TD_CEA1_Python_Provisions_v3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TD CEA 1 - Autres provisions techniques : initiation à Python\n",
    "## 3 Octobre 2019\n",
    "\n",
    "### Préliminaires\n",
    "Ce document est ce que l'on appelle un \"Notebook\". Il s'agit d'un format un peu particulier qui permet de combiner à la fois du texte et des morceaux de code, contenus dans des cellules, qui peuvent s'exécuter les unes à la suite des autres. Il est possible de faire apparaître dans le Notebook les résultats de l'exécution du code (chiffres, graphiques) à mesure que celui-ci est excécuté. Pour exécuter une cellule de code, on peut cliquer sur \"Exécuter\" ci-dessus, ou encore appuyer simultanément sur \"Maj\" et \"Entrée\".\n",
    "\n",
    "Ceci est rendu possible par le fait que, tout comme R ou Matlab, Python est un language interprêté. A l'inverse d'un langage compilé (p.ex. C) qui doit être lu d'un bloc pour être exécuté, un langage interprêté peut être lu au fur et à mesure de son exécution.\n",
    "\n",
    "Remarque : Le format Notebook n'est en rien obligatoire et il est aussi tout à fait possible de créer des programmes python d'un seul bloc ! De manière générale, si vous le souhaitez et si vous disposez de pas ou peu de bases en termes de programmation, vous pouvez vous reporter au tutoriel OpenClassroom suivant:\n",
    "https://openclassrooms.com/fr/courses/235344-apprenez-a-programmer-en-python\n",
    "\n",
    "## Introduction à Python\n",
    "Tout d'abord, quelques rappels ou règles de base en python.\n",
    "\n",
    "### Les variables\n",
    "Pour déclarer une variable, il suffit de la nommer et de lui assigner une valeur, par exemple, les variables a et b ci-dessous:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a=3\n",
    "b=5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut alors créer deux autres variables c et d que l'on définit comme le produit et la somme de a et b et afficher leurs valeurs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c = 15\n",
      "d = 8\n"
     ]
    }
   ],
   "source": [
    "c=a*b\n",
    "d=a+b\n",
    "\n",
    "print(\"c =\",c)\n",
    "print(\"d =\",d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vous pouvez alors remonter quelques lignes plus haut et changer la valeur de a et b, puis actualiser les calculs en exécutant les briques de code.\n",
    "L'instruction print est une fonction dont les arguments (renseignés à l'intérieur de parenthèses) sont une liste de choses à afficher à la suite sur une même ligne. \n",
    "\n",
    "Dans l'instruction print(\"c =\",c), on a demandé l'affichage de la chaine de caractères \"c =\" (entourée de guillemets pour signifier qu'il s'agit de texte), puis de c."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Les listes\n",
    "Il est possible de regrouper des variables dans des \"listes\". Une liste se présente sous la forme d'une suite d'éléments délimitée par des crochets et séparés par des virgules.\n",
    "\n",
    "On peut appeler les éléments constituant une boucle à l'aide de crochets. Le i-ème élément peut ainsi être appelé par liste[i].\n",
    "Par exemple :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 3, 5]\n",
      "1er élément: 1\n",
      "dernier élément: 5\n"
     ]
    }
   ],
   "source": [
    "liste=[1,3,5]\n",
    "print(liste)\n",
    "print(\"1er élément:\",liste[0])\n",
    "print(\"dernier élément:\",liste[2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Attention, comme dans Matlab mais contrairement à R, les listes sont indexées à partir de 0 et non à partir de 1.\n",
    "Pour récupérer le N-ième élément d'une liste, il faut donc appeler liste[N-1].\n",
    "\n",
    "On peut concaténer deux listes ensemble en utilisant l'opérateur d'addition + :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 3, 5, 'a']\n"
     ]
    }
   ],
   "source": [
    "liste=liste+[\"a\"]\n",
    "print(liste)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Python est un langage dit \"objet\". Une liste est ainsi un objet qui contient à la fois des données (les termes de la liste), mais également des méthodes. Il s'agit de fonctions qui peuvent effectuer des opérations spécifiques sur la liste. De manière générale, on accède aux méthodes en utilisant le point (.) : liste.fonction(argument de la fonction).\n",
    "\n",
    "On peut alors par exemple ajouter un élément à la liste en utilisant la fonction append: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 3, 5, 'a', 'un terme ajouté']\n"
     ]
    }
   ],
   "source": [
    "liste.append(\"un terme ajouté\")\n",
    "print(liste)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut également utiliser l'instruction \"pop\" pour supprimer. De manière générale pour voir la documentation associée à un objet et les différentes fonctions utilisables, on peut utiliser la fonction help."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on list object:\n",
      "\n",
      "class list(object)\n",
      " |  list() -> new empty list\n",
      " |  list(iterable) -> new list initialized from iterable's items\n",
      " |  \n",
      " |  Methods defined here:\n",
      " |  \n",
      " |  __add__(self, value, /)\n",
      " |      Return self+value.\n",
      " |  \n",
      " |  __contains__(self, key, /)\n",
      " |      Return key in self.\n",
      " |  \n",
      " |  __delitem__(self, key, /)\n",
      " |      Delete self[key].\n",
      " |  \n",
      " |  __eq__(self, value, /)\n",
      " |      Return self==value.\n",
      " |  \n",
      " |  __ge__(self, value, /)\n",
      " |      Return self>=value.\n",
      " |  \n",
      " |  __getattribute__(self, name, /)\n",
      " |      Return getattr(self, name).\n",
      " |  \n",
      " |  __getitem__(...)\n",
      " |      x.__getitem__(y) <==> x[y]\n",
      " |  \n",
      " |  __gt__(self, value, /)\n",
      " |      Return self>value.\n",
      " |  \n",
      " |  __iadd__(self, value, /)\n",
      " |      Implement self+=value.\n",
      " |  \n",
      " |  __imul__(self, value, /)\n",
      " |      Implement self*=value.\n",
      " |  \n",
      " |  __init__(self, /, *args, **kwargs)\n",
      " |      Initialize self.  See help(type(self)) for accurate signature.\n",
      " |  \n",
      " |  __iter__(self, /)\n",
      " |      Implement iter(self).\n",
      " |  \n",
      " |  __le__(self, value, /)\n",
      " |      Return self<=value.\n",
      " |  \n",
      " |  __len__(self, /)\n",
      " |      Return len(self).\n",
      " |  \n",
      " |  __lt__(self, value, /)\n",
      " |      Return self<value.\n",
      " |  \n",
      " |  __mul__(self, value, /)\n",
      " |      Return self*value.n\n",
      " |  \n",
      " |  __ne__(self, value, /)\n",
      " |      Return self!=value.\n",
      " |  \n",
      " |  __new__(*args, **kwargs) from builtins.type\n",
      " |      Create and return a new object.  See help(type) for accurate signature.\n",
      " |  \n",
      " |  __repr__(self, /)\n",
      " |      Return repr(self).\n",
      " |  \n",
      " |  __reversed__(...)\n",
      " |      L.__reversed__() -- return a reverse iterator over the list\n",
      " |  \n",
      " |  __rmul__(self, value, /)\n",
      " |      Return self*value.\n",
      " |  \n",
      " |  __setitem__(self, key, value, /)\n",
      " |      Set self[key] to value.\n",
      " |  \n",
      " |  __sizeof__(...)\n",
      " |      L.__sizeof__() -- size of L in memory, in bytes\n",
      " |  \n",
      " |  append(...)\n",
      " |      L.append(object) -> None -- append object to end\n",
      " |  \n",
      " |  clear(...)\n",
      " |      L.clear() -> None -- remove all items from L\n",
      " |  \n",
      " |  copy(...)\n",
      " |      L.copy() -> list -- a shallow copy of L\n",
      " |  \n",
      " |  count(...)\n",
      " |      L.count(value) -> integer -- return number of occurrences of value\n",
      " |  \n",
      " |  extend(...)\n",
      " |      L.extend(iterable) -> None -- extend list by appending elements from the iterable\n",
      " |  \n",
      " |  index(...)\n",
      " |      L.index(value, [start, [stop]]) -> integer -- return first index of value.\n",
      " |      Raises ValueError if the value is not present.\n",
      " |  \n",
      " |  insert(...)\n",
      " |      L.insert(index, object) -- insert object before index\n",
      " |  \n",
      " |  pop(...)\n",
      " |      L.pop([index]) -> item -- remove and return item at index (default last).\n",
      " |      Raises IndexError if list is empty or index is out of range.\n",
      " |  \n",
      " |  remove(...)\n",
      " |      L.remove(value) -> None -- remove first occurrence of value.\n",
      " |      Raises ValueError if the value is not present.\n",
      " |  \n",
      " |  reverse(...)\n",
      " |      L.reverse() -- reverse *IN PLACE*\n",
      " |  \n",
      " |  sort(...)\n",
      " |      L.sort(key=None, reverse=False) -> None -- stable sort *IN PLACE*\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Data and other attributes defined here:\n",
      " |  \n",
      " |  __hash__ = None\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(liste)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 3, 5, 'a']\n"
     ]
    }
   ],
   "source": [
    "liste.pop(4)\n",
    "print(liste)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Il n'y a pas de contrainte particulière sur les listes et on peut ainsi faire facilement des listes de liste"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1, 0.25, 0.25], [0.25, 1, 0], [0.25, 0, 1]]\n"
     ]
    }
   ],
   "source": [
    "matrice=[[1,0.25,0.25],[0.25,1,0],[0.25,0,1]]\n",
    "print(matrice)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Puis on accède par double crochet aux éléments de la liste de liste : matrice[i][j] renvoie ainsi la i-ème ligne et j-ème colonne:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "0.25\n"
     ]
    }
   ],
   "source": [
    "print(matrice[0][0])\n",
    "print(matrice[1][0])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Les conditions et tests logiques\n",
    "Les tests logiques s'écrivent comme à l'aide des opérateurs \"==\" pour vérifier une égalité ou != pour une différence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 égal 0? False\n",
      "1 différent de 0 ? True\n"
     ]
    }
   ],
   "source": [
    "print(\"1 égal 0?\",1==0)\n",
    "print(\"1 différent de 0 ?\",1!=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Il est également possible de tester des inégalités (inférieur strict, inférieur ou égal):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n",
      "False\n",
      "False\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "print(1<0)\n",
    "print(1<=0)\n",
    "print(1>1)\n",
    "print(1>=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les tests logiques peuvent également être combinés à l'aide des opérateurs ET (&) et OU (barre verticale : |)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "un_test=(1==0)|(1!=0)\n",
    "print(un_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n"
     ]
    }
   ],
   "source": [
    "un_test=(1==0)&(1!=0)\n",
    "print(un_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "à partir de ces tests logiques, il est possible d'écrire des conditions.\n",
    "\n",
    "Python se caractérise par une syntaxe minimaliste et très visuelle. Contrairement à des langages comme le C ou le Java, il n'est pas nécessaire d'entourer une boucle de parenthèses ou d'accolades : on utilisera la tabulation pour indiquer les instructions qui font partie de la boucle. Ainsi, l'intendation du code n'est pas une simple bonne pratique mais fait partie intégrante de la syntaxe de Python.\n",
    "\n",
    "Les \"si\" s'écrirons simplement:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i est égal à 0\n"
     ]
    }
   ],
   "source": [
    "i=1\n",
    "if i==0:\n",
    "    #on écrit les instructions à l'intérieur du if en les décalant d'une largeur de tabulation.\n",
    "    print(\"i est égal à 0\")\n",
    "elif i==1:\n",
    "    print(\"i est égal à 0\")\n",
    "else:\n",
    "    print(\"i n'est ni égal à 0, ni à 1\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Les boucles\n",
    "Pour écrire des boucles \"for\", la syntaxe de Python aura ici aussi recours à la tabulation. \n",
    "\n",
    "### Exemple"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 1\n",
      "1 2\n",
      "2 3\n",
      "3 4\n",
      "4 5\n",
      "5 6\n",
      "6 7\n",
      "7 8\n",
      "8 9\n",
      "9 10\n"
     ]
    }
   ],
   "source": [
    "a=0\n",
    "#ici, i va de 0 à 10 (exclu) et pour chaque valeur de i, les instructions dans la boucle sont exécutées\n",
    "for i in range(0,10):\n",
    "    a=a+1\n",
    "    print(i,a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ici, on a initialisé une variable a, puis on a incrémentée celle-ci 10 fois de 1.\n",
    "La variable de boucle i a quant à elle pris ses valeurs entre 1 et 0 et 9 mais n'a pas été utilisée explicitement pour les calculs.\n",
    "\n",
    "Dans l'instruction range, on indique les deux extrémités de l'intervalle d'entiers à parcourir : la première est inclue, la seconde exclue. Ainsi, un range(0,n) comprendra n termes, de 0 à n-1.\n",
    "\n",
    "Les instructions à l'intérieur de la boucle peuvent être identifiées par une tabulation (touche tab). Pour sortir de la boucle, il suffira de revenir au niveau de tabulation inférieur. On peut bien entendu imbriquer plusieurs boucles les unes dans les autres en utilisant des doubles ou triples tabulations.\n",
    "\n",
    "N.B. : Les instructions For se terminent par un \":\" "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pratique\n",
    "#### 1. Adaptez la boucle de l'exemple précédent pour calculer la somme de i = 1 à 10 (inclus) de i et afficher les valeurs intermédiaires calculées."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 1\n",
      "2 3\n",
      "3 6\n",
      "4 10\n",
      "5 15\n",
      "6 21\n",
      "7 28\n",
      "8 36\n",
      "9 45\n",
      "10 55\n"
     ]
    }
   ],
   "source": [
    "#écrivez ici votre réponse\n",
    "a=0\n",
    "for i in range(1,11):\n",
    "    a=a+i\n",
    "    print(i,a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2. Modifiez à la marge pour n'afficher que le résultat final obtenu à la dernière itération."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 55\n"
     ]
    }
   ],
   "source": [
    "#écrivez ici votre réponse puis appuyez sur MAJ+Entrée pour exécuter la cellule\n",
    "a=0\n",
    "for i in range(1,11):\n",
    "    a=a+i\n",
    "print(i,a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "De la même manière, il est possible de réaliser des boucles conditionnelles \"while\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 1\n",
      "1 2\n",
      "2 3\n",
      "3 4\n",
      "4 5\n",
      "5 6\n",
      "6 7\n",
      "7 8\n",
      "8 9\n",
      "9 10\n"
     ]
    }
   ],
   "source": [
    "a=0\n",
    "i=0\n",
    "while i<10:\n",
    "    a=a+1\n",
    "    print(i,a)\n",
    "    i=i+1\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3. Réalisez une boucle \"while\" équivalente à la boucle \"for\" de la question 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#écrivez ici votre réponse\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Les librairies : exemple de numpy et matplotlib"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Python fait partie des langages dont la richesse se base sur les nombreuses librairies déjà développées et disponibles pour l'utilisateur. Outre les fonctions et la flexibilité qu'elles apportent, elles améliorent aussi le temps de calcul. Tout comme dans Matlab, les librairies orientées calcul sont ainsi implémentées dans des langages plus performants sur le plan du temps de calcul (p.ex. C++) sans que l'utilisateur en ait à supporter la lourdeur syntaxique.\n",
    "\n",
    "## Numpy\n",
    "Numpy est l'une des librairies centrales dès lors qu'il est question de calcul. Elle permet de travailler avec des tableaux de chiffres ou des matrices.\n",
    "\n",
    "Pour utiliser une librairie, on commence toujours par l'importer afin de charger ses composantes. On lui donne souvent un alias (ici, numpy sera raccourci en np)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les fonctions et composantes de la librairie sont ainsi accessibles via le \".\" : np.composante. Parmi les nombreux composants disponibles pour l'utilisateur, on s'intéressera ici à \"array\", qui permet de définir des tableaux, et à \"random\" (et en particulier random.randn) qui génère des nombres aléatoires (suivant la loi normale)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tableau [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.]\n",
      "matrice [[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "liste [1 2 3 4]\n",
      "alea [-0.39239984  0.80211896  2.00790568  0.19456283  3.10064802  0.81332984\n",
      " -0.17329428  0.44336226  0.14800345 -0.82027738  1.47899508  1.15235877\n",
      "  1.92203003  1.73278736  2.18264052  1.1186342   1.45092902  0.64442724\n",
      "  2.36395787 -1.57367621  0.30899914  0.492661    0.3075851  -0.17320867\n",
      " -1.01072094 -1.02052472 -1.26045262 -0.9356953  -1.21905538  1.92140652\n",
      " -2.13631235 -0.9024904   0.46060992 -0.08561596  0.32511261 -0.14695728\n",
      "  0.39493679  1.33062168 -0.56710075  1.46234752  1.25496015  0.79340983\n",
      " -1.94395163  1.01675632  0.08312633  0.19972001 -0.68180127 -0.49036658\n",
      "  0.10599703  0.90460368 -0.53696559  0.43507748 -0.38892847  1.01202993\n",
      "  0.09915313  0.63623299 -0.35799623 -0.3059775  -0.41678735  0.55394978\n",
      " -0.16412737 -1.12400791 -0.21009229 -0.8061895  -0.06769692  2.29945076\n",
      "  0.31895991 -0.09521317  0.69499666  0.66370094 -0.02452465 -0.38624183\n",
      " -0.15115659 -0.25131688 -1.53692902 -0.72404094 -1.0118703   0.35604137\n",
      "  0.89254141  0.41021231 -0.61458741  0.71527295  0.16152651 -0.02949801\n",
      "  0.41790497  0.27305028 -1.09542514 -0.87868886  1.39121041 -1.23302722\n",
      " -0.21293107 -1.0165739   0.81857536  0.79524745 -0.82107392 -1.09577548\n",
      "  0.6194336   0.22282005  0.0351348   1.48555259]\n"
     ]
    }
   ],
   "source": [
    "#on définit un tableau unidimensionnel de dimension 10 (un vecteur) rempli de zeros :\n",
    "tableau=np.zeros(10)\n",
    "print(\"tableau\",tableau)\n",
    "#et une matrice de la même manière en donnant un couple de dimensions :\n",
    "matrice=np.zeros((10,3))\n",
    "print(\"matrice\",matrice)\n",
    "#Il est aussi possible de transformer une liste en tableau numpy :\n",
    "liste=np.array([1,2,3,4])\n",
    "print(\"liste\",liste)\n",
    "#On peut facilement générer des nombres aléatoires à l'aide de :\n",
    "alea=np.random.randn(100)\n",
    "print(\"alea\",alea)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ces tableaux sont des objets qui ont donc eux-mêmes des fonctions telles que max, sum (somme), mean (moyenne), std (écart-type)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "par exemple: 17.1360753363 0.171360753363 0.99311634985 3.10064801649\n"
     ]
    }
   ],
   "source": [
    "print(\"par exemple:\",alea.sum(),alea.mean(),alea.std(),alea.max())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour représenter graphiquement les résultats, on peut utiliser la librairie matplotlib (voir google pour de nombreux exemples). Un graphique simple peut par exemple s'écrire :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAD8CAYAAABjAo9vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nw+FMGDywczgczoTBAzuHw+FMGP8/nMqic57PTvMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x271f1964668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "#on s'assure que toutes les figures sont fermées:\n",
    "plt.close()\n",
    "#on crée une figure\n",
    "plt.figure()\n",
    "plt.plot(alea)\n",
    "#on affiche la figure\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En pratique, toutes les instructions plot écrites avant d'afficher la figure seront superposées sur le même graphe, ce qui permet d'afficher plusieurs courbes sur une même figure. Ainsi, par exemple, on peut utiliser la fonction \"bar\" qui trace des barres verticales étant donné des vecteurs x (abscisses) et y (ordonnées). Pour créer les abscisses, on utilise par exemple ci-dessous la fonction linspace qui crée un vecteur (une grille de 1 à 100 contenant 100 points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAD8CAYAAABjAo9vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x271f13e40f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x: [   1.    2.    3.    4.    5.    6.    7.    8.    9.   10.   11.   12.\n",
      "   13.   14.   15.   16.   17.   18.   19.   20.   21.   22.   23.   24.\n",
      "   25.   26.   27.   28.   29.   30.   31.   32.   33.   34.   35.   36.\n",
      "   37.   38.   39.   40.   41.   42.   43.   44.   45.   46.   47.   48.\n",
      "   49.   50.   51.   52.   53.   54.   55.   56.   57.   58.   59.   60.\n",
      "   61.   62.   63.   64.   65.   66.   67.   68.   69.   70.   71.   72.\n",
      "   73.   74.   75.   76.   77.   78.   79.   80.   81.   82.   83.   84.\n",
      "   85.   86.   87.   88.   89.   90.   91.   92.   93.   94.   95.   96.\n",
      "   97.   98.   99.  100.]\n"
     ]
    }
   ],
   "source": [
    "#on s'assure que toutes les figures sont fermées:\n",
    "plt.close()\n",
    "#on crée une figure\n",
    "plt.figure()\n",
    "plt.plot(alea)\n",
    "plt.bar(np.linspace(1,100,100),alea,color=\"r\")\n",
    "#on affiche la figure\n",
    "plt.show()\n",
    "print(\"x:\",np.linspace(1,100,100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A. Provision pour participation aux bénéfices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1. Quel est le but de la provision pour participation aux bénéfices ? Rappelez ci-dessous ses règles de dotation et de reprise"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[double cliquer pour afficher l'espace de réponse]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2. L'assureur A commercialise des produits d'épargne et souhaite distribuer à ses assurés un rendement stable année après année. Il s'est engagé contractuellement auprès de ses assurés à leur redistribuer 100% des produits financiers issus des actifs qu'il détient. Les produits financiers générés par ces actifs sont toutefois volatiles et l'assureur souhaite utiliser la PPB pour lisser le rendement servi aux assurés. \n",
    "\n",
    "On se placera dans la suite sur un horizon de projection de T=30 ans.\n",
    "\n",
    "##### 2.a. On propose de simuler aléatoirement les produits financiers dont dispose l'assureur chaque année : ils sont ainsi supposés suivre une loi normale de moyenne 5 M€ et de variance 5 M€.\n",
    "\n",
    "Définir un vecteur de réalisation des produis financiers disponibles année après année (sous la forme d'un tableau numpy à une dimension) en utilisant la fonction np.random.randn(n) qui renvoie un vecteur de n réalisations d'une loi normale N(0,1) (pour plus d'information sur cette fonction, help(np.random.randn).\n",
    "\n",
    "##### 2.b. On supposera dans un premier temps que la contrainte de reprise sous 8 ans des sommes dotées en PPB ne s'applique pas. \n",
    "- la PPB est initialement constituée de 5 M€\n",
    "- la cible de revalorisation, fixe à chaque année de projection, est de 4,5 M€.\n",
    "\n",
    "Lorsque les produits financiers sont suffisants pour remplir la cible de 4,5 M€, l'excédent est doté en PPB, lorsqu'ils sont inssufisants, une reprise est réalisée (sans toutefois que la provision puisse prendre des valeurs négatives).\n",
    "\n",
    "Calculez le vecteur \"revalo\" qui contiendra les revalorisations futures ainsi que le vecteur \"PPB\" qui représente l'évolution de la PPB tout au long de la projection.\n",
    "\n",
    "##### 2.c. Afficher à l'aide de la fonction \"plt.bar\" de matplotlib les trois vecteurs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA3YAAAGrCAYAAACMkgVVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x271f193dda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#écrivez ici votre réponse\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "#2.a On définit l'horizon temporel\n",
    "T=30\n",
    "pfi=np.random.randn(T)*5+5\n",
    "cible=4.5\n",
    "\n",
    "#Pour afficher le graphique, on utilise \"bar(x,y)\" où x correspond ici aux années de\n",
    "#projection et y à la valeur calculée (hauteur des barres).\n",
    "u=np.linspace(1,T,T)\n",
    "\n",
    "#2.b \n",
    "#On initialise les tableaux\n",
    "revalo=np.zeros(T+1)\n",
    "PPB=np.zeros(T+1)\n",
    "#On initialise le vecteur PPB\n",
    "PPB[0]=5\n",
    "#Puis on réalise une boucle de projection\n",
    "for t in range(0,T):\n",
    "    if pfi[t]>cible:\n",
    "        PPB[t+1]=PPB[t]+(pfi[t]-cible)\n",
    "        revalo[t]=cible\n",
    "    elif pfi[t]<cible:\n",
    "        #Si PPB + Pfi suffisant\n",
    "        if PPB[t]+pfi[t]>cible:\n",
    "            PPB[t+1]=PPB[t]-(cible-pfi[t])\n",
    "            revalo[t]=cible\n",
    "        else:\n",
    "            PPB[t+1]=0\n",
    "            revalo[t]=np.max((0,pfi[t]+PPB[t]))\n",
    "plt.close()\n",
    "plt.figure(figsize=(15,7))\n",
    "plt.subplot(1,3,1)\n",
    "plt.title(\"produits\")\n",
    "plt.bar(u,pfi[0:T])\n",
    "plt.subplot(1,3,2)\n",
    "plt.bar(u,revalo[1:T+1])\n",
    "plt.title(\"revalorisation\")\n",
    "plt.subplot(1,3,3)\n",
    "plt.bar(u,PPB[0:T])\n",
    "plt.title(\"PPB\")\n",
    "\n",
    "\n",
    "plt.show()\n",
    "plt.close()\n",
    "\n",
    "            "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "#### 3. On souhaite maintenant calculer à chaque pas de projection la probabilité que la revalorisation cible ne soit pas atteinte. \n",
    "\n",
    "Adaptez la réponse à la question 2 pour simuler un grand nombre de trajectoires et déterminier empiriquement cette probabilité."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEKCAYAAAAfGVI8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n3P8HNhapMO0UiuAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x271f11ec5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#On définit le nombre d'itérations \n",
    "N=10000\n",
    "\n",
    "T=30\n",
    "\n",
    "cible=4.5\n",
    "\n",
    "#On initialise le vecteur de probabilité de ne pas servir la cible :\n",
    "Proba=np.zeros(T)\n",
    "\n",
    "#Pour afficher le graphique, on utilise \"bar(x,y)\" où x correspond ici aux années de\n",
    "#projection et y à la valeur calculée (hauteur des barres).\n",
    "u=np.linspace(1,T,T)\n",
    "\n",
    "for i in range(0,N):\n",
    "    #Puis on réalise une boucle de projection\n",
    "    #en faisant attention de bien réinitialiser les variables dans la boucle !\n",
    "    pfi=np.random.randn(T)*5+5\n",
    "    #On initialise les tableaux\n",
    "    revalo=np.zeros(T+1)\n",
    "    PPB=np.zeros(T+1)\n",
    "    #On initialise le vecteur PPB\n",
    "    PPB[0]=5\n",
    "\n",
    "    for t in range(0,T):\n",
    "        if pfi[t]>cible:\n",
    "            PPB[t+1]=PPB[t]+(pfi[t]-cible)\n",
    "            revalo[t]=cible\n",
    "        elif pfi[t]<cible:\n",
    "            #Si PPB + Pfi suffisant\n",
    "            if PPB[t]+pfi[t]>cible:\n",
    "                PPB[t+1]=PPB[t]-(cible-pfi[t])\n",
    "                revalo[t]=cible\n",
    "            else:\n",
    "                PPB[t+1]=0\n",
    "                revalo[t]=np.max((0,pfi[t]+PPB[t]))\n",
    "                Proba[t]+=1./N\n",
    "plt.close()\n",
    "plt.bar(u,Proba*100)\n",
    "plt.ylabel(\"Probabilité de ne pas servir la cible (en %)\")\n",
    "plt.xlabel(\"nombre d'années de projection\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4. On tient maintenant compte de la contrainte de reprise des sommes dotées en PPB sous 8 ans.  Modifiez le code de la question 2 pour déterminer les chroniques de revalorisation dans ces nouvelles conditions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA3YAAAGrCAYAAACMkgVVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYOIEOwAAgIn7/wE929ZHFIp27QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x271f1963898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#écrivez ici votre réponse\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "#2.a On définit l'horizon temporel\n",
    "T=30\n",
    "pfi=np.random.randn(T)*5+5\n",
    "cible=4.5\n",
    "\n",
    "#Pour afficher le graphique, on utilise \"bar(x,y)\" où x correspond ici aux années de\n",
    "#projection et y à la valeur calculée (hauteur des barres).\n",
    "u=np.linspace(1,T,T)\n",
    "\n",
    "#2.b \n",
    "#On initialise les tableaux\n",
    "revalo=np.zeros(T+1)\n",
    "#Cette fois-ci, la PPB est à un tableau multidimensionnel (T+1,8)\n",
    "PPB=np.zeros((T+1,8))\n",
    "#On initialise le vecteur PPB\n",
    "PPB[0,0]=5\n",
    "#Puis on réalise une boucle de projection\n",
    "for t in range(0,T):\n",
    "    PPB[t+1,1:7]=PPB[t,0:6]\n",
    "    if pfi[t]+PPB[t,6]>cible:\n",
    "        if PPB[t,6]>cible:\n",
    "            revalo[t]=PPB[t,6]\n",
    "            PPB[t+1,0]=pfi[t]\n",
    "        else:\n",
    "            revalo[t]=cible\n",
    "            PPB[t+1,0]=(pfi[t]-cible)\n",
    "        \n",
    "    elif pfi[t]+PPB[t,6]<=cible:\n",
    "        #Si PPB + Pfi suffisant : on regarde pour ça la somme suivant la dimension (1) (et non 0)\n",
    "        #des sommes disponibles sur la PPB.\n",
    "        servi=pfi[t]\n",
    "\n",
    "        #Dans tous les cas on sert les sommes en 8ème année\n",
    "        servi+=PPB[t,6]\n",
    "\n",
    "        k=1\n",
    "        #on fait une boucle while pour itérer sur les anciennetés de PPB\n",
    "        while (servi<cible)&(k<=7):\n",
    "            #astuce de syntaxe: plutôt que d'écrire a=a+1, on peut écrire a+=1\n",
    "            #8 = 5\n",
    "            servi_old=servi\n",
    "            servi+=np.min((PPB[t+1,7-k],np.max((0,cible-servi))))\n",
    "            PPB[t+1,7-k]-=servi-servi_old\n",
    "\n",
    "            k+=1\n",
    "        revalo[t]=servi\n",
    "        \n",
    "\n",
    "plt.close()\n",
    "plt.figure(figsize=(15,7))\n",
    "plt.subplot(1,3,1)\n",
    "plt.title(\"produits\")\n",
    "plt.bar(u,pfi[0:T])\n",
    "plt.subplot(1,3,2)\n",
    "plt.bar(u,revalo[1:T+1])\n",
    "plt.title(\"revalorisation\")\n",
    "plt.subplot(1,3,3)\n",
    "plt.bar(u,PPB[0:T,:].sum(1))\n",
    "plt.title(\"PPB\")\n",
    "\n",
    "\n",
    "plt.show()\n",
    "plt.close()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 5. Par analogie avec la question 3, calculez la nouvelle probabilité de ne pas servir la cible de revalorisation. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmsAAAENCAYAAABQCSI+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nS2UtIiIiooelshYRERHRw/4/VOarakv+oBoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x271f14a7588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#écrivez ici votre réponse\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "#On définit le nombre d'itérations \n",
    "N=10000\n",
    "\n",
    "T=30\n",
    "\n",
    "cible=4.5\n",
    "\n",
    "#On initialise le vecteur de probabilité de ne pas servir la cible :\n",
    "Proba_sup=np.zeros(T)\n",
    "Proba_inf=np.zeros(T)\n",
    "\n",
    "\n",
    "#Pour afficher le graphique, on utilise \"bar(x,y)\" où x correspond ici aux années de\n",
    "#projection et y à la valeur calculée (hauteur des barres).\n",
    "u=np.linspace(1,T,T)\n",
    "\n",
    "for i in range(0,N):\n",
    "    #on initialise l'aléa\n",
    "    pfi=np.random.randn(T)*5+5\n",
    "    #On initialise les tableaux\n",
    "    revalo=np.zeros(T+1)\n",
    "    #Cette fois-ci, la PPB est à un tableau multidimensionnel (T+1,8)\n",
    "    PPB=np.zeros((T+1,8))\n",
    "    #On initialise le vecteur PPB\n",
    "    PPB[0,0]=5\n",
    "    #Puis on réalise une boucle de projection\n",
    "    for t in range(0,T):\n",
    "        PPB[t+1,1:7]=PPB[t,0:6]\n",
    "        if pfi[t]+PPB[t,6]>cible:\n",
    "            if PPB[t,6]>cible:\n",
    "                revalo[t]=PPB[t,6]\n",
    "                PPB[t+1,0]=pfi[t]\n",
    "            else:\n",
    "                revalo[t]=cible\n",
    "                PPB[t+1,0]=(pfi[t]-cible)\n",
    "\n",
    "        elif pfi[t]+PPB[t,6]<=cible:\n",
    "            #Si PPB + Pfi suffisant : on regarde pour ça la somme suivant la dimension (1) (et non 0)\n",
    "            #des sommes disponibles sur la PPB.\n",
    "            servi=pfi[t]\n",
    "\n",
    "            #Dans tous les cas on sert les sommes en 8ème année\n",
    "            servi+=PPB[t,6]\n",
    "\n",
    "            k=1\n",
    "            #on fait une boucle while pour itérer sur les anciennetés de PPB\n",
    "            while (servi<cible)&(k<=7):\n",
    "                #astuce de syntaxe: plutôt que d'écrire a=a+1, on peut écrire a+=1\n",
    "                #8 = 5\n",
    "                servi_old=servi\n",
    "                servi+=np.min((PPB[t+1,7-k],np.max((0,cible-servi))))\n",
    "                PPB[t+1,7-k]-=servi-servi_old\n",
    "\n",
    "                k+=1\n",
    "            revalo[t]=servi\n",
    "        if revalo[t]<cible:\n",
    "            Proba_inf[t]+=1/N\n",
    "        if revalo[t]>cible:\n",
    "            Proba_sup[t]+=1/N\n",
    "\n",
    "plt.close()\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.subplot(121)\n",
    "plt.bar(u,Proba_inf[0:T]*100)\n",
    "plt.ylabel(\"Probabilité de servir moins que la cible (en %)\")\n",
    "plt.xlabel(\"nombre d'années de projection\")\n",
    "plt.subplot(122)\n",
    "plt.bar(u,Proba_sup[0:T]*100)\n",
    "plt.ylabel(\"Probabilité de servir plus que la cible (en %)\")\n",
    "plt.xlabel(\"nombre d'années de projection\")\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 6. Affichez alors le résultat sur le même graphique que le résultat obtenu en question 3 et commentez. \n",
    "\n",
    "Précision : dans un Notebook, les variables définies dans les cellules précédentes restent disponibles une fois calculées. Il n'est donc pas nécessaire de les re-calculer dans la cellule courante."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEKCAYAAAAB0GKPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nnnF8SNyfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x271f1a0c588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Comparaison des deux graphiques\n",
    "plt.close()\n",
    "plt.figure()\n",
    "plt.bar(u,Proba[0:T]*100)\n",
    "plt.bar(u,Proba_inf[0:T]*100,alpha=0.6)\n",
    "plt.legend([\"sans 8 ans\",\"avec 8 ans\"])\n",
    "plt.ylabel(\"Probabilité de servir plus que la cible (en %)\")\n",
    "plt.xlabel(\"nombre d'années de projection\")\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "[double cliquer pour afficher l'espace de réponse]\n",
    "\n",
    "Sur les premières années, le comportement est relativement similaire, puis partir de 8 ans, la contrainte réglementaire de reprise des sommes dotées sous 8 ans commence à détériorer le niveau des revalorisations. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 7. Que deviennent les résultats précédents si les sommes dotées en PPB doivent être reprises non pas sous 8 mais sous 10 ans ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Indiquez la réponse dans cette case"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## B. Réserve de capitalisation\n",
    "\n",
    "#### 1. Quel est le but de la réserve de capitalisation ? Rappelez ci-dessous ses règles de dotation et de reprise"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[double cliquer pour afficher l'espace de réponse]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2. Calcul de la valeur d'une obligation : on suppose que l'on dispose des caractéristiques d'une obligation achetée au pair en fin d'année (nominal N, taux de coupon C, maturité M) et dont les échéances sont en fin d'année. On dispose également d'une courbe de taux sans risque spot r(t). En faisant l'hypothèse de l'absence de risque de crédit, écrire la formule de calcul de la valeur de marché d'une obligation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[double cliquer pour afficher l'espace de réponse]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dans la suite du problème, on utilisera la courbe de taux spot EIOPA à fin 2018 jusqu'à la maturité 10 ans: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAD8CAYAAAB3u9PLAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xl4VNX9x/H3l4R9R/ZAWMO+MyzihoqKqKC2Kqh1bVEr\nrq2Kbd1rRbQq/FQsVlptlYCoFZFNFBesC2ELJBAIeyAhCUgIhJDt/P7I2AaKyQBJ7kzm83qePMnM\nPSfzvfOQ+XDPOfdec84hIiJSzesCREQkOCgQREQEUCCIiIifAkFERAAFgoiI+CkQREQEUCCIiIif\nAkFERAAFgoiI+EUG0sjMRgJTgAjgr865ScdsN//2UUAOcJNzbqV/2wzgUiDdOderRJ8mwCygPbAN\nuNo590NpdTRt2tS1b98+kJJFRMRvxYoVmc65ZmW1s7IuXWFmEcBG4AIgBVgOjHPOJZZoMwq4i+JA\nGAJMcc4N8W87GzgIvHVMIEwG9jnnJpnZRKCxc+6h0mrx+XwuLi6urH0SEZESzGyFc85XVrtAhowG\nA8nOuS3OuTwgFhhzTJsxFH/gO+fct0AjM2sF4Jz7Eth3nN87BnjT//ObwOUB1CIiIhUkkECIAnaW\neJzif+5E2xyrhXMu1f9zGtAigFpERKSCBMWksisetzru2JWZjTezODOLy8jIqOTKRETCRyCBsAto\nW+JxG/9zJ9rmWHt+HFbyf08/XiPn3HTnnM8552vWrMw5EREROUmBBMJyIMbMOphZDWAsMPeYNnOB\nG6zYUCCrxHDQT5kL3Oj/+UbgwxOoW0REylmZgeCcKwAmAIuA9cBs51yCmd1uZrf7m80HtgDJwOvA\nr3/sb2YzgW+ArmaWYma3+jdNAi4ws03ACP9jERHxSJnLToOJlp2KiJy48lx2KiIiHsk8eITH5yZw\nIDe/wl8roDOVRUSkchUUFvH2dzv48+IkcvIKObNzU0b0qNjV+QoEEZEgs3zbPh79MIH1qQc4s3NT\nHh/dk87N61X46yoQRESCRPqBXJ5ZsIEPVu2idcNaTLtuACN7taT4cnEVT4EgIuKx/MIi3vz3Nl5a\nsom8giImnNuZX5/biTo1KvcjWoEgIuKhbzbv5bG569i45yDDuzbjsct60qFpXU9qUSCIiHggNesw\nf5q/gY/W7KZN49q8foOPEd2bV9rw0PEoEEREKlFeQREzvt7K1E83UVDkuOf8GO4Y3ola1SO8Lk2B\nICJSWb7alMFjcxPYknGIEd1b8OilPYg+rY7XZf2HAkFEpILt2n+YP85LZMG6NNqdVoe/3TSIc7s1\n97qs/6FAEBGpIEcKCnn9yy28vDQZgN9e2IVfntUxKIaHjkeBICJSAZZuSOeJjxLYtjeHi3u15A+X\n9iCqUW2vyyqVAkFEpBzt2JvDk/MSWLI+nY7N6vKPWwdzVkxo3MtFgSAiUg5y8wuZ9vlmpn2xmchq\nxsSLu3HLGR2oERk61xBVIIiInALnHJ8k7uHJeYmk/HCYy/q25nejutGqYXAPDx2PAkFE5CRtzTzE\nEx8l8HlSBjHN6/HOr4YwrFNTr8s6aQoEEZETlJNXwCtLk3n9y63UiKzGHy7pzo3D2lM9InSGh45H\ngSAiEiDnHAvWpfHHeYnszsrlyv5RTBzVjeb1a3ldWrlQIIiIBCA5PZvH5yayLDmTbi3rM2Vcfwa1\nb+J1WeVKgSAiUoqDRwr4v0838cayrdSuEcETo3ty3ZBoIkN8eOh4FAgiIsfhnOOj+FSe/jiRPQeO\ncLWvDQ+O7EbTejW9Lq3CKBBERI6RmnWY33+wjs82pNMrqgHTrh/IgOjGXpdV4RQIIiJ+zjlmx+3k\nj/PWk19UxB8u6c7NZ3Qgopp39yioTAoEERFg574cHn5/LcuSMxnSoQnP/qwP7T26c5lXFAgiEtaK\nihz//G47kxZswICnLu/FdYOjqRYmRwUlKRBEJGxtzTzEQ3Pi+X7bPs6KacozV/amTePguWFNZVMg\niEjYKSxyzFi2lecXJ1EjshqTf96Hqwa28fR+xsFAgSAiYWXTnmwemBPP6p37GdG9OU9f0ZsWDarG\nmcanSoEgImEhv7CI6V9uYcqSTdStGcGUsf0Y3bd12B8VlBTQqXZmNtLMksws2cwmHme7mdlU//Z4\nMxtQVl8z62dm35rZajOLM7PB5bNLIiJHS9x9gMtf+ZrnFiVxQY8WfHL/OYzpF6UwOEaZRwhmFgG8\nAlwApADLzWyucy6xRLOLgRj/1xBgGjCkjL6TgSeccwvMbJT/8fBy2zMRCXt5BUW8vDSZV5cm06hO\nDaZdN4CLe7fyuqygFciQ0WAg2Tm3BcDMYoExQMlAGAO85ZxzwLdm1sjMWgHtS+nrgAb+/g2B3ae+\nOyIixdbs3M+Dc+JJ2pPNlf2jeOTSHjSuW8PrsoJaIIEQBews8TiF4qOAstpEldH3XmCRmT1P8dDV\nsOO9uJmNB8YDREdHB1CuiISz3PxCXlyykde/3ELz+rWYcZOP87q18LqskODlpPIdwH3OuffM7Grg\nDWDEsY2cc9OB6QA+n89VbokiEkritu3jwTnxbMk8xLjBbXl4VHca1KrudVkhI5BA2AW0LfG4jf+5\nQNpUL6XvjcA9/p/fBf4aWMkiIkfLySvguUVJ/P3f24hqVJt/3jqEM2NC91aWXgkkEJYDMWbWgeIP\n87HAtce0mQtM8M8RDAGynHOpZpZRSt/dwDnA58B5wKZT3BcRCUP/Ts7koffj2bnvMDee3o4HR3aj\nbk2tqD8ZZb5rzrkCM5sALAIigBnOuQQzu92//TVgPjAKSAZygJtL6+v/1b8CpphZJJCLf55ARCQQ\n2bn5PLNgA+98t4P2p9Vh9m2nM7hD1bqDWWWz4oVBocHn87m4uDivyxARj32elM7D769lz4FcfnlW\nR+4b0YXaNSK8LitomdkK55yvrHY6rhKRkJGVk89THycyZ0UKMc3r8eodw+gfBjeuqSwKBBEJCYsT\n0vj9v9ax71Aed53XmQnndaZmpI4KypMCQUSC2t6DR3j8o0Q+WrOb7q0a8LebBtErqqHXZVVJCgQR\nCUrOOebFp/LY3ASyc/P5zQVduH14J6pHBHQJNjkJCgQRCTrp2bk88q91LErYQ982DXnuqqF0aVHf\n67KqPAWCiASV+WtT+d0HazmcV8jvRnXjljM6EKmjgkqhQBCRoJCdm8/jcxN5b2UKfds05IVr+tGp\nWT2vyworCgQR8dz3W/dx/+zV7N5/mLvPj+Gu8zprrsADCgQR8UxeQREvLdnItC8207ZxHd69fRgD\n2+m8Aq8oEETEE8np2dw7azXrdh3gGl9bHrmsB/V0DSJP6d0XkUrlnOMf327n6Y/XU7dmJH/5xUAu\n6tnS67IEBYKIVKL0A7k8MCeeLzZmMLxrMyb/vA/N69fyuizxUyCISKVYuC6Nh9+P53B+IU+N6cn1\nQ9vpJvdBRoEgIhXq4JECnpibwLsrUugd1ZAXr+lH5+ZaThqMFAgiUmFWbN/HfbPWkPJDDhPO7czd\n58dQI1LLSYOVAkFEyl1+YRFTP93EK0uTiWpcm9m3nY6vvW5eE+wUCCJSrjZnHOS+WauJT8niqoFt\nePSyHtTXje5DggJBRMqFc45/freDpz9OpFb1CF67fgAje7Xyuiw5AQoEETll6dm5PDQnnqVJGZzd\npRnP/bwPLRpoOWmoUSCIyClZnJDGxPfXcuhIAU+M7skNp2s5aahSIIjISTl0pICn5iUSu3wnPVs3\n4KVr+hGjexaENAWCiJywFdt/4P7Zq9mxL4dfD+/EvSO6aDlpFaBAEJGA5RcW8X+fJfPyZ5to1bA2\ns8afzuAOWk5aVSgQRCQgW/zLSdekZHHlgCgeH92TBlpOWqUoEESkVM45Zn6/k6fmJVIjshqvXDuA\nS/poOWlVpEAQkZ+UefAID82J59MN6ZzZuSnPX9WXlg21nLSqUiCIyHEtSdzDQ+/Fk32kgEcv7cFN\nw9pTrZqWk1ZlCgQROUpOXgFPzVvPzO930L1VA2aO7UcXLScNCwGtEzOzkWaWZGbJZjbxONvNzKb6\nt8eb2YBA+prZXWa2wcwSzGzyqe+OiJyKNTv3c8nUZcQu38Ft53TkX3cOUxiEkTKPEMwsAngFuABI\nAZab2VznXGKJZhcDMf6vIcA0YEhpfc3sXGAM0Nc5d8TMmpfnjolI4IqKHG8s28qzCzfQvH5NZv5q\nKEM7nuZ1WVLJAhkyGgwkO+e2AJhZLMUf5CUDYQzwlnPOAd+aWSMzawW0L6XvHcAk59wRAOdcevns\nkoiciH2H8vjN7NUsTcrgop4tmPyzvjSso+Wk4SiQIaMoYGeJxyn+5wJpU1rfLsBZZvadmX1hZoNO\npHAROXXfbtnLxVO+5OvkvTw5pievXT9QYRDGvJxUjgSaAEOBQcBsM+voP8r4DzMbD4wHiI6OrvQi\nRaqiwiLHy58lM+XTjbQ7rS5v3DiIXlENvS5LPBZIIOwC2pZ43Mb/XCBtqpfSNwV43x8A35tZEdAU\nyCj5i51z04HpAD6f76iwEJETl34gl3tiV/PNlr1c3q81f7yiN/VqasGhBDZktByIMbMOZlYDGAvM\nPabNXOAG/2qjoUCWcy61jL7/As4FMLMuQA0g85T3SER+0hcbM7h4yles3rmfyT/vw4vX9FMYyH+U\n+S/BOVdgZhOARUAEMMM5l2Bmt/u3vwbMB0YByUAOcHNpff2/egYww8zWAXnAjccOF4lI+cgvLOLP\nizfy2heb6dqiPi9f21+Xqpb/YaH0Gezz+VxcXJzXZYiElJQfcrh75ipW7tjPuMHRPHZZD2pVj/C6\nLKlEZrbCOecrq52OFUWqsIXr0nhwzhqcg5ev7c+lfVp7XZIEMQWCSBWUm1/IM/PX8+Y32+nTpiEv\njxtA9Gl1vC5LgpwCQaSK2ZJxkAnvrCIx9QC3ntmBh0Z2093MJCAKBJEq5F+rdvH7D9ZSPbIaf73B\nx4geLbwuSUKIAkGkCsjJK+CxDxN4d0UKg9o3ZsrY/rRuVNvrsiTEKBBEQlxSWjZ3vrOSzRkHueu8\nztxzfgyRERoikhOnQBAJUc45Ypfv5PG5CdSvVZ1/3DKEM2Oael2WhDAFgkgIys7N5+H31zIvPpWz\nYprywtX9aFa/ptdlSYhTIIiEmPiU/Ux4ZxW79h/mgYu6csc5nXRrSykXCgSREOHcf29i06xeTWaN\nH4qvfROvy5IqRIEgEgJ+OJTHA3PWsGR9OiO6t+D5q/rQqE4Nr8uSKkaBIBLklm/bx90zV7H3YB6P\nXdaDm4a1x0xDRFL+FAgiQaqwyDHt82ReXLKJNo1r894dw+jdRjexkYqjQBAJQunZudw/aw3LkjO5\nrG9r/nRFL+rX0q0tpWIpEESCzFebMrhv1moOHilg0pW9uWZQWw0RSaVQIIgEiYLCIl5cspFXP99M\n52b1ePuXQ+naUjexkcqjQBAJArv3H+bumauI2/4D1/ja8vjontSuoZvYSOVSIIh47IuNGdwbu4q8\ngiKmjO3HmH5RXpckYUqBIOKRwiLH1E83MfWzTXRpXp9p1w+gY7N6XpclYUyBIOKBfYfyuCd2FV9t\nyuTKAVE8fXlvDRGJ5xQIIpVs5Y4fuPPtlew9lMczV/ZmrFYRSZBQIIhUEuccf//3Np7+eD2tGtXi\n/TuG0StKJ5pJ8FAgiFSCg0cKeOi9eD6OT2VE9+b8+ap+NKyjE80kuCgQRCpYUlo2d7y9gm2Zh5h4\ncTfGn9VRl6uWoKRAEKlA769M4XcfrKVezeq886uhDO14mtclifwkBYJIBcjNL+TJeYm8890OBndo\nwsvj+tO8QS2vyxIplQJBpJzt3JfDHW+vYN2uA9x+Tid+e2EX3fReQoICQaQcLUncw/2zV+OA12/w\ncUGPFl6XJBKwgP7bYmYjzSzJzJLNbOJxtpuZTfVvjzezASfQ9zdm5sys6antioh3CgqLeHbhBn75\nVhxtm9Th47vOUhhIyCnzCMHMIoBXgAuAFGC5mc11ziWWaHYxEOP/GgJMA4aU1dfM2gIXAjvKb5dE\nKld6di53z1zFt1v2MW5wWx67rCe1quusYwk9gQwZDQaSnXNbAMwsFhgDlAyEMcBbzjkHfGtmjcys\nFdC+jL4vAg8CH5bDvohUuu+27OWumas4kJvP81f15ecD23hdkshJCyQQooCdJR6nUHwUUFabqNL6\nmtkYYJdzbo1O25dQ45xj+pdbmLwoiegmdXjr1sF0a9nA67JEToknk8pmVgf4HcXDRWW1HQ+MB4iO\njq7gykTKlnU4n9++u4ZPEvcwqndLnv1ZH93eUqqEQAJhF9C2xOM2/ucCaVP9J57vBHQAfjw6aAOs\nNLPBzrm0kr/YOTcdmA7g8/lcAPWKVJh1u7L49dsr2b3/MI9c2oNbzmivC9NJlRFIICwHYsysA8Uf\n5mOBa49pMxeY4J8jGAJkOedSzSzjeH2dcwlA8x87m9k2wOecyzzVHRKpCM45Zsft5JEPE2hSpwaz\nbhvKwHZNvC5LpFyVGQjOuQIzmwAsAiKAGc65BDO73b/9NWA+MApIBnKAm0vrWyF7IlJBDucV8siH\n65izIoUzOzflpbH9aFqvptdliZQ7K14YFBp8Pp+Li4vzugwJI1szD3HHP1eQtCebu86L4Z7zY4jQ\nhekkxJjZCuecr6x2OlNZ5CcsWJvKA3PiiYww/nbTIIZ3bV52J5EQpkAQOUZ+YRGTFmzgjWVb6du2\nEa9eN4CoRrW9LkukwikQREpIy8rlzndWsmL7D9x4ejt+d0l3akbqrGMJDwoEEb9lmzK5J3YVh/ML\nmTquP6P7tva6JJFKpUCQsFdU5HhlaTIvLNlIp2b1mHX9ADo3r+91WSKVToEgYW1/Th73zlrN50kZ\njOnXmj9d0Zu6NfVnIeFJ//IlbK1PPcBt/1hBatZhnrq8F9cPidZZxxLWFAgSlubF7+aBd+OpXyuS\nWbedzoDoxl6XJOI5BYKElcIix+RFG/jLF1sY2K4x064boHsdi/gpECRs7M/J466Zq/hqUybXDonm\n8ct6UiNS9zoW+ZECQcJCyfmCZ67szbjBupS6yLEUCFLllZwviB1/OgPbab5A5HgUCFJlFRY5nluU\nxGtfbNZ8gUgAFAhSJe3PyePu2NV8uTFD8wUiAVIgSJWzIe0A49/SfIHIiVIgSJWi+QKRk6dAkCqh\n5HzBgOhGvHb9QM0XiJwgBYKEvJLzBeMGR/P46B66ZLXISVAgSEgrOV/wpyt6c+0QzReInCwFgoQs\nzReIlC8FgoScY+cLpl0/kBaaLxA5ZQoECSmaLxCpOAoECRmaLxCpWAoECQkfx6fywJw11Kup+QKR\niqJAkKBWWOR4fnES0z7XfIFIRVMgSNA6er6gLY+P7qn5ApEKpECQoKT5ApHKp0CQoDN/bSq/fXcN\ndWtGEjt+KAPbNfG6JJGwoECQoFFY5Pjz4iRe/Xwz/f3XI9J8gUjlCegC8WY20sySzCzZzCYeZ7uZ\n2VT/9ngzG1BWXzN7zsw2+Nt/YGaNymeXJBRl5eRzy9+X8+rnmxk3uC2x44cqDEQqWZmBYGYRwCvA\nxUAPYJyZ9Tim2cVAjP9rPDAtgL6fAL2cc32AjcDDp7w3EpKS0rIZ/coy/r05kz9d0ZtnruyjyWMR\nDwRyhDAYSHbObXHO5QGxwJhj2owB3nLFvgUamVmr0vo65xY75wr8/b8F2pTD/kiImb82lSte/Zqc\nvEJixw/V5LGIhwIJhChgZ4nHKf7nAmkTSF+AW4AFx3txMxtvZnFmFpeRkRFAuRIKCgqLmLxwA79+\neyVdW9Zn3l1navJYxGOeTyqb2e+BAuDt4213zk0HpgP4fD5XiaVJBdm1/zD3xq5i+bYfGDuoLU+M\n0fkFIsEgkEDYBbQt8biN/7lA2lQvra+Z3QRcCpzvnNOHfRiYvzaVie/FU1jkePGavlzRXyOFIsEi\nkEBYDsSYWQeKP8zHAtce02YuMMHMYoEhQJZzLtXMMn6qr5mNBB4EznHO5ZTL3kjQyskr4MmPEold\nvpO+bRsxdWw/2p1W1+uyRKSEMgPBOVdgZhOARUAEMMM5l2Bmt/u3vwbMB0YByUAOcHNpff2/+mWg\nJvCJmQF865y7vTx3ToJDwu4s7p65ii2Zh7hjeCfuv6AL1SMCWvEsIpXIQmmkxufzubi4OK/LkAA5\n55jx9TaeXbCBRnWq8+I1/Tijc1OvyxIJO2a2wjnnK6ud55PKUjVlHjzCA++uYWlSBiO6N2fyz/vS\npG4Nr8sSkVIoEKTcfbkxg/tnr+FAbj5PjunJL4a2wz8sKCJBTIEg5SavoIjnFm3g9a+20qVFPf75\ny8F0a9nA67JEJEAKBCkXWzIOcnfsKtbtOsD1Q6P5wyU9qFVd5xaIhBIFgpwS5xxzVqTw2NwEakRW\n4y+/GMhFPVt6XZaInAQFgpy0A7n5/P6DdXy0ZjdDOjThpbH9aNWwttdlichJUiDISVmx/QfuiV1F\nalYuv72wC3cM70xENU0ci4QyBYKckMIix6tLk3np0020aliL2bedzsB2jb0uS0TKgQJBApaadZh7\nY1fz3dZ9jO7bmj9e0YsGtap7XZaIlBMFggRk4bo0HnovnvzCIp6/qi8/GxClcwtEqhgFgpTqcF4h\nf/w4kbe/20HvqIZMGduPjs3qeV2WiFQABYL8pA1pB7jrnVVsSj/I+LM78tsLu1IjUhelE6mqFAjy\nP5xzvPXNdp6ev54Gtarz1i2DObtLM6/LEpEKpkCQo+w7lMeDc9awZH0653ZtxnNX9aVpvZpelyUi\nlUCBIP/xdXIm981azf6cfB69tAc3n9FeE8ciYUSBIOQXFvHCJxt57YvNdGhal7/dPIierRt6XZaI\nVDIFQpjbvvcQd8euZs3O/Ywd1JZHL+tBnRr6ZyESjvSXH8Y+WJXCI/9KoJrBq9cNYFTvVl6XJCIe\nUiCEoezcfB79MIEPVu1icPsmvDi2H1GNdFE6kXCnQAgjRUWOj+J3M3lhEqlZh7lvRBfuPLcTkbrh\nvYigQAgbX27MYNKCDSSmHqBHqwZMGdsPX/smXpclIkFEgVDFrduVxaQFG1iWnEmbxrWZMrYfl/Vp\nTTVdqlpEjqFAqKJ27M3h+cVJzF2zm8Z1qvPopT24bmg0NSN1W0sROT4FQhWz9+AR/u+zZN7+bjsR\n1YwJ53Zm/DkddZlqESmTAqGKyMkr4I2vtvKXL7dwOL+Qq31tuXdEDC0a1PK6NBEJEQqEEJdfWMTs\nuJ28tGQTGdlHuKhnCx64qBudm+sS1SJyYhQIIco5x6KENCYvTGJL5iF87Rrz2vUDGNhOK4dE5OQo\nEELQ91v38cyC9azasZ/Ozevx+g0+RnRvrgvRicgpCeiMJDMbaWZJZpZsZhOPs93MbKp/e7yZDSir\nr5k1MbNPzGyT/7vu1F6GjXuyufXvy7n6L9+we/9hnv1ZbxbecxYX9GihMBCRU1bmEYKZRQCvABcA\nKcByM5vrnEss0exiIMb/NQSYBgwpo+9E4FPn3CR/UEwEHiq/Xas6UrMO88Lijby3MoW6NSN5cGRX\nbh7Wgdo1tIRURMpPIENGg4Fk59wWADOLBcYAJQNhDPCWc84B35pZIzNrBbQvpe8YYLi//5vA5ygQ\njpKVk8+rXyTz96+34RzcemYHfj28M43r1vC6NBGpggIJhChgZ4nHKRQfBZTVJqqMvi2cc6n+n9OA\nFgHWXOXl5hfy1jfbeGXpZg7k5nNFvyjuv7ALbRrX8bo0EanCgmJS2TnnzMwdb5uZjQfGA0RHR1dq\nXZWtsMjxwapdvLA4id1ZuZzTpRkPjexGj9YNvC5NRMJAIIGwC2hb4nEb/3OBtKleSt89ZtbKOZfq\nH15KP96LO+emA9MBfD7fcUMj1Dnn+Dwpg2cXbmBDWjZ92jTk+av6MqxzU69LE5EwEkggLAdizKwD\nxR/mY4Frj2kzF5jgnyMYAmT5P+gzSuk7F7gRmOT//uGp7kwoWr1zP5MWrOfbLftod1odXr62P5f0\nbqVVQyJS6coMBOdcgZlNABYBEcAM51yCmd3u3/4aMB8YBSQDOcDNpfX1/+pJwGwzuxXYDlxdrnsW\n5LZmHuL5RUl8vDaV0+rW4MkxPRk7KJoakbo3gYh4w4oXBoUGn8/n4uLivC7jlGRkH2HKpxuJ/X4n\nNSKr8auzOvKrsztSr2ZQTOeISBVkZiucc76y2ulTqBIUFTlW7dzP/LWpzPx+B3kFRYwbHM3d58fQ\nrH5Nr8sTEQEUCBUmv7CI77fuY+G6NBYlpJGefYTqEcZFPVvymwu70qFpXa9LFBE5igKhHOXmF7Js\nUyYLE9JYsn4P+3PyqV09guFdmzGyV0vO7dZc9yUQkaClQDhF2bn5LE3KYFFCGks3pJOTV0iDWpGM\n6N6Ci3q15OyYZrrEhIiEBAXCSdh3KI8liXtYmJDGsk2Z5BUW0bReTS7vH8XIni0Z2vE0rRYSkZCj\nQAhQatZhFifsYeG6NL7bupciB1GNanPD6e0Y2asl/aMbE6Eb14tICFMglGJr5iEWJaSxcF0aq3fu\nByCmeT3uPLczF/VsSc/WDXQCmYhUGQqEEpxzbEjL/s/KoA1p2QD0adOQBy7qykU9W+rWlCJSZYV9\nIPx4jsDihDQWJqSxfW8OZjCofRMevbQHF/ZsoauMikhYCMtA+KlzBIZ1asrt53RiRPcWOmFMRMJO\n2ATC8c4RqFW9GsO7NP/POQINa+scAREJX2ERCFM/3cRfvtjMobxC6v94jkDPlpzTRecIiIj8KCwC\noWXDWozuF8XIXi05XecIiIgcV1gEwtW+tlzta1t2QxGRMKb/KouICKBAEBERPwWCiIgACgQREfFT\nIIiICKBAEBERPwWCiIgACgQREfEz55zXNQTMzDKA7V7XcYqaApleFxFE9H78l96Lo+n9ONqpvB/t\nnHPNymoUUoFQFZhZnHPO53UdwULvx3/pvTia3o+jVcb7oSEjEREBFAgiIuKnQKh8070uIMjo/fgv\nvRdH0/txtAp/PzSHICIigI4QRETET4FQScysrZktNbNEM0sws3u8rslrZhZhZqvMbJ7XtXjNzBqZ\n2Rwz22AZ+/GsAAACaklEQVRm683sdK9r8oqZ3ef/G1lnZjPNrJbXNVUmM5thZulmtq7Ec03M7BMz\n2+T/3rgiXluBUHkKgN8453oAQ4E7zayHxzV57R5gvddFBIkpwELnXDegL2H6vphZFHA34HPO9QIi\ngLHeVlXp/g6MPOa5icCnzrkY4FP/43KnQKgkzrlU59xK/8/ZFP/BR3lblXfMrA1wCfBXr2vxmpk1\nBM4G3gBwzuU55/Z7W5WnIoHaZhYJ1AF2e1xPpXLOfQnsO+bpMcCb/p/fBC6viNdWIHjAzNoD/YHv\nvK3EUy8BDwJFXhcSBDoAGcDf/ENofzWzul4X5QXn3C7geWAHkApkOecWe1tVUGjhnEv1/5wGtKiI\nF1EgVDIzqwe8B9zrnDvgdT1eMLNLgXTn3AqvawkSkcAAYJpzrj9wiAoaEgh2/rHxMRSHZGugrpld\n721VwcUVLw2tkOWhCoRKZGbVKQ6Dt51z73tdj4fOAEab2TYgFjjPzP7pbUmeSgFSnHM/HjHOoTgg\nwtEIYKtzLsM5lw+8DwzzuKZgsMfMWgH4v6dXxIsoECqJmRnFY8TrnXMveF2Pl5xzDzvn2jjn2lM8\nYfiZcy5s/xfonEsDdppZV/9T5wOJHpbkpR3AUDOr4/+bOZ8wnWA/xlzgRv/PNwIfVsSLKBAqzxnA\nLyj+3/Bq/9cor4uSoHEX8LaZxQP9gD95XI8n/EdJc4CVwFqKP6PC6oxlM5sJfAN0NbMUM7sVmARc\nYGabKD6KmlQhr60zlUVEBHSEICIifgoEEREBFAgiIuKnQBAREUCBICIifgoEEREBFAgiIuKnQBAR\nEQD+Hyt0ui4zN6x8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x271f1a2e470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "r0=np.array([-0.093,-0.035,0.063,0.194,0.339,0.478,0.612,0.739,0.858,0.966])*1/100\n",
    "t=np.linspace(1,10,10)\n",
    "plt.close()\n",
    "plt.plot(t,r0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3. Implémentez une fonction qui applique la formule précédente et renvoie le prix de l'obligation comme une fonction des caractéristiques (M, C, N) et de la courbe de taux (tableau r)\n",
    "\n",
    "En python, il est possible de définir des fonctions personnalisées en utilisant \"def\". Par exemple :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def ma_fonction(x,y):\n",
    "    #On indique dans cette partie tout ce que fait la fonction (peut inclure des boucles, des conditions, etc.)\n",
    "    z=x+y\n",
    "    return y #valeur retournée par la fonction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#écrivez votre réponse ici\n",
    "def valeur(M,C,N,r):\n",
    "    valeur=0\n",
    "    for t in range(0,M):\n",
    "        valeur+=C*N*np.exp(-r[t]*(t+1)) #en convention exponentielle, sinon convention actuarielle 1/(1+r)^M\n",
    "    valeur+=N*np.exp(-r[t]*M)\n",
    "    return valeur"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.90791910115\n"
     ]
    }
   ],
   "source": [
    "#testez la fonction définie précédemment sur une obligation\n",
    "print(valeur(10,0,1,r0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4. Le portefeuille d'un assureur A des composé des obligations suivantes achetées au pair :\n",
    "- Obligation 1, maturité 10 ans, coupon 3.2%, nominal 50 M€ ;\n",
    "- Obligation 2, maturité 7 ans, coupon 2.8%, nominal 50 M€ ;\n",
    "- Obligation 3, maturité 5 ans, coupon 1.8%, nominal 50 M€ ;\n",
    "- Obligation 4, maturité 2 ans, coupon 1.2%, nominal 25 M€ ;\n",
    "- Obligation 5, maturité 1 ans, coupon 1%, nominal 25 M€ ;\n",
    "\n",
    "Calculez la valeur de marché du portefeuille d'actifs de A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "248.258408005\n"
     ]
    }
   ],
   "source": [
    "#écrivez votre réponse ici\n",
    "\n",
    "Portefeuille=[[10,3.2/100,50],\n",
    "              [7,2.8/100,50],\n",
    "              [5,1.8/100,50],\n",
    "              [2,1.2/100,25],\n",
    "              [1,1/100,50]]\n",
    "vm=0\n",
    "for obligation in Portefeuille:#On boucle sur les objets de portefeuille\n",
    "    vm+=valeur(obligation[0],obligation[1],obligation[2],r0)\n",
    "print(vm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "#### 5.a On suppose de la valeur de la réserve de capitalisation de l'assureur est aujourd'hui nulle. Que se passerait-il si les obligations en portefeuille étaient cédées aujourd'hui ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RKPI: 48.2584080047\n"
     ]
    }
   ],
   "source": [
    "#écrivez votre réponse ici\n",
    "\n",
    "#On doterait la réserve de capitalisation à hauteur de :\n",
    "print(\"RKPI:\",vm-200)#On retire la VNC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 5.b Décrivez le nouveau portefeuille d'actif si l'on rachetait une obligation au pair et sans risque de maturité 10 ans dont on précisera les caractéristiques ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.00093043  1.00070025  0.99811178  0.99227003  0.98319284  0.97172737\n",
      "  0.95806467  0.94259365  0.92568618  0.9079191 ]\n",
      "Taux de coupon:  0.951131409288 % , VM = N = 248.258408005\n"
     ]
    }
   ],
   "source": [
    "#écrivez votre réponse ici\n",
    "\n",
    "#On calcule les zero-coupons associés à la courbe de taux r0:\n",
    "#astuce:il est possible de donner à une fonction telle que exponentielle un tableau de valeur, ou un produit \n",
    "#terme à terme de tableaux de valeurs. On obtient alors en sortie la fonction appliquée à chaque terme du tableau\n",
    "ZC0=np.exp(-np.linspace(1,10,10)*r0)\n",
    "\n",
    "print(ZC0)\n",
    "\n",
    "#Pour rappel, VM_oblig=Sum_t C*N*ZC(t) + N ZC(M), c'est à dire\n",
    "#C=(VM-N ZC(M))/(N Sum_t ZC(t))\n",
    "#Si l'obligation est achetée au pair, alors vm=N=248,...\n",
    "C=(1-ZC0[9])/(ZC0.sum())\n",
    "print(\"Taux de coupon: \",C*100,\"%\", \", VM = N =\",vm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### On suppose que la participation aux bénéfices prévue contractuellement inclût 90 % des produits des actifs en représentation des provisions mathématiques et les coupons et nominaux reçus sont réinvestis en trésorerie, laquelle est revalorisée d'année en année au taux sans risque calculé à partir de la courbe des taux fournie.\n",
    "\n",
    "#### 6. Calculez les produits financiers entrant dans la participation aux bénéfices associés avec les deux stratégies d'investissement ainsi que la part de produits financiers revenant à l'assureur.\n",
    "\n",
    "##### 6.a stratégie 1 : conservation des actifs du portefeuille initial jusqu'à l'échéance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Produits financiers 50.4210162529\n",
      "Produits financiers partagés 45.3789146276\n",
      "Produits financiers assureur 5.04210162529\n"
     ]
    }
   ],
   "source": [
    "#écrivez votre réponse ici\n",
    "\n",
    "pfi=0\n",
    "cash=0\n",
    "\n",
    "for t in range(0,10):\n",
    "    if t>0:\n",
    "        cash*=ZC0[t-1]/ZC0[t]\n",
    "        pfi+=cash*(ZC0[t-1]/ZC0[t]-1)\n",
    "\n",
    "    for oblig in Portefeuille:\n",
    "        if t<=oblig[0]:#t<=Maturité\n",
    "            pfi+=oblig[1]*oblig[2]#coupon * nominal\n",
    "            cash+=oblig[1]*oblig[2]\n",
    "        if t==oblig[0]:#==Maturité\n",
    "            cash+=oblig[2]#nominal\n",
    "\n",
    "            \n",
    "print(\"Produits financiers\",pfi)\n",
    "print(\"Produits financiers partagés\",pfi*0.9)\n",
    "print(\"Produits financiers assureur\",pfi*0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 6.b stratégie 2 : vente de l'ensemble des actifs puis conservation jusqu'à l'échéance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Produits financiers 25.2037003232\n",
      "Produits finannciers partagés 18.2739674142\n",
      "Produits financiers assureur 6.929732909\n"
     ]
    }
   ],
   "source": [
    "#écrivez votre réponse ici\n",
    "\n",
    "pfi=0\n",
    "cash=0\n",
    "\n",
    "Portefeuille2=[[10,C,vm]]\n",
    "\n",
    "for t in range(0,10):\n",
    "    if t>0:\n",
    "        cash*=ZC0[t-1]/ZC0[t]\n",
    "        pfi+=cash*(ZC0[t-1]/ZC0[t]-1)\n",
    "    for oblig in Portefeuille2:\n",
    "        if t<=oblig[0]:#t<=Maturité\n",
    "            pfi+=oblig[1]*oblig[2]#coupon * nominal\n",
    "            cash+=oblig[1]*oblig[2]\n",
    "        if t==oblig[0]:#==Maturité\n",
    "            cash+=oblig[2]#nominal\n",
    "\n",
    "            \n",
    "print(\"Produits financiers\",pfi)\n",
    "#On partage seulement les produits financiers en face de la PM (le total des provisions étant constitué \n",
    "#de la PM et de la réserve de capitalisation)\n",
    "print(\"Produits finannciers partagés\",pfi*0.9*200/vm)\n",
    "print(\"Produits financiers assureur\",pfi*(1-0.9*200/vm))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 6.c Commentez : sans la réserve de capitalisation, le montant de produits financiers in fine partagés avec les assurés aurait-il été inférieur à celui partagé avec celle-ci ? Quel est l'objet de la réserve de capitalisation ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Produits financiers 73.4621083278\n",
      "Produits financiers partagés 53.2637730391\n",
      "Produits financiers assureur 20.1983352887\n"
     ]
    }
   ],
   "source": [
    "#écrivez votre réponse ici\n",
    "\n",
    "pfi=vm-200\n",
    "cash=0\n",
    "\n",
    "Portefeuille2=[[10,C,vm]]\n",
    "\n",
    "for t in range(0,10):\n",
    "    if t>0:\n",
    "        cash*=ZC0[t-1]/ZC0[t]\n",
    "        pfi+=cash*(ZC0[t-1]/ZC0[t]-1)\n",
    "    for oblig in Portefeuille2:\n",
    "        if t<=oblig[0]:#t<=Maturité\n",
    "            pfi+=oblig[1]*oblig[2]#coupon * nominal\n",
    "            cash+=oblig[1]*oblig[2]\n",
    "        if t==oblig[0]:#==Maturité\n",
    "            cash+=oblig[2]#nominal\n",
    "\n",
    "            \n",
    "print(\"Produits financiers\",pfi)\n",
    "#On partage seulement les produits financiers en face de la PM (le total des provisions étant constitué \n",
    "#de la PM et de la réserve de capitalisation)\n",
    "print(\"Produits financiers partagés\",pfi*0.9*200/vm)\n",
    "print(\"Produits financiers assureur\",pfi*(1-0.9*200/vm))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En l'absence de réserve de capitalisation, les montants partagés au titre de la PB ainsi que les produits financiers conservés par l'assureur auraient été nettement plus importants, ce qui aurait fait peser le risque que les produits financiers conservés par l'assureur soient distribués sous forme de dividendes. La réserve de capitalisation conduit à conserver les richesses obligataires et à limiter l'intérêt de cessions brutales de titres obligataires en période de taux bas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}