{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "bond_pricing2.ipynb",
"provenance": [],
"collapsed_sections": [],
"authorship_tag": "ABX9TyPIvQI3UOX77ZiSaAgsAexX",
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"![\"Open](\"https://colab.research.google.com/assets/colab-badge.svg\")
"
]
},
{
"cell_type": "markdown",
"source": [
"# Bond Pricing\n",
"$$price \\ of \\ a \\ coupon \\ bond = \\Sigma \\frac{Coupon}{(1+YTM)^t} + \\frac{Par \\ Value}{(1 + YTM)^t} \n",
"$$"
],
"metadata": {
"id": "U7ic90H8WFEA"
}
},
{
"cell_type": "code",
"source": [
"def bondprice(ytm, period, par, coupon):\n",
" price_bond = par*coupon/2*(1-(1+ytm/2)**(-2*period))/(ytm/2) + par/(1+ytm/2)**(2*period)\n",
" return price_bond"
],
"metadata": {
"id": "12VmbHwzJe-H"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [
"# create a list of YTMs from 0.01 to 0.50\n",
"ytm_list = [x/100 for x in range(1, 51)]\n",
"\n",
"print(ytm_list)"
],
"metadata": {
"id": "Qouu1luRiN6h",
"outputId": "397c1aaa-8bf9-4318-fdee-82eb912cfb5e",
"colab": {
"base_uri": "https://localhost:8080/"
}
},
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"[0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1, 0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2, 0.21, 0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.3, 0.31, 0.32, 0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39, 0.4, 0.41, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5]\n"
]
}
]
},
{
"cell_type": "code",
"source": [
"# create a list of bond prices\n",
"output = []\n",
"for element in ytm_list:\n",
" output.append(bondprice(ytm=element, period=50, par=1000, coupon=0.10))\n",
"\n",
"print(output)"
],
"metadata": {
"id": "k-ffCLqpiN1_",
"outputId": "280f6129-b470-4f41-ee35-2d034ec8f66e",
"colab": {
"base_uri": "https://localhost:8080/"
}
},
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"[4534.419014459948, 3521.155150683525, 2806.8646283949465, 2292.9505492033823, 1915.3526316119737, 1631.9781067665274, 1414.831381030019, 1245.0499899715198, 1109.7492637116093, 1000.0, 909.5208030589646, 833.82453770479, 769.655601135766, 714.6149858198504, 666.907675144676, 625.170473045163, 588.3532379676428, 555.6359391991529, 526.3699991720615, 500.0362828579507, 476.2146277727387, 454.56146710237505, 434.7931946198022, 416.6736508322453, 400.0046014955424, 384.61841363639905, 370.3723633323073, 357.14416822330287, 344.82844880189464, 333.3339010409298, 322.5810189784025, 312.5002463053128, 303.03046544351673, 294.11775424681923, 285.7143565227709, 277.7778246019509, 270.27030126779437, 263.1579152805246, 256.4102700417318, 250.00000905600507, 243.90244504822635, 238.09524210726335, 232.5581422104622, 227.27272905939245, 222.22222341688865, 217.39130514772208, 212.76595798310893, 208.3333336933925, 204.081632895127, 200.00000016296286]\n"
]
}
]
},
{
"cell_type": "code",
"source": [
"from matplotlib import pyplot as plt\n",
"plt.plot(ytm_list, output)\n",
"plt.show()"
],
"metadata": {
"id": "OphzxslYiNzZ",
"outputId": "18061a60-0ede-4592-f404-6cd766c9cb11",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 265
}
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
""
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"source": [
""
],
"metadata": {
"id": "ITqZJHWX1G9E"
},
"execution_count": null,
"outputs": []
}
]
}