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   "id": "38c6b854-4605-4f99-a6f0-9a0692b2e025",
   "metadata": {},
   "outputs": [],
   "source": [
    "from rateslib import *"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a31e9be-2101-4a15-9efd-2362a240915e",
   "metadata": {},
   "source": [
    "# Constructing Curves from (CC) Zero Rates\n",
    "\n",
    "A common type of curve definition in quantitative analysis is to construct a `Curve` from continuously compounded zero coupon rates.\n",
    "\n",
    "There is a one-to-one equivalence relation between discount factors (DFs) and cc zero rates: "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7785e60-76eb-4b5a-96e2-0ebdfbca2d2e",
   "metadata": {},
   "source": [
    "$$\n",
    "v = exp ( - d \\bar{r} )\n",
    "$$\n",
    "where $d$ is the day count fraction (DCF) measured between 'today' and the 'maturity' date of the rate, using the ``convention`` assocoiated with the rates. \n",
    "\n",
    "In **rateslib** a ``Curve`` is defined by DF nodes, so if one wants to construct a ``Curve`` from zero rates either these have to be manually converted to DFs or the ``Solver`` can be used to determine them via calibration."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f58cb040-c516-4ae0-9eb4-9bece0d4315f",
   "metadata": {},
   "source": [
    "### Direct conversion\n",
    "\n",
    "Writing a manual conversion function is not difficult. We just need to use the above formula directly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6105c526-0c8d-474b-acc0-bc574c472d63",
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   "source": [
    "def curve_from_zero_rates(nodes, convention, calendar):\n",
    "    start = list(nodes.keys())[0]\n",
    "    nodes_ = {\n",
    "        **{date: dual_exp(-dcf(start, date, convention=convention) * r/100.0) \n",
    "           for (date,r) in list(nodes.items())}\n",
    "    }\n",
    "    return Curve(nodes=nodes_, convention=convention, calendar=calendar)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bdd95731-050d-4acd-8c47-a42c44ae8529",
   "metadata": {},
   "outputs": [],
   "source": [
    "curve = curve_from_zero_rates(\n",
    "    {dt(2024, 7, 15): 0.0, dt(2025, 7, 15): 5.00, dt(2026, 7, 15): 4.65},\n",
    "    convention=\"act365f\",\n",
    "    calendar=\"nyc\",\n",
    ")\n",
    "curve.plot(\"1d\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "436743a0-4444-4f2c-818a-fc938df2f7b5",
   "metadata": {},
   "outputs": [],
   "source": [
    "curve.nodes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4face5a4-0e12-4632-bdb0-bbbcfa2fbd20",
   "metadata": {},
   "source": [
    "If cubic spline interpolation was required this could be included within the ``curve_from_zero_rates`` function using the ``t`` argument from a ``Curve``."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab2249f1-4730-4acd-87b6-8dd7abd10e72",
   "metadata": {},
   "source": [
    "### Using a Solver"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2bc3a56-ff37-468a-a67d-ddbb58f6d401",
   "metadata": {},
   "source": [
    "The advantage of using a ``Solver`` is that the ``Curve`` can be calibrated directly without a manually written construction function and derivatives and risk sensitivities are automatically obtained. The easiest way to directly specify this is to use the ``Value`` class. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "17b52a8f-eaf3-4864-84f8-bc592c0529be",
   "metadata": {},
   "outputs": [],
   "source": [
    "curve = Curve(\n",
    "    {dt(2024, 7, 15): 1.0, dt(2025, 7, 15): 1.0, dt(2026, 7, 15): 1.0},\n",
    "    convention=\"act365f\", calendar=\"nyc\", id=\"ccz_curve\"\n",
    ")\n",
    "solver = Solver(\n",
    "    curves=[curve],\n",
    "    instruments=[\n",
    "        Value(dt(2025, 7, 15), \"act365f\" ,metric=\"cc_zero_rate\", curves=curve),\n",
    "        Value(dt(2026, 7, 15), \"act365f\" ,metric=\"cc_zero_rate\", curves=curve),\n",
    "    ],\n",
    "    s=[5.0, 4.65]  # <- Same rates to observe same derived discount factors\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "249fd6d5-7714-4b7c-9812-1f2ddfee09f9",
   "metadata": {},
   "outputs": [],
   "source": [
    "curve.plot(\"1d\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "82bd302e-0439-4c5f-b717-8ad61b2be8fe",
   "metadata": {},
   "outputs": [],
   "source": [
    "curve.nodes"
   ]
  }
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