://github.com/open-source-modelling/insurance_python/tree/main/vasicek_one_factor\n[Wiki Vasicek]: https://en.wikipedia.org/wiki/Vasicek_model\n[Vasicek two factor]: https://github.com/open-source-modelling/insurance_python/tree/main/vasicek_two_factor\n\n## Algorithms planned\n\n| Algorithm              | Source                              | Description                                                            |\n| ---------------------- | ----------------------------------- | ---------------------------------------------------------------------- |\n| Matrix on fraction     | TBD                                 | Heuristics for calculating transition matrices on fractions of power   |\n| G2++ with piec cons vol| TBD                                 | Calibration of a G2++ model with piecewise constant volatility          |\n| Carter-Lee model       | TBD                                 | Simple stochastic mortality model                                      |\n| Metropolis-Hastings    | TBD                                 | Sampling of probability distributions                                  |\n\n\u003cb\u003e New suggestions for algorithms are welcome. \u003c/b\u003e\n\n\u003cb\u003e If anybody is interested in publishing an algorithm they implemented, or help with the project, contact us and we will make it happen. \u003c/b\u003e\n\nQueries and suggestions; gregor@osmodelling.com\n","funding_links":[],"categories":["Jupyter 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