Creating premium table#

This notebook shows how to create the premium table from BasicTerm_M model to be used in BasicTerm_SE and BasicTerm_ME.

To calculate premiums, the present values of claims and annuities need to be taken at the beginning of the policy terms, but BasicTerm_SE and BasicTerm_ME start projections for in-force model points at time zero after their issues, so the present values are not available. Such being the case, a premium rate table needs to be fed into the models. This notebook demonstrates how to create the premium table using BasicTerm_M model.

By default, BasicTerm_M and BasicTerm_ME models the same product using the same assumption, and BasicTerm_M is the new business version of BasicTerm_ME.

Here’re the steps to create the premium table.

  • Read the BasicTerm_M model.

  • Replace the model point table with the one for the premium table. By default, the premium rates vary only by age_at_entry and policy_term. The range of age_at_entry is 20 to 59, and policy_term takes the value of either 10, 15 or 20. The model point data for the premium table is created from the combinations of the two attributes.

  • Calculate per-policy premiums for the model points.

  • Create the premium table by processing the result of the above.

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The next code cell below is relevant only when you run this notebook on Google Colab. It installs lifelib and creates a copy of the library for this notebook.

[1]:

import sys, os

if 'google.colab' in sys.modules:
    lib = 'basiclife'; lib_dir = '/content/'+ lib
    if not os.path.exists(lib_dir):
        !pip install lifelib
        import lifelib; lifelib.create(lib, lib_dir)

    %cd $lib_dir

The next code imports the necessary Python modules.

[2]:

import itertools
import modelx as mx
import pandas as pd

The code below reads the BasicTerm_M model and assign it to model and the Pojection space to space for later use.

[3]:

model = mx.read_model('BasicTerm_M')
space = model.Projection

The code below creates the model point table for the premium table. To calculate the premium rates as premium per sum assured, 1’s are entered in the sum_assured column.

[4]:

df = pd.DataFrame(itertools.product(range(20, 60), [10, 15, 20]), columns=['age_at_entry', 'policy_term'])
df.index += 1
df.index.name = 'point_id'
df["sum_assured"] = 1
df

[4]:
age_at_entry policy_term sum_assured
point_id
1 20 10 1
2 20 15 1
3 20 20 1
4 21 10 1
5 21 15 1
... ... ... ...
116 58 15 1
117 58 20 1
118 59 10 1
119 59 15 1
120 59 20 1

120 rows × 3 columns

The code below replaces the default model point table with the new one just created above.

[5]:

space.model_point_table = df

Since the sum assured of all the model points are all 1, premium_pp returns 0 because of the rounding operation in its formula. Below defines the premium_rate by modifying the premium_pp formula and removing the rounding so that the formula can be used for creating the premium rates.

[6]:

space.premium_pp.formula

[6]:

def premium_pp():
    """Monthly premium per policy

    Monthly premium amount per policy defined as::

        round((1 + loading_prem()) * net_premium(), 2)

    .. versionchanged:: 0.2.0
       The ``t`` parameter is removed.

    .. seealso::

        * :func:`loading_prem`
        * :func:`net_premium_pp`

    """
    return np.around((1 + loading_prem()) * net_premium_pp(), 2)

[7]:

@mx.defcells
def premium_rate():
    return (1 + loading_prem()) * net_premium_pp()

[8]:

premium_rate()

[8]:

array([4.64097874e-05, 5.20142609e-05, 5.74163309e-05, 4.76585304e-05,
       5.35875832e-05, 5.93505736e-05, 4.90033193e-05, 5.52810740e-05,
       6.14333696e-05, 5.04508489e-05, 5.71036033e-05, 6.36762900e-05,
       5.20084360e-05, 5.90648826e-05, 6.60920324e-05, 5.36840817e-05,
       6.11755527e-05, 6.86945406e-05, 5.54865410e-05, 6.34472793e-05,
       7.14991376e-05, 5.74253987e-05, 6.58928613e-05, 7.45226753e-05,
       5.95111559e-05, 6.85263505e-05, 7.77837009e-05, 6.17553240e-05,
       7.13631858e-05, 8.13026444e-05, 6.41705320e-05, 7.44203428e-05,
       8.51020274e-05, 6.67706437e-05, 7.77165017e-05, 8.92066979e-05,
       6.95708907e-05, 8.12722349e-05, 9.36440944e-05, 7.25880198e-05,
       8.51102174e-05, 9.84445414e-05, 7.58404584e-05, 8.92554627e-05,
       1.03641583e-04, 7.93484996e-05, 9.37355878e-05, 1.09272355e-04,
       8.31345102e-05, 9.85811110e-05, 1.15378012e-04, 8.72231632e-05,
       1.03825787e-04, 1.22004196e-04, 9.16416996e-05, 1.09506983e-04,
       1.29201578e-04, 9.64202228e-05, 1.15666105e-04, 1.37026460e-04,
       1.01592029e-04, 1.22349075e-04, 1.45541457e-04, 1.07193980e-04,
       1.29606875e-04, 1.54816273e-04, 1.13266925e-04, 1.37496152e-04,
       1.64928569e-04, 1.19856171e-04, 1.46079913e-04, 1.75964954e-04,
       1.27012023e-04, 1.55428306e-04, 1.88022101e-04, 1.34790385e-04,
       1.65619502e-04, 2.01208012e-04, 1.43253447e-04, 1.76740699e-04,
       2.15643451e-04, 1.52470461e-04, 1.88889258e-04, 2.31463569e-04,
       1.62518620e-04, 2.02173994e-04, 2.48819743e-04, 1.73484055e-04,
       2.16716638e-04, 2.67881664e-04, 1.85462968e-04, 2.32653505e-04,
       2.88839696e-04, 1.98562923e-04, 2.50137387e-04, 3.11907554e-04,
       2.12904306e-04, 2.69339702e-04, 3.37325333e-04, 2.28622001e-04,
       2.90452947e-04, 3.65362941e-04, 2.45867287e-04, 3.13693489e-04,
       3.96323966e-04, 2.64810009e-04, 3.39304745e-04, 4.30550057e-04,
       2.85641059e-04, 3.67560794e-04, 4.68425846e-04, 3.08575204e-04,
       3.98770509e-04, 5.10384491e-04, 3.33854326e-04, 4.33282251e-04,
       5.56913884e-04, 3.61751124e-04, 4.71489217e-04, 6.08563590e-04])

The code below creates the premium table as a Series indexed by age_at_entry and policy_term from the result above. The table is created by modifying the copy of the model point table and assigning the result of premium_rate above.

[9]:

premium_rate_table = df.copy()
premium_rate_table["premium_rate"] = space.premium_rate()
del premium_rate_table["sum_assured"]
premium_rate_table.set_index(["age_at_entry", "policy_term"], inplace=True)
premium_rate_table["premium_rate"]   # As Series

[9]:

age_at_entry  policy_term
20            10             0.000046
              15             0.000052
              20             0.000057
21            10             0.000048
              15             0.000054
                               ...
58            15             0.000433
              20             0.000557
59            10             0.000362
              15             0.000471
              20             0.000609
Name: premium_rate, Length: 120, dtype: float64