The BasicTerm_S Model¶
Overview¶
The BasicTerm_S model is the most basic cashflow model in lifelib.
The model is a monthly step, new business model and projects insurance cashflows of a sample model point. The modeled product is a levelpremium plain term product with no surrender value. The projected cashflows are premiums, claims, expenses and commissions. The assumptions used are mortality rates, lapse rates, discount rates, expense, inflation and commission rates. The present values of the cashflows are also calculated. The premium amount for each individual model point is calculated as the net premium with loadings, where the net premium is calculated from the present value of the claims.
Basic Usage¶
Reading the model¶
Create your copy of the basiclife library by following the steps on the Quick Start page. The model is saved as the folder named BasicTerm_S in the copied folder.
To read the model from Spyder, rightclick on the empty space in MxExplorer, and select Read Model. Click the folder icon on the dialog box and select the BasicTerm_S folder.
Getting the results¶
By default, the model has Cells
for outputting projection results as listed in the
Results section.
result_cf()
outputs cashflows of the selected model point,
and result_pv()
outputs the present values of the cashflows.
Both Cells outputs the results as pandas DataFrame.
See the Quick Start page for how to get the results in an MxConsole and view the results in MxDataViewer.
Changing the model point¶
The model point to be selected is determined by
point_id
in Projection
.
It is 1
by default.
model_point_table
contains all the 10,000 sample model points
as a pandas DataFrame.
To change the model point to another one, set the other model point’s ID
to point_id
. Setting the new point_id
clears
all the values of Cells that are specific to the previous model point.
Getting multiple results¶
The Projection
space
is parameterized with point_id
,
i.e. the Projection space can have dynamic child spaces, such as
Projection[1]
, Projection[2]
, Projection[3]
…, each of which
represents the Projection for each of the model points.
Note
Getting results for too many dynamic child spaces
takes a considerable amount of time.
The default BasicTerm_S model would take more than a minute
for 1000 model points on an ordinary spec PC.
To calculate for many model points,
consider using the BasicTerm_M
model.
Model Specifications¶
The BasicTerm_S model has only one UserSpace,
named Projection
,
and all the Cells and References are defined in the space.
The Projection Space¶
The main Space in the BasicTerm_S
model.
Projection
is the only Space defined
in the BasicTerm_S
model, and it contains
all the logic and data used in the model.
Parameters and References
(In all the sample code below,
the global variable Projection
refers to the
Projection
Space.)
 point_id¶
The ID of the selected model point.
point_id
is defined as a Reference, and its value is used for determining the selected model point. By default,1
is assigned. To select another model point, assign its model point ID to it:>>> Projection.point_id = 2
point_id
is also defined as the parameter of theProjection
Space, which makes it possible to create dynamic child space for multiple model points:>>> Projection.parameters ('point_id',) >>> Projection[1] <ItemSpace BasicTerm_S.Projection[1]> >>> Projection[2] <ItemSpace BasicTerm_S.Projection[2]>
See also
 model_point_table¶
All model point data as a DataFrame. The sample model point data was generated by generate_model_points.ipynb included in the library. The DataFrame has an index named
point_id
, andmodel_point()
returns a record as a Series whose index value matchespoint_id
. The DataFrame has columns labeledage_at_entry
,sex
,policy_term
,policy_count
andsum_assured
. Cells defined inProjection
with the same names as these columns return the corresponding column’s values for the selected model point. (policy_count
is not used by default.)>>> Projection.model_poit_table age_at_entry sex policy_term policy_count sum_assured point_id 1 47 M 10 1 622000 2 29 M 20 1 752000 3 51 F 10 1 799000 4 32 F 20 1 422000 5 28 M 15 1 605000 ... .. ... ... ... 9996 47 M 20 1 827000 9997 30 M 15 1 826000 9998 45 F 20 1 783000 9999 39 M 20 1 302000 10000 22 F 15 1 576000 [10000 rows x 5 columns]
The DataFrame is saved in the Excel file model_point_table.xlsx placed in the model folder.
model_point_table
is created by Projection’s new_pandas method, so that the DataFrame is saved in the separate file. The DataFrame has the injected attribute of_mx_dataclident
:>>> Projection.model_point_table._mx_dataclient <PandasData path='model_point_table.xlsx' filetype='excel'>
 disc_rate_ann¶
Annual discount rates by duration as a pandas Series.
>>> Projection.disc_rate_ann year 0 0.00000 1 0.00555 2 0.00684 3 0.00788 4 0.00866 146 0.03025 147 0.03033 148 0.03041 149 0.03049 150 0.03056 Name: disc_rate_ann, Length: 151, dtype: float64
The Series is saved in the Excel file disc_rate_ann.xlsx placed in the model folder.
disc_rate_ann
is created by Projection’s new_pandas method, so that the Series is saved in the separate file. The Series has the injected attribute of_mx_dataclident
:>>> Projection.disc_rate_ann._mx_dataclient <PandasData path='disc_rate_ann.xlsx' filetype='excel'>
See also
 mort_table¶
Mortality table by age and duration as a DataFrame. See basic_term_sample.xlsx included in this library for how the sample mortality rates are created.
>>> Projection.mort_table 0 1 2 3 4 5 Age 18 0.000231 0.000254 0.000280 0.000308 0.000338 0.000372 19 0.000235 0.000259 0.000285 0.000313 0.000345 0.000379 20 0.000240 0.000264 0.000290 0.000319 0.000351 0.000386 21 0.000245 0.000269 0.000296 0.000326 0.000359 0.000394 22 0.000250 0.000275 0.000303 0.000333 0.000367 0.000403 .. ... ... ... ... ... ... 116 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 117 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 118 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 119 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 120 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 [103 rows x 6 columns]
The DataFrame is saved in the Excel file mort_table.xlsx placed in the model folder.
mort_table
is created by Projection’s new_pandas method, so that the DataFrame is saved in the separate file. The DataFrame has the injected attribute of_mx_dataclident
:>>> Projection.mort_table._mx_dataclient <PandasData path='mort_table.xlsx' filetype='excel'>
See also
Projection parameters¶
This is a new business model and all model points are issued at time 0.
The time step of the model is monthly. Cashflows and other timedependent
variables are indexed with t
.
Cashflows and other flows that accumulate throughout a period
indexed with t
denote the sums of the flows from t
til t+1
.
Balance items indexed with t
denote the amount at t
.

Projection length in months 
Model point data¶
The model point data is stored in an Excel file named model_point_table.xlsx under the model folder.
The selected model point as a Series 


The sex of the selected model point 
The sum assured of the selected model point 

The policy term of the selected model point. 


The attained age at time t. 
The age at entry of the selected model point 


Duration in force in years 
Assumptions¶
The mortality table is stored in an Excel file named mort_table.xlsx
under the model folder, and is read into mort_table
as a DataFrame.
mort_rate()
looks up mort_table
and picks up
the annual mortality rate to be applied for the selected
model point at time t
.
mort_rate_mth()
converts mort_rate()
to the monthly mortality
rate to be applied during the month starting at time t
.
The discount rate data is stored in an Excel file named disc_rate_ann.xlsx
under the model folder, and is read into disc_rate_ann
as a Series.
The lapse by duration is defined by a formula in lapse_rate()
.
expense_acq()
holds the acquisition expense per policy at t=0.
expense_maint()
holds the maintenance expense per policy per annum.
The maintenance expense inflates at a constant rate
of inflation given as inflation_rate()
.

Mortality rate to be applied at time t 
Monthly mortality rate to be applied at time t 

Discount factors. 

Monthly discount rate 


Lapse rate 
Acquisition expense per policy 

Annual maintenance expense per policy 

The inflation factor at time t 

Inflation rate 
Policy values¶
By default, the amount of death benefit for each policy (claim_pp()
)
is set equal to sum_assured
.
The payment method is monthly whole term payment for all model points.
The monthly premium per policy (premium_pp()
)
is calculated for each policy
as (1 + loading_prem()
) times net_premium_pp()
.
The net premium is calculated so that the present value of the
net premiums equates to the present values of claims.
This product is assumed to have no surrender value.

Claim per policy 
Net premium per policy 

Loading per premium 

Monthly premium per policy 
Policy decrement¶
The initial number of policies is set to 1 per model point by default, and decreases through out the policy term by lapse and death. At the end of the policy term the remaining number of policies mature.

Number of death occurring at time t 

Number of policies inforce 
Initial Number of Policies Inforce 


Number of lapse occurring at time t 
Number of maturing policies 
Cashflows¶
An acquisition expense at t=0 and maintenance expenses thereafter comprise expense cashflows.
Commissions are assumed to be paid out during the first year and the commission amount is assumed to be 100% premium during the first year and 0 afterwards.

Claims 

Commissions 

Premium income 

Acquisition and maintenance expenses 

Net cashflow 
Present values¶
The Cells whose names start with pv_
are for calculating
the present values of the cashflows indicated by the rest of their names.
pols_if()
is not a cashflow, but used as an annuity factor
in calculating net_premium_pp()
.
Present value of claims 

Present value of commissions 

Present value of expenses 

Present value of net cashflows. 

Present value of policies inforce 

Present value of premiums 

Check present value summation 
Results¶
result_cf()
outputs the cashflows of the selected model point
as a DataFrame:
>>> result_cf()
Premiums Claims ... Policies Death Policies Exits
0 94.840000 34.180793 ... 0.000055 0.008742
1 94.005734 33.880120 ... 0.000054 0.008665
2 93.178806 33.582091 ... 0.000054 0.008588
3 92.359153 33.286684 ... 0.000054 0.008513
4 91.546710 32.993876 ... 0.000053 0.008438
.. ... ... ... ... ...
116 62.432465 63.534771 ... 0.000102 0.001107
117 62.317757 63.418038 ... 0.000102 0.001105
118 62.203260 63.301519 ... 0.000102 0.001103
119 62.088973 63.185215 ... 0.000102 0.001101
120 0.000000 0.000000 ... 0.000000 0.000000
[121 rows x 8 columns]
result_pv()
outputs the present values of the cashflows
and also their percentages against the present value of premiums as a DataFrame:
>>> result_pv()
Premiums Claims Expenses Commissions Net Cashflow
PV 8251.931435 5501.074678 748.303591 1084.601434 917.951731
% Premium 1.000000 0.666641 0.090682 0.131436 0.111241
Result table of cashflows 

Result table of present value of cashflows 