Another demonstration that not all is right with the convex monotone implementation in QuantLib - https://imgur.com/a/ksS7OD8

convexMonotoneClassic.csv

interpolations.cpp

#include <iostream>
#include <vector>

#include <ql/math/interpolations/convexmonotoneinterpolation.hpp>
#include <ql/math/interpolations/cubicinterpolation.hpp>

using QuantLib::ConvexMonotone;
using QuantLib::Cubic;
using QuantLib::CubicInterpolation;
using QuantLib::Interpolation;

/*
interpolations >interpolations.csv
gnuplot

set datafile separator ","
set key autotitle columnhead
plot "interpolations.csv" using 1:2 with lines, \
     "interpolations.csv" using 1:3 with lines, \
     "interpolations.csv" using 1:4 with lines, \
     "convexMonotoneClassic.csv" using 1:3 with lines title "classic"
*/
int main(int argc, char** argv) {
  std::vector<std::pair<double, double>> termsAndRates = {{0.280556, -0.00318307},            //
                                                          {0.530556, -0.0026903956984000005}, //
                                                          {0.780556, -0.00214323187344},      //
                                                          {1.03889, -0.0017452071299945025},  //
                                                          {1.29167, 5.503605550280881E-4},    //
                                                          {1.54167, 0.002717478248399999},    //
                                                          {1.79444, 0.005391184238635917},    //
                                                          {2.04167, 0.007665870736439757},    //
                                                          {3.05278, 0.007744242110581442},    //
                                                          {4.06389, 0.017729991087517678},    //
                                                          {5.07778, 0.021453060571363754},    //
                                                          {6.09444, 0.02390489440875023},     //
                                                          {7.10833, 0.026754087375356297},    //
                                                          {8.12778, 0.028447902197263206},    //
                                                          {9.13889, 0.028451203745388735},    //
                                                          {10.1528, 0.029868841405055697},    //
                                                          {12.1806, 0.025411253397770967},    //
                                                          {15.225, 0.023525252364998035},     //
                                                          {20.3, 0.017342100000000006},       //
                                                          {25.375, 0.007401899999999994},     //
                                                          {30.45, 0.007900499999999987},      //
                                                          {40.5889, 0.011248767804199675},    //
                                                          {50.7361, 0.00575108261786502}};

  std::vector<double> terms;
  std::vector<double> rates;
  for (std::pair<double, double> termAndRate : termsAndRates) {
    terms.push_back(termAndRate.first);
    rates.push_back(termAndRate.second);
  }

  Interpolation krugerCubic = Cubic(CubicInterpolation::Kruger).interpolate(terms.begin(), terms.end(), rates.begin());
  Interpolation convexMonotone = ConvexMonotone(0.3, 0.7, false).interpolate(terms.begin(), terms.end(), rates.begin());
  // A setting of monotonicity = 1 and quadraticity = 0 will reproduce the basic Hagan/West method.
  Interpolation basicConvexMonotone =
      ConvexMonotone(0, 1, false).interpolate(terms.begin(), terms.end(), rates.begin());

  std::cout << "term, krugerCubic, convexMonotone, basicConvexMonotone" << '\n';
  for (double term = std::max(0.0, convexMonotone.xMin()); term <= convexMonotone.xMax(); term += 0.1) {
    std::cout << term << ", "                 //
              << krugerCubic(term) << ", "    //
              << convexMonotone(term) << ", " //
              << basicConvexMonotone(term) << '\n';
  }
}