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insurance_python

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All Python algorithms published by Open Source Modelling in one place.

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<h1 align="center" style="border-botom: none">
  <b>
    🐍 Actuarial models in Python 🐍     
  </b>
</h1>

</br>

<p align="center">
  Collection of useful models that actuaries can use to speed up their tasks. 
</p>

## Algorithms available

| Algorithm                | Source                              | Description                                                                   |
| -------------------------| ----------------------------------- | ----------------------------------------------------------------------------- |
| [Smith_Wilson]           | [Technical-documentation]           | Interpolation and extrapolation of missing interest rates.                    |
| [Stationary_boot_calib]  | [Whitepaper-2004]                   | Automatic calibration of the stationary bootstrap algorithm.                  |
| [Stationary_bootstrap]   | [Politis-Romano-1994]               | Resampling procedure for weakly dependent stationary observations.            |
| [Calibration_of_alpha]   | [Technical-documentation]           | Calibration of the Smith & Wilson's alpha parameter.                          |
| [Correlated Brownian]    | [Wiki Brownian motion]              | Simple function to generate correlated Brownian motion in multiple dimensions.|
| [Nel_Si_Svansson]        | [BIS whitepaper]                    | Nelson-Siegel-Svansson model for approximating the yield curve.               |
| [Black_Scholes]          | [Wiki Black&Sholes]                 | Black&Scholes model for pricing option contracts.                             |
| [Vasicek one factor]     | [Wiki Vasicek]                      | Vasicek model for modelling the evolution of interest rates.                  |
| [Vasicek two factor]     | [Wiki Vasicek]                      | Vasicek model for modelling the evolution of a pair of interest rates.        |
| [1F Hull White]          | [Wiki Hull White]                   | One factor Hull White model of short rates.                                   |
| [Dothan one factor]      | [Quant Exchange]                    | One factor Dothan model of short rates.                                       |
| [Singular Spectrum analysis]      | [Paper SSA]                | Non-parametric technique used for time series analysis and forecasting.       |

[Singular Spectrum analysis]:https://github.com/open-source-modelling/singular_spectrum_analysis
[Paper SSA]:https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5136637
[Quant Exchange]:https://quant.stackexchange.com/questions/16017/for-the-dothan-model-eqbt-infty
[Dothan one factor]:https://github.com/open-source-modelling/insurance_python/tree/main/dothan_one_factor
[Wiki Hull White]:https://en.wikipedia.org/wiki/Hull%E2%80%93White_model
[1F Hull White]:https://github.com/open-source-modelling/insurance_python/tree/main/hull_white_one_factor
[Smith_Wilson]: https://github.com/open-source-modelling/insurance_python/tree/main/smith_wilson
[Technical-documentation]: https://www.eiopa.europa.eu/sites/default/files/risk_free_interest_rate/12092019-technical_documentation.pdf
[Stationary_boot_calib]: https://github.com/open-source-modelling/insurance_python/tree/main/stationary_bootstrap_calibration
[Whitepaper-2004]: http://public.econ.duke.edu/~ap172/Politis_White_2004.pdf
[Stationary_bootstrap]: https://github.com/open-source-modelling/insurance_python/tree/main/stationary_bootstrap
[Politis-Romano-1994]: https://www.jstor.org/stable/2290993
[Calibration_of_alpha]: https://github.com/open-source-modelling/insurance_python/tree/main/bisection_alpha
[Correlated Brownian]: https://github.com/open-source-modelling/insurance_python/tree/main/correlated_brownian_motion
[Wiki Brownian motion]: https://en.wikipedia.org/wiki/Brownian_motion
[Nel_Si_Svansson]: https://github.com/open-source-modelling/insurance_python/tree/main/nelson_siegel_svansson
[BIS whitepaper]: https://www.bis.org/publ/bppdf/bispap25l.pdf
[Black_Scholes]: https://github.com/open-source-modelling/insurance_python/tree/main/black_sholes
[Wiki Black&Sholes]: https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model
[Vasicek one factor]: https://github.com/open-source-modelling/insurance_python/tree/main/vasicek_one_factor
[Wiki Vasicek]: https://en.wikipedia.org/wiki/Vasicek_model
[Vasicek two factor]: https://github.com/open-source-modelling/insurance_python/tree/main/vasicek_two_factor

## Algorithms planned

| Algorithm              | Source                              | Description                                                            |
| ---------------------- | ----------------------------------- | ---------------------------------------------------------------------- |
| Matrix on fraction     | TBD                                 | Heuristics for calculating transition matrices on fractions of power   |
| G2++ with piec cons vol| TBD                                 | Calibration of a G2++ model with piecewise constant volatility          |
| Carter-Lee model       | TBD                                 | Simple stochastic mortality model                                      |
| Metropolis-Hastings    | TBD                                 | Sampling of probability distributions                                  |

<b> New suggestions for algorithms are welcome. </b>

<b> If anybody is interested in publishing an algorithm they implemented, or help with the project, contact us and we will make it happen. </b>

Queries and suggestions; gregor@osmodelling.com

insurance_python

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