# lifelib v0.3.1 (24 October 2021)¶

This release adds a new example in the `savings`

library,
and updates some formulas in the `savings`

models.

To update lifelib, execute the command:

```
>>> pip install lifelib --upgrade
```

## New Example¶

An example is added to the `savings`

library.
This example shows how to extend `CashValue_ME`

to a stochastic model,
by going through a classic exercise of calculating the time value of options and guarantees
on a plain variable annuity with GMAB by two methods,
the Black-Scholes-Merton formula and Monte Carlo simulation with risk-neutral scenarios.

This example consists of an example model, a Jupyter notebook
and some Python scripts.
The model is developed from `CashValue_ME`

and named `CashValue_ME_EX1`

.
The Python scripts included in `savings`

are used to
draw graphs on the Gallery page
The Jupyter notebook describes the `CashValue_ME_EX1`

model,
explains the changes from the original model,
and outputs some graphs on the Gallery page.

File or Folder |
Description |
---|---|

CashValue_ME_EX1 |
The example model for |

savings_example1.ipynb |
Jupyter notebook Simple Stochastic Example |

plot_av_paths.py |
Python script for Account value paths |

plot_rand.py |
Python script for Account value distribution |

plot_option_value.py |
Python script for Monte Carlo vs Black-Scholes-Merton |

## Fixes and Updates¶

The following formulas are updated.