// 4.4.js
// 2024-09-25
// $Id: 4.4.js 1.1 2024/11/01 22:01:26 s Exp $

'use strict'
const math = require("./math.js"); // https://mathjs.org
// An extensive math library for JavaScript and Node.js

//# input
const face_value  = 1000
const coupon_rate = [6 + 5/8, 9 + 1/8, 7 + 7/8,  8 + 1/4, 8 + 1/4, 
                     8 + 3/8, 8,       8 + 3/4,  6 + 7/8, 8 + 7/8, 
                     6 + 7/8, 8 + 5/8, 7 + 3/4, 11 + 1/4, 8 + 1/2, 
                    10 + 1/2, 7 + 7/8, 8 + 7/8];
const ask_price = [100+ 0/32, 100+22/32, 100+24/32, 101+1/32, 101+ 7/32, 
                   101+12/32, 100+26/32, 102+ 1/32,  98+5/32, 102+ 9/32, 
                    97+13/32, 101+23/32,  99+ 5/32, 109+4/32, 101+13/32, 
                   107+27/32,  99+13/32, 103+ 0/32];
const today       = new Date("2011-11-05");
const last_coupon = new Date("2011-08-15");
const next_coupon = new Date("2012-02-15");

// calculating
const coupon = coupon_rate.map(x => face_value * x / 100 / 2);
const t = [(new Date("2012-02-15") - today) /1000/60/60/24 / 365, 
           (new Date("2012-08-15") - today) /1000/60/60/24 / 365, 
           (new Date("2013-02-15") - today) /1000/60/60/24 / 365, 
           (new Date("2013-08-15") - today) /1000/60/60/24 / 365, 
           (new Date("2014-02-15") - today) /1000/60/60/24 / 365, 
           (new Date("2014-08-15") - today) /1000/60/60/24 / 365, 
           (new Date("2015-02-15") - today) /1000/60/60/24 / 365, 
           (new Date("2015-08-15") - today) /1000/60/60/24 / 365, 
           (new Date("2016-02-15") - today) /1000/60/60/24 / 365];

const number_of_days_since_last_coupon        =
      (today - last_coupon) /1000/60/60/24;  //.days
const number_of_days_in_current_coupon_period =
      (next_coupon - last_coupon) /1000/60/60/24;//.days
const accrued_interest =
    coupon.map(x =>
       number_of_days_since_last_coupon /
       number_of_days_in_current_coupon_period * x);

const  total_price =
    ask_price.map((_, i) =>
        face_value * ask_price[i] / 100 + accrued_interest[i]);

    const cf0 = [coupon[ 0]+face_value,0,0,0,0,0,0,0,0];
const cf1 = [coupon[ 1]+face_value,0,0,0,0,0,0,0,0];
const cf2 = [coupon[ 2],coupon[ 2]+face_value,0,0,0,0,0,0,0];
const cf3 = [coupon[ 3],coupon[ 3]+face_value,0,0,0,0,0,0,0];
const cf4 = [coupon[ 4],coupon[ 4],coupon[ 4]+face_value,0,0,0,0,0,0];
const cf5 = [coupon[ 5],coupon[ 5],coupon[ 5]+face_value,0,0,0,0,0,0];
const cf6 = [coupon[ 6],coupon[ 6],coupon[ 6],coupon[ 6]+face_value, 
             0,0,0,0,0];
const cf7 = [coupon[ 7],coupon[ 7],coupon[ 7],coupon[ 7]+face_value, 
             0,0,0,0,0];
const cf8 = [coupon[ 8],coupon[ 8],coupon[ 8],coupon[ 8],coupon[ 8]+ 
             face_value,0,0,0,0];
const cf9 = [coupon[ 9],coupon[ 9],coupon[ 9],coupon[ 9],coupon[ 9]+ 
             face_value,0,0,0,0];
const cf10= [coupon[10],coupon[10],coupon[10],coupon[10],coupon[10], 
             coupon[10]+face_value,0,0,0];
const cf11= [coupon[11],coupon[11],coupon[11],coupon[11],coupon[11], 
             coupon[11]+face_value,0,0,0];
const cf12= [coupon[12],coupon[12],coupon[12],coupon[12],coupon[12], 
             coupon[12],coupon[12]+face_value,0,0];
const cf13= [coupon[13],coupon[13],coupon[13],coupon[13],coupon[13], 
             coupon[13],coupon[13]+face_value,0,0];
const cf14= [coupon[14],coupon[14],coupon[14],coupon[14],coupon[14], 
             coupon[14],coupon[14],coupon[14]+face_value,0];
const cf15= [coupon[15],coupon[15],coupon[15],coupon[15],coupon[15], 
             coupon[15],coupon[15],coupon[15]+face_value,0];
const cf16= [coupon[16],coupon[16],coupon[16],coupon[16],coupon[16], 
             coupon[16],coupon[16],coupon[16],coupon[16]+face_value];
const cf17= [coupon[17],coupon[17],coupon[17],coupon[17],coupon[17], 
             coupon[17],coupon[17],coupon[17],coupon[17]+face_value];
const w1 =  [cf0,  cf1,  cf2,  cf3,  cf4,  cf5,  cf6,  cf7, cf8, cf9, 
            cf10, cf11, cf12, cf13, cf14, cf15, cf16, cf17];
const y1 =  total_price;

// least suquare method
//        [w1]{beta1} =  {y1}
// [w1]^T [w1]{beta1} =  [w1]^T {y1}
//            {beta1} = ([w1]^T [w1])^-1 [w1]^T]{y1}
const A1 = math.multiply(math.transpose(w1), w1);
const b1 = math.multiply(math.transpose(w1), y1);
const beta1 = math.lusolve(A1, b1).flat();

const d = beta1;
const r = d.map((_, i) => - Math.log(d[i]) / t[i]);
const w2 = [[0,1,2,3,4].map(x => t[0] ** x),
            [0,1,2,3,4].map(x => t[1] ** x),
            [0,1,2,3,4].map(x => t[2] ** x),
            [0,1,2,3,4].map(x => t[3] ** x),
            [0,1,2,3,4].map(x => t[4] ** x),
            [0,1,2,3,4].map(x => t[5] ** x),
            [0,1,2,3,4].map(x => t[6] ** x),
            [0,1,2,3,4].map(x => t[7] ** x),
            [0,1,2,3,4].map(x => t[8] ** x)];
const y2 = r;
const A2 = math.multiply(math.transpose(w2), w2);
const b2 = math.multiply(math.transpose(w2), y2);
const beta2 = math.lusolve(A2, b2).flat();

// output
console.log('4.4.js');
console.log('face value',  face_value);
console.log('last_coupon', last_coupon.toISOString().substring(0,10));
console.log('today      ',       today.toISOString().substring(0,10));
console.log('next coupon', next_coupon.toISOString().substring(0,10));

console.log('number_of_days_since_last_coupon= ', 
       number_of_days_since_last_coupon);
console.log('number_of_days_in_current_coupon_period= ', 
       number_of_days_in_current_coupon_period);
console.log();
console.log('i'.padStart(10),
      'a_price'.padStart(10),
       'coupon'.padStart(10),
   'a.interest'.padStart(10),
  'total_price'.padStart(10))
console.log("-".repeat(54));
for(let i = 0; i < ask_price.length; i++){
          console.log(i.toFixed(0).padStart(10),
           ask_price[i].toFixed(1).padStart(10), 
              coupon[i].toFixed(2).padStart(10),
    accrued_interest[i].toFixed(2).padStart(10), 
         total_price[i].toFixed(2).padStart(10));
}
console.log("-".repeat(54));
console.log('a_price = ask price');
console.log('a.interest = accrued interest');
console.log();

// print t
console.log('i'.padStart(10), 't'.padStart(10));
console.log('-'.repeat(21));
for(let i = 0; i < t.length; i++){
     console.log(i.toFixed(0).padStart(10),
              t[i].toFixed(3).padStart(10));
}
console.log('-'.repeat(21));console.log();

// print y1
console.log('i'.padStart(10), 'y1'.padStart(10));
console.log('-'.repeat(21));
for(let i = 0; i < y1.length; i++){
     console.log(i.toFixed(0).padStart(10),
             y1[i].toFixed(0).padStart(10));
}
console.log('-'.repeat(21));console.log();

// print w1
console.log('w1, matrix of cf(in integer) in row');
let nn = 5;
console.log( 'i'.padStart(nn), "t0".padStart(nn),
            "t1".padStart(nn), "t2".padStart(nn),
            "t3".padStart(nn), "t4".padStart(nn),
            "t5".padStart(nn), "t6".padStart(nn),
            "t7".padStart(nn), "t8".padStart(nn));
console.log("-".repeat(60));
for(let i = 0; i < w1.length; i++){
     console.log(i.toFixed(0).padStart(nn),
                 w1[i][0].toFixed(0).padStart(nn),
                 w1[i][1].toFixed(0).padStart(nn),
                 w1[i][2].toFixed(0).padStart(nn),
                 w1[i][3].toFixed(0).padStart(nn),
                 w1[i][4].toFixed(0).padStart(nn),
                 w1[i][5].toFixed(0).padStart(nn),
                 w1[i][6].toFixed(0).padStart(nn),
                 w1[i][7].toFixed(0).padStart(nn),
                 w1[i][8].toFixed(0).padStart(nn));
}
console.log("-".repeat(60));console.log();

// print beta1
console.log('estimated beta1, d(t[i])');
console.log('i'.padStart(10), 'beta1[i]'.padStart(10));
console.log('-'.repeat(20+1));
for(let i = 0; i < beta1.length; i++){
     console.log(i.toFixed(0).padStart(10),
          beta1[i].toFixed(3).padStart(10));
}
console.log('-'.repeat(20 + 1));console.log();

// print r
console.log('estimated r(t[i])');
console.log('i'.padStart(10), 'r(t[i])'.padStart(10));
console.log('-'.repeat(20 +1));
for(let i = 0; i < r.length; i++){
console.log(i.toFixed(0).padStart(10), r[i].toFixed(4).padStart(10));
}
console.log('-'.repeat(20 + 1));console.log();

// print w2
nn = 8;
console.log('w2, coefficent matrix');
console.log('i'.padStart(nn),   '1'.padStart(nn),   't'.padStart(nn),
          't^2'.padStart(nn), 't^3'.padStart(nn), 't^4'.padStart(nn));
console.log('-'.repeat(6 *(nn + 1)));
for(let i = 0; i < w2.length; i++){
    console.log(i.toFixed(0).padStart(nn),
         w2[i][0].toFixed(3).padStart(nn),
         w2[i][1].toFixed(3).padStart(nn),
         w2[i][2].toFixed(3).padStart(nn),
         w2[i][3].toFixed(3).padStart(nn),
         w2[i][4].toFixed(3).padStart(nn));
}
console.log('-'.repeat(6 * (nn + 1)));console.log();

// print beta2
console.log('beta2, estimated a[i] for r(t)');
console.log('i'.padStart(10), 'a[i]'.padStart(15));
console.log('-'.repeat(30));
for(let i = 0; i < beta2.length; i++){
     console.log(i.toFixed(0).padStart(10),
          beta2[i].toFixed(5).padStart(15));
}
console.log('-'.repeat(30));console.log();

// print r equation estimated
const a = beta2.flat();
console.log('estimated r(t)=');
console.log(a[0].toFixed(5), '+',
            a[1].toFixed(5), 't +',
            a[2].toFixed(5), 't^2 +',
            a[3].toFixed(5), 't^3 +',
            a[4].toFixed(5), 't^4');
// end