.. module:: basiclife.BasicTerm_SE The **BasicTerm_SE** Model ========================== .. py:currentmodule:: basiclife.BasicTerm_SE.Projection Overview ----------- The :mod:`~basiclife.BasicTerm_SE` model is a variation of :mod:`~basiclife.BasicTerm_S`, and it projects the cashslows of in-force policies at time 0 and future new business policies issued at or after time 0. While :mod:`~basiclife.BasicTerm_S` is a new business model and it assumes all model points are issued at time 0, :mod:`~basiclife.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 :attr:`premium_table`. The rates are calculated by :mod:`~basiclife.BasicTerm_M`. How to create the table is demonstrated in the :doc:`create_premium_table.ipynb ` notebook included in this library. Other specifications of :mod:`~basiclife.BasicTerm_SE` are the same as :mod:`~basiclife.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 level-premium 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 :mod:`~basiclife.BasicTerm_S`. * :attr:`model_point_table` * :attr:`premium_table` * :func:`duration` * :func:`duration_mth` * :func:`expenses` * :func:`pols_death` * :func:`pols_if` * :func:`pols_if_at` * :func:`pols_if_init` * :func:`pols_lapse` * :func:`pols_maturity` * :func:`pols_new_biz` * :func:`premiums` * :func:`premium_pp` * :func:`proj_len` * :func:`result_pols` 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, :func:`pols_if_at(t, timing)` is introduced. :func:`pols_if_at(t, timing)` calculates the number of policies in-force 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 in-force 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 ``t-1`` to time ``t``. :func:`pols_lapse(t)` and :func:`pols_death(t)` are the number of lapse and death from ``t-1`` 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. .. figure:: /images/libraries/pols_if_at_illustration.png :attr:`model_point_table` has the ``duration_mth`` column, and the column is read into the :func:`duration_mth(0)`. If :func:`duration_mth(0)` is positive, the model point is in-force policies and the number of policies at time 0 is read from the ``policy_count`` column in :attr:`model_point_table` into :func:`pols_if_init`, and :func:`pols_if_at(0, "BEF_MAT")` is set from :func:`pols_if_init`. :func:`duration_mth` increments by 1 each step. If :func:`duration_mth` is negative, ``policy_count`` is read into :func:`pols_new_biz` when :func:`duration_mth` becomes 0. Since projections for in-force policies do not start from their issuance, the premium rates are calculated externaly by :mod:`~basiclife.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 :attr:`premium_table` as a Series. Basic Usage ----------- Reading the model ^^^^^^^^^^^^^^^^^ Create your copy of the *basiclife* library by following the steps on the :doc:`/quickstart/index` page. The model is saved as the folder named *BasicTerm_SE* in the copied folder. To read the model from Spyder, right-click 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 :ref:`basicterm_se-results` section. :func:`result_cf` outputs cashflows of the selected model point, :func:`result_pv` outputs the present values of the cashflows, :func:`result_pols` outputs the decrement table of the model point. All the Cells outputs the results as pandas DataFrame. See the :doc:`/quickstart/index` 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 :attr:`point_id` in :mod:`~basiclife.BasicTerm_SE.Projection`. It is ``1`` by default. :attr:`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 :attr:`point_id`. Setting the new :attr:`point_id` clears all the values of Cells that are specific to the previous model point. Getting multiple results ^^^^^^^^^^^^^^^^^^^^^^^^ The :mod:`~basiclife.BasicTerm_SE.Projection` space is parameterized with :attr:`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. .. figure:: /images/libraries/basiclife/BasicTerm_SE/diagram1.png .. 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 :mod:`~basiclife.BasicTerm_ME` model. Model Specifications --------------------- The *BasicTerm_SE* model has only one UserSpace, named :mod:`~basiclife.BasicTerm_SE.Projection`, and all the Cells and References are defined in the space. The Projection Space ^^^^^^^^^^^^^^^^^^^^ .. automodule:: basiclife.BasicTerm_SE.Projection Projection parameters ^^^^^^^^^^^^^^^^^^^^^ The time step of the model is monthly. Cashflows and other time-dependent variables are indexed with ``t``. Projection is carried out separately for individual model points. :func:`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``. .. autosummary:: :toctree: ../generated/ :template: mxbase.rst ~proj_len Model point data ^^^^^^^^^^^^^^^^^^ The model point data is stored in an Excel file named *model_point_table.xlsx* under the model folder. .. autosummary:: :toctree: ../generated/ :template: mxbase.rst ~model_point ~sex ~sum_assured ~policy_term ~age ~age_at_entry ~duration ~duration_mth Assumptions ^^^^^^^^^^^^^^^^^^ The mortality table is stored in an Excel file named *mort_table.xlsx* under the model folder, and is read into :attr:`mort_table` as a DataFrame. :func:`mort_rate` looks up :attr:`mort_table` and picks up the annual mortality rate to be applied for the selected model point at time ``t``. :func:`mort_rate_mth` converts :func:`mort_rate` to the monthly mortality rate to be applied during the month starting at time ``t``. .. figure:: /images/libraries/basiclife/BasicTerm_SE/diagram2.png The discount rate data is stored in an Excel file named *disc_rate_ann.xlsx* under the model folder, and is read into :attr:`disc_rate_ann` as a Series. .. figure:: /images/libraries/basiclife/BasicTerm_SE/diagram3.png The lapse by duration is defined by a formula in :func:`lapse_rate`. :func:`expense_acq` holds the acquisition expense per policy at `t=0`. :func:`expense_maint` holds the maintenance expense per policy per annum. The maintenance expense inflates at a constant rate of inflation given as :func:`inflation_rate`. .. autosummary:: :toctree: ../generated/ :template: mxbase.rst ~mort_rate ~mort_rate_mth ~disc_factors ~disc_rate_mth ~lapse_rate ~expense_acq ~expense_maint ~inflation_factor ~inflation_rate Policy values ^^^^^^^^^^^^^^^^^^ By default, the amount of death benefit for each policy (:func:`claim_pp`) is set equal to :attr:`sum_assured`. The payment method is monthly whole term payment for all model points. The monthly premium per policy (:func:`premium_pp`) is calculated for each policy as :func:`sum_assured` times the premium rate in :attr:`premium_table`. for :func:`age_at_entry` and :func:`policy_term` of the policy. :func:`net_premium_pp` and :func:`loading_prem` are not used in :mod:`~basiclife.BasicTerm_SE` and :mod:`~basiclife.BasicTerm_ME`. This product is assumed to have no surrender value. .. autosummary:: :toctree: ../generated/ :template: mxbase.rst ~claim_pp ~net_premium_pp ~loading_prem ~premium_pp Policy decrement ^^^^^^^^^^^^^^^^^^ .. rubric:: At ``t=0`` If the selected model point represents in-force policies, i.e. the ``duration_mth`` of the model point in :attr:`model_point_table` is positive, :func:`pols_if_at(0, "BEF_MAT")` is set to the value through :func:`pols_if_init`. .. rubric:: At each projection step :func:`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 in-force at each timing from ``t-1`` to ``t`` are calculated recursively as follows: * :func:`pols_if_at(t-1, "BEF_DECR")` is calculated by adding :func:`pols_new_biz(t-1)` to :func:`pols_if_at(t-1, "BEF_NB")`. * :func:`pols_if_at(t, "BEF_MAT")` is calculated by deducting :func:`pols_lapse(t)` and :func:`pols_death(t)` from :func:`pols_if_at(t-1, "BEF_DECR")`. * :func:`pols_if_at(t, "BEF_NB")` is calculated by deducting :func:`pols_maturity(t)` from :func:`pols_if_at(t, "BEF_MAT")`. * :func:`pols_if_at(t, "BEF_DECR")` is calculated by :func:`pols_new_biz(t)` from :func:`pols_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. :func:`pols_if(t)` is an alias for :func:`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 ``t-1`` to time ``t``. .. figure:: /images/libraries/pols_if_at_illustration.png .. autosummary:: :toctree: ../generated/ :template: mxbase.rst ~pols_death ~pols_if ~pols_if_at ~pols_if_init ~pols_lapse ~pols_maturity ~pols_new_biz 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. .. autosummary:: :toctree: ../generated/ :template: mxbase.rst ~claims ~commissions ~premiums ~expenses ~net_cf 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. :func:`pv_pols_if` is not used in :mod:`~basiclife.BasicTerm_SE` and :mod:`~basiclife.BasicTerm_ME`. .. autosummary:: :toctree: ../generated/ :template: mxbase.rst ~pv_claims ~pv_commissions ~pv_expenses ~pv_net_cf ~pv_pols_if ~pv_premiums ~check_pv_net_cf .. _basicterm_se-results: Results ^^^^^^^^^^^^^^^^^^ :func:`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 :func:`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 .. autosummary:: :toctree: ../generated/ :template: mxbase.rst ~result_cf ~result_pv ~result_pols