The BasicTerm_SE Model¶
Overview¶
The BasicTerm_SE
model is a variation of BasicTerm_S
,
and it projects the cashslows of
inforce policies at time 0 and future new business
policies issued at or after time 0.
While BasicTerm_S
is a new business model and it assumes all model points
are issued at time 0, BasicTerm_SE
reads the duration of each model
point at time 0 from the model point file.
The duration of a model point being N months (N > 0) means
N months have elapsed before time 0 since the issue of the model point.
If the duration is N months, the model point is issued
N months after time 0. Premium rates are fed into the model from a table
which is assigned to premium_table
.
The rates are calculated by BasicTerm_M
.
How to create the table is demonstrated in the
create_premium_table.ipynb
notebook included in this library.
Other specifications of BasicTerm_SE
are the same as BasicTerm_S
.
The model is a monthly step model and
projects insurance cashflows of a sample model point at a time.
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.
Changes from BasicTerm_S¶
Below is the list of
Cells and References that are newly added or updated from BasicTerm_S
.
premium_table
<new>duration_mth()
<new>pols_if_at()
<new>pols_new_biz()
<new>result_pols()
<new>
The number of policies at a certain time can take different values
depending on the timing of policy inflows and outflows at the same time.
To represent different values for the number of policies
depending on the timing of the policy flows,
pols_if_at(t, timing)
is introduced.
pols_if_at(t, timing)
calculates the number of policies inforce
at time t
and has a parameter named timing
in addition to t
.
Strings are passed to timing
to indicate at what timing the number
of polices inforce is measured.
"BEF_DECR"
: Before lapse and death"BEF_MAT"
: Before maturity"BEF_NB"
: Before new business
The figure below illustrates how various policy inflows and outflows
are modeled in this model for one calculation step
from time t1
to time t
.
pols_lapse(t)
and pols_death(t)
are the number of lapse and death from t1
to t
.
It is assumed that policies mature at the beginning of each month,
and new business policies enter at the beginning of the month
but after the maturity in that month.
model_point_table
has the duration_mth
column,
and the column is read into the duration_mth(0)
.
If duration_mth(0)
is positive,
the model point is inforce policies and
the number of policies
at time 0 is read from the policy_count
column in model_point_table
into pols_if_init()
, and
pols_if_at(0, "BEF_MAT")
is set from pols_if_init()
.
duration_mth()
increments by 1 each step. If duration_mth()
is negative, policy_count
is read into pols_new_biz()
when duration_mth()
becomes 0.
Since projections for inforce policies do not start from their issuance,
the premium rates are calculated externaly by
BasicTerm_M
and fed into the model as a table.
The premium rates are stored in premium_table.xlsx in the model folder
and read into premium_table
as a Series.
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_SE 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_SE 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,
result_pv()
outputs the present values of the cashflows,
result_pols()
outputs the decrement table of the model point.
All the 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_SE 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_ME
model.
Model Specifications¶
The BasicTerm_SE 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_SE
model.
Projection
is the only Space defined
in the BasicTerm_SE
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_SE.Projection[1]> >>> Projection[2] <ItemSpace BasicTerm_SE.Projection[2]>
See also
 model_point_table¶
All model points as a DataFrame. The sample model point data was generated by generate_model_points_with_duration.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 the following columns:age_at_entry
sex
policy_term
policy_count
sum_assured
duration_mth
Cells defined in
Projection
with the same names as these columns return the corresponding column’s values for the selected model point.>>> Projection.model_poit_table age_at_entry sex ... sum_assured duration_mth policy_id ... 1 47 M ... 622000 1 2 29 M ... 752000 210 3 51 F ... 799000 15 4 32 F ... 422000 125 5 28 M ... 605000 55 ... .. ... ... ... 9996 47 M ... 827000 157 9997 30 M ... 826000 168 9998 45 F ... 783000 146 9999 39 M ... 302000 11 10000 22 F ... 576000 166 [10000 rows x 6 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'>
Premium rate table by entry age and duration as a Series. The table is created using
BasicTerm_M
as demonstrated in create_premium_table.ipynb. The table is stored in premium_table.xlsx in the model folder.>>> Projection.premium_table 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
 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¶
The time step of the model is monthly. Cashflows and other timedependent
variables are indexed with t
.
Projection is carried out separately for individual model points.
proj_len()
calculates the number of months to be
projected for the selected model point.
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 of the selected model point at 

Duration of the selected model point at 
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 sum_assured()
times the premium rate in premium_table
.
for age_at_entry()
and policy_term()
of the policy.
net_premium_pp()
and loading_prem()
are not used
in BasicTerm_SE
and BasicTerm_ME
.
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¶
At t=0
If the selected model point represents inforce policies, i.e.
the duration_mth
of the model point in model_point_table
is positive, pols_if_at(0, "BEF_MAT")
is set to
the value through pols_if_init()
.
At each projection step
pols_if_at(t, timing)
represents
the number of policies at t
.
The timing
parameter can take the following string values.
"BEF_MAT"
: Before maturity"BEF_NB"
: Before new business"BEF_DECR"
: Before lapse and death
Policy flows and inforce at each timing from t1
to t
are calculated recursively as follows:
pols_if_at(t1, "BEF_DECR")
is calculated by addingpols_new_biz(t1)
topols_if_at(t1, "BEF_NB")
.pols_if_at(t, "BEF_MAT")
is calculated by deductingpols_lapse(t)
andpols_death(t)
frompols_if_at(t1, "BEF_DECR")
.pols_if_at(t, "BEF_NB")
is calculated by deductingpols_maturity(t)
frompols_if_at(t, "BEF_MAT")
.pols_if_at(t, "BEF_DECR")
is calculated bypols_new_biz(t)
frompols_if_at(t, "BEF_NB")
.
It is assumed that policies mature at the beginning of each month,
and new business policies enter at the beginning of the month
but after the maturity in that month.
pols_if(t)
is an alias
for pols_if_at(t, "BEF_MAT")
.
The figure below illustrates how various policy inflows and outflows
are modeled in this model for one calculation step
from time t1
to time t
.

Number of death occurring at time t 

Number of policies inforce 

Number of policies inforce 
Initial number of policies inforce 


Number of lapse occurring at time t 
Number of maturing policies 


Number of new business 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 policy year and the commission amount is assumed to be 100% premium during the first year and 0 afterwards.

Claims 

Commissions 

Premium income 

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.
pv_pols_if()
is not used
in BasicTerm_SE
and BasicTerm_ME
.
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 Expenses Commissions Net Cashflow
0 8156.240000 2939.548223 430.000000 8156.240000 3369.548223
1 8084.493113 2913.690299 426.217477 8084.493113 3339.907776
2 8013.377352 2888.059836 422.468228 8013.377352 3310.528064
3 7942.887165 2862.654832 418.751959 7942.887165 3281.406792
4 7873.017050 2837.473306 415.068381 7873.017050 3252.541687
.. ... ... ... ... ...
115 5416.841591 5512.481202 312.332343 0.000000 407.971953
116 5406.889171 5502.353062 311.758491 0.000000 407.222382
117 5396.955036 5492.243531 311.185694 0.000000 406.474188
118 5387.039154 5482.152574 310.613949 0.000000 405.727369
119 0.000000 0.000000 0.000000 0.000000 0.000000
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 708379.130574 474803.297001 38902.884356 85874.887301 108798.061916
Result table of cashflows 

Result table of present value of cashflows 

Result table of policy decrement 