[lmi-commits] [lmi] master 09d67a8 4/7: Calculate 7PP and CVAT corridor from first principles

[Greg Chicares]

branch: master
commit 09d67a8fe33866eec676416f9e0211c5f36e8170
Author: Gregory W. Chicares <address@hidden>
Commit: Gregory W. Chicares <address@hidden>

    Calculate 7PP and CVAT corridor from first principles
    
    The unit test validates these new calculations against spreadsheets.
---
 Makefile.am                    |   3 +
 commutation_functions_test.cpp | 567 ++++++++++++++++++++++++++++++++++++++++-
 irc7702_tables.cpp             |  99 +++++++
 irc7702_tables.hpp             |  64 +++++
 objects.make                   |   2 +
 5 files changed, 734 insertions(+), 1 deletion(-)

diff --git a/Makefile.am b/Makefile.am
index fe5ae91..f1bdebe 100644
--- a/Makefile.am
+++ b/Makefile.am
@@ -411,6 +411,7 @@ liblmi_la_SOURCES = \
     ihs_irc7702a.cpp \
     ihs_mortal.cpp \
     ihs_server7702.cpp \
+    irc7702_tables.cpp \
     lmi.cpp \
     md5.cpp \
     mec_input.cpp \
@@ -632,6 +633,7 @@ test_commutation_functions_SOURCES = \
   commutation_functions.cpp \
   commutation_functions_test.cpp \
   cso_table.cpp \
+  irc7702_tables.cpp \
   timer.cpp
 test_commutation_functions_CXXFLAGS = $(AM_CXXFLAGS)
 
@@ -1241,6 +1243,7 @@ noinst_HEADERS = \
     input_sequence_parser.hpp \
     interest_rates.hpp \
     interpolate_string.hpp \
+    irc7702_tables.hpp \
     istream_to_string.hpp \
     ledger.hpp \
     ledger_base.hpp \
diff --git a/commutation_functions_test.cpp b/commutation_functions_test.cpp
index 0a435f9..58e8916 100644
--- a/commutation_functions_test.cpp
+++ b/commutation_functions_test.cpp
@@ -25,13 +25,16 @@
 
 #include "cso_table.hpp"
 #include "et_vector.hpp"
+#include "irc7702_tables.hpp"
+#include "materially_equal.hpp"
 #include "math_functions.hpp"
 #include "ssize_lmi.hpp"
 #include "test_tools.hpp"
 #include "timer.hpp"
 
 #include <algorithm>
-#include <cmath>                        // fabs()
+#include <cfloat>                       // DBL_EPSILON
+#include <cmath>                        // fabs(), log()
 #include <functional>                   // bind()
 #include <iomanip>                      // setw() etc.
 #include <ios>                          // ios_base::fixed()
@@ -709,6 +712,567 @@ void Test_1980_CSO_Male_ANB()
         ;
 }
 
+// These two arrays are pasted from the "corridor mult" and "7Pt"
+// columns of 'validate_2001cso', after loading that spreadsheet
+// in 'gnumeric' and formatting those columns to twenty decimals.
+// They use UL commutation functions. See:
+//   https://lists.nongnu.org/archive/html/lmi/2015-07/msg00004.html
+
+static double const ss_ul_corr[100] =
+{16.05428685334679173025
+,15.58833599045649087600
+,15.08131070200895074152
+,14.56342500447235721595
+,14.04800434985640045227
+,13.54397833171609022429
+,13.05507387234714933300
+,12.58409661481673680328
+,12.13030984655223143420
+,11.69174091577074925397
+,11.26914166185736476677
+,10.86078105527353621085
+,10.47029884268147448267
+,10.09843359081480329564
+, 9.74294658529263379876
+, 9.40759852219825454256
+, 9.09057733647785148889
+, 8.79027993284445763322
+, 8.50397918973384925323
+, 8.22818279387080941945
+, 7.96118932260834633041
+, 7.70160265863622406357
+, 7.44976553796342688685
+, 7.20499258154732391546
+, 6.96714059909527883008
+, 6.73646229302490073820
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+, 5.68759233818214315903
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+, 5.30831030469870679411
+, 5.12719475896684162564
+, 4.95191511278486373726
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+, 4.16231281496283944676
+, 4.02117206738939625410
+, 3.88525584688570946312
+, 3.75459497560775545821
+, 3.62916166404261142375
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+, 2.78925893311157580001
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+, 2.31641149864538897774
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+, 2.18485859704871998588
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+, 1.67882810972211782286
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+, 1.23349050718607222699
+, 1.21741784864651991782
+, 1.20250900968492024923
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+, 1.16443752080775975166
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+, 1.11805918549405669538
+, 1.10585007755591901990
+, 1.09272887195287826678
+, 1.07768889207696427768
+, 1.05889467902677236744
+, 1.03392745267212093907
+};
+
+static double const ss_ul_7pp[100] =
+{0.00999062440751989980
+,0.01028589716601673552
+,0.01062994889232243140
+,0.01100709650196978612
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+,0.35965728769722676850
+,0.42686340219691948361
+,0.56031960772985123231
+,0.96718584791956385693
+};
+
+static double const ss_ol_corr[100] =
+{16.03069515721970
+,15.56545542916450
+,15.05919070490880
+,14.54207568908480
+,14.02741865395940
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+, 8.77746677844702
+, 8.49159356632208
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+, 5.87699437244831
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+, 4.01541830136802
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+, 1.09224812150223
+, 1.07730439700387
+, 1.05861825755067
+, 1.03377932830447
+};
+
+static double const ss_ol_7pp[100] =
+{0.010005327186958
+,0.010301016999909
+,0.010645562907928
+,0.011023256091546
+,0.011427447066149
+,0.011852778725528
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+,0.359815590009435
+,0.427015751779345
+,0.560465915779944
+,0.967324430485689
+};
+
+/// Test CVAT corridor and seven-pay premium.
+
+void Test_Corridor_and_7PP()
+{
+    std::vector<double> const naar_discount
+        (100
+        ,i_upper_12_over_12_from_i<double>()(0.04)
+        );
+    irc7702_tables z
+        (oe_2001cso
+        ,oe_orthodox
+        ,oe_age_last_birthday
+        ,mce_unisex
+        ,mce_unismoke
+        ,naar_discount
+        ,1.0 / 12.0
+        ,0
+        ,100
+        );
+    std::vector<double> const& ul_corr = z.ul_corr();
+    std::vector<double> const& ul_7pp  = z.ul_7pp ();
+    std::vector<double> const& ol_corr = z.ol_corr();
+    std::vector<double> const& ol_7pp  = z.ol_7pp ();
+
+    // In the last year, the OL formula reduces to:
+    //   NSP[omega-1] = vq * (i/delta) + vp
+    //   (0.30285 / 1.04) * (0.04 / ln(1.04)) + (1 - 0.30285) / 1.04
+    BOOST_TEST(materially_equal(0.30285, z.q_[99], 0.0));
+    double ol_nsp99 =
+          (       z.q_[99]  / 1.04) * (0.04 / std::log(1.04))
+        +  (1.0 - z.q_[99]) / 1.04
+        ;
+    BOOST_TEST(materially_equal(ol_corr[99], 1.0 / ol_nsp99, DBL_EPSILON));
+
+    for(int j = 0; j < lmi::ssize(ol_corr); ++j)
+        {
+        // Values calculated here must match spreadsheet values to
+        // within a minuscule tolerance.
+        BOOST_TEST(materially_equal(ss_ul_corr[j], ul_corr[j]));
+        BOOST_TEST(materially_equal(ss_ul_7pp [j], ul_7pp [j]));
+        BOOST_TEST(materially_equal(ss_ol_corr[j], ol_corr[j]));
+        BOOST_TEST(materially_equal(ss_ol_7pp [j], ol_7pp [j]));
+        // The 0.0015 tolerance was found experimentally, not by any
+        // sort of mathematical law. It represents the inherent
+        // discrepancy between the UL method on the one hand, and the
+        // OL method (with the i/delta approximation) on the other.
+        BOOST_TEST(materially_equal(   ol_corr[j], ul_corr[j], 0.0015));
+        BOOST_TEST(materially_equal(   ol_7pp [j], ul_7pp [j], 0.0015));
+        }
+
+    // At least for now, display plenty of detail.
+
+    std::cout << std::endl;
+
+    std::cout
+        << ol_corr[99] << " OL corr[omega-1]\n"
+        << 1.0 / ol_nsp99 << " vq * (i/delta) + vp\n"
+        << std::endl
+        ;
+
+    std::cout << "q, UL corr, UL 7pp, OL corr, OL 7pp\n";
+    for(int j = 0; j < lmi::ssize(ol_corr); ++j)
+        {
+        std::cout
+            << j
+            << '\t' << z.q_[j]
+            << '\t' << ul_corr[j]
+            << '\t' << ul_7pp[j]
+            << '\t' << ol_corr[j]
+            << '\t' << ol_7pp[j]
+            << '\n';
+        }
+    std::cout << std::endl;
+
+    std::vector<double> q12(lmi::ssize(ol_corr));
+    assign(q12, apply_binary(coi_rate_from_q<double>(), z.q_, 1.0 / 12.0));
+    std::cout << "q, q upper (12), UL corr, UL 7pp\n";
+    for(int j = 0; j < lmi::ssize(ul_corr); ++j)
+        {
+        std::cout
+            << j
+            << '\t' << z.q_[j]
+            << '\t' << q12[j]
+            << '\t' << ul_corr[j]
+            << '\t' << ul_7pp[j]
+            << '\n';
+        }
+    std::cout << std::endl;
+
+    std::cout << "UL corr, OL corr, relative error\n";
+    for(int j = 0; j < lmi::ssize(ul_corr); ++j)
+        {
+        std::cout
+            << j
+            << '\t' << ul_corr[j]
+            << '\t' << ol_corr[j]
+            << '\t' << (ol_corr[j] - ul_corr[j]) / ul_corr[j]
+            << '\n';
+        }
+    std::cout << std::endl;
+
+    std::cout << "UL 7pp, OL 7pp, relative error\n";
+    for(int j = 0; j < lmi::ssize(ul_corr); ++j)
+        {
+        std::cout
+            << j
+            << '\t' << ul_7pp[j]
+            << '\t' << ol_7pp[j]
+            << '\t' << (ol_7pp[j] - ul_7pp[j]) / ul_7pp[j]
+            << '\n';
+        }
+    std::cout << std::endl;
+
+    std::cout << "UL corr, 7pp: {calculated, spreadsheet, relative error}\n";
+    for(int j = 0; j < lmi::ssize(ss_ul_corr); ++j)
+        {
+        std::cout
+            << j
+            << '\t' << ul_corr[j]
+            << '\t' << ss_ul_corr[j]
+            << '\t' << (ss_ul_corr[j] - ul_corr[j]) / ul_corr[j]
+            << '\t' << ul_7pp[j]
+            << '\t' << ss_ul_7pp[j]
+            << '\t' << (ss_ul_7pp[j] - ul_7pp[j]) / ul_7pp[j]
+            << '\n';
+        }
+    std::cout << std::endl;
+
+    std::cout << "OL corr, 7pp: {calculated, spreadsheet, relative error}\n";
+    for(int j = 0; j < lmi::ssize(ss_ul_corr); ++j)
+        {
+        std::cout
+            << j
+            << '\t' << ol_corr[j]
+            << '\t' << ss_ol_corr[j]
+            << '\t' << (ss_ol_corr[j] - ol_corr[j]) / ol_corr[j]
+            << '\t' << ol_7pp[j]
+            << '\t' << ss_ol_7pp[j]
+            << '\t' << (ss_ol_7pp[j] - ol_7pp[j]) / ol_7pp[j]
+            << '\n';
+        }
+}
+
 /// Test UL commutation functions in extreme cases.
 ///
 /// For example, ic and ig can both be zero, and qc may round to zero
@@ -727,6 +1291,7 @@ int test_main(int, char*[])
     ULCommFnsTest();
     OLCommFnsTest();
     Test_1980_CSO_Male_ANB();
+    Test_Corridor_and_7PP();
     TestLimits();
 
     return EXIT_SUCCESS;
diff --git a/irc7702_tables.cpp b/irc7702_tables.cpp
new file mode 100644
index 0000000..40ddf3e
--- /dev/null
+++ b/irc7702_tables.cpp
@@ -0,0 +1,99 @@
+// 7PP and CVAT corridor from first principles.
+//
+// Copyright (C) 2019 Gregory W. Chicares.
+//
+// This program is free software; you can redistribute it and/or modify
+// it under the terms of the GNU General Public License version 2 as
+// published by the Free Software Foundation.
+//
+// This program is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU General Public License
+// along with this program; if not, write to the Free Software Foundation,
+// Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA
+//
+// http://savannah.nongnu.org/projects/lmi
+// email: <address@hidden>
+// snail: Chicares, 186 Belle Woods Drive, Glastonbury CT 06033, USA
+
+#include "pchfile.hpp"
+
+#include "irc7702_tables.hpp"
+
+#include "commutation_functions.hpp"
+#include "cso_table.hpp"
+#include "et_vector.hpp"
+#include "math_functions.hpp"
+#include "ssize_lmi.hpp"
+
+#include <cmath>                        // log()
+
+irc7702_tables::irc7702_tables
+    (oenum_cso_era              cso_era
+    ,oenum_autopisty            autopisty
+    ,oenum_alb_or_anb           alb_or_anb
+    ,mcenum_gender              gender
+    ,mcenum_smoking             smoking
+    ,std::vector<double> const& naar_discount
+    ,double                     max_coi_rate
+    ,int                        min_age
+    ,int                        max_age
+    )
+    :q_       {cso_table(cso_era, autopisty, alb_or_anb, gender, smoking, 
min_age, max_age)}
+    ,length_  {lmi::ssize(q_)}
+    // Initialize to proper length to support PETE usage below:
+    ,ul_corr_ (length_)
+    ,ul_7pp_  (length_)
+    ,ol_corr_ (length_)
+    ,ol_7pp_  (length_)
+{
+    std::vector<double> q12(length_);
+    assign(q12, apply_binary(coi_rate_from_q<double>(), q_, max_coi_rate));
+
+    // ic: 0.04 is the statutory rate.
+    // ig: Argument 'naar_discount' corresponds to DB_NaarDiscount,
+    //   which is assumed to be rounded appropriately if at all.
+    std::vector<double> const ic
+        (length_
+        ,i_upper_12_over_12_from_i<double>()(0.04)
+        );
+    std::vector<double> const& ig(naar_discount);
+
+    ULCommFns const ulcf(q12, ic, ig, mce_option1_for_7702, mce_monthly);
+
+    ul_corr_ += ulcf.aD() / (ulcf.aDomega() + ulcf.kM());
+
+    // 'E' is the shift operator, so E(7) f(x) = f(x+7).
+    std::vector<double> E7aN(ulcf.aN());
+    E7aN.insert(E7aN.end(), 7, 0.0);
+    E7aN.erase(E7aN.begin(), 7 + E7aN.begin());
+    ul_7pp_ += (ulcf.aDomega() + ulcf.kM()) / (ulcf.aN() - E7aN);
+
+    double const i_over_delta = 0.04 / std::log(1.04);
+    std::vector<double> const i(length_, 0.04);
+    OLCommFns const olcf(q_, i);
+
+    // Alternative calculations that may be useful someday are given
+    // in comments.
+
+    // reciprocal of (Mx - Momega-1) / Dx
+    ol_corr_ +=
+          olcf.D()
+//      / ((olcf.M() - olcf.M().back()) * i_over_delta + olcf.Domega())
+        / ((olcf.M()                  ) * i_over_delta + olcf.Domega())
+        ;
+
+    // (Mx - Momega-1 + Domega-1) / (Nx - Nx+7)
+    std::vector<double> E7N(olcf.N());
+    E7N.insert(E7N.end(), 7, 0.0);
+    E7N.erase(E7N.begin(), 7 + E7N.begin());
+    ol_7pp_ +=
+//        ((olcf.M() - olcf.M().back()) * i_over_delta + olcf.Domega())
+//        ((olcf.M() - olcf.M().back())                + olcf.Domega())
+          ((olcf.M()                  ) * i_over_delta + olcf.Domega())
+        / (olcf.N() - E7N)
+        ;
+}
diff --git a/irc7702_tables.hpp b/irc7702_tables.hpp
new file mode 100644
index 0000000..661593a
--- /dev/null
+++ b/irc7702_tables.hpp
@@ -0,0 +1,64 @@
+// 7PP and CVAT corridor from first principles.
+//
+// Copyright (C) 2019 Gregory W. Chicares.
+//
+// This program is free software; you can redistribute it and/or modify
+// it under the terms of the GNU General Public License version 2 as
+// published by the Free Software Foundation.
+//
+// This program is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU General Public License
+// along with this program; if not, write to the Free Software Foundation,
+// Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA
+//
+// http://savannah.nongnu.org/projects/lmi
+// email: <address@hidden>
+// snail: Chicares, 186 Belle Woods Drive, Glastonbury CT 06033, USA
+
+#ifndef irc7702_tables_hpp
+#define irc7702_tables_hpp
+
+#include "config.hpp"
+
+#include "mc_enum_types.hpp"
+#include "oecumenic_enumerations.hpp"
+#include "so_attributes.hpp"
+
+#include <vector>
+
+class LMI_SO irc7702_tables final
+{
+    friend void Test_Corridor_and_7PP();
+
+  public:
+    irc7702_tables
+        (oenum_cso_era
+        ,oenum_autopisty
+        ,oenum_alb_or_anb
+        ,mcenum_gender
+        ,mcenum_smoking
+        ,std::vector<double> const& naar_discount
+        ,double                     max_coi_rate
+        // Potentially defaultable.
+        ,int                        min_age
+        ,int                        max_age
+        );
+    std::vector<double> const& ul_corr() {return ul_corr_;}
+    std::vector<double> const& ul_7pp () {return ul_7pp_ ;}
+    std::vector<double> const& ol_corr() {return ol_corr_;}
+    std::vector<double> const& ol_7pp () {return ol_7pp_ ;}
+
+  private:
+    std::vector<double> const q_       {};
+    int                 const length_  {};
+    std::vector<double>       ul_corr_ {};
+    std::vector<double>       ul_7pp_  {};
+    std::vector<double>       ol_corr_ {};
+    std::vector<double>       ol_7pp_  {};
+};
+
+#endif // irc7702_tables_hpp
diff --git a/objects.make b/objects.make
index 05c045c..19574bd 100644
--- a/objects.make
+++ b/objects.make
@@ -295,6 +295,7 @@ lmi_common_objects := \
   ihs_irc7702a.o \
   ihs_mortal.o \
   ihs_server7702.o \
+  irc7702_tables.o \
   lmi.o \
   md5.o \
   mec_input.o \
@@ -564,6 +565,7 @@ commutation_functions_test$(EXEEXT): \
   commutation_functions.o \
   commutation_functions_test.o \
   cso_table.o \
+  irc7702_tables.o \
   timer.o \
 
 configurable_settings_test$(EXEEXT): \