This is the Gist the For Python Quants Bootcamp in London 22. November 2017 (http://fpq.io)
This second boocamp day is about Financial Data Science.
http://pyalgo.tpq.io | http://certificate.tpq.io
| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "<img src='http://hilpisch.com/tpq_logo.png' width=\"300px\" align=\"right\">" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "# FPQ Bootcamp — Day 2" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "**NumPy & pandas**" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## NumPy" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "import numpy as np" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Regular Arrays" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 2, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "a = np.arange(15)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 3, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14])" | |
| ] | |
| }, | |
| "execution_count": 3, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "a" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 4, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "dtype('int64')" | |
| ] | |
| }, | |
| "execution_count": 4, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "a.dtype" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 5, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "120" | |
| ] | |
| }, | |
| "execution_count": 5, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "a.nbytes" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 6, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array([ 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28])" | |
| ] | |
| }, | |
| "execution_count": 6, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "2 * a " | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 7, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array([ 0. , 0.5, 1. , 1.5, 2. , 2.5, 3. , 3.5, 4. , 4.5, 5. ,\n", | |
| " 5.5, 6. , 6.5, 7. ])" | |
| ] | |
| }, | |
| "execution_count": 7, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "a * 0.5" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 8, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "dtype('float64')" | |
| ] | |
| }, | |
| "execution_count": 8, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "(a * 0.5).dtype" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 9, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array([ 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144,\n", | |
| " 169, 196])" | |
| ] | |
| }, | |
| "execution_count": 9, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "a ** 2" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 10, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array([ 1, 2, 4, 8, 16, 32, 64, 128, 256,\n", | |
| " 512, 1024, 2048, 4096, 8192, 16384])" | |
| ] | |
| }, | |
| "execution_count": 10, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "2 ** a" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 11, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "105" | |
| ] | |
| }, | |
| "execution_count": 11, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "a.sum()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 12, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "7.0" | |
| ] | |
| }, | |
| "execution_count": 12, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "a.mean()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 13, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "14" | |
| ] | |
| }, | |
| "execution_count": 13, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "a.max()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 14, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array([ 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78,\n", | |
| " 91, 105])" | |
| ] | |
| }, | |
| "execution_count": 14, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "a.cumsum()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 15, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "105" | |
| ] | |
| }, | |
| "execution_count": 15, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "np.sum(a)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 16, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array([ 0. , 1. , 1.41421356, 1.73205081, 2. ,\n", | |
| " 2.23606798, 2.44948974, 2.64575131, 2.82842712, 3. ,\n", | |
| " 3.16227766, 3.31662479, 3.46410162, 3.60555128, 3.74165739])" | |
| ] | |
| }, | |
| "execution_count": 16, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "np.sqrt(a)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 17, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array([ 0. , 1. , 1.41421356, 1.73205081, 2. ,\n", | |
| " 2.23606798, 2.44948974, 2.64575131, 2.82842712, 3. ,\n", | |
| " 3.16227766, 3.31662479, 3.46410162, 3.60555128, 3.74165739])" | |
| ] | |
| }, | |
| "execution_count": 17, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "a ** 0.5" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 18, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "import math" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 19, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "3.1622776601683795" | |
| ] | |
| }, | |
| "execution_count": 19, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "math.sqrt(10)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 20, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "2.23606797749979" | |
| ] | |
| }, | |
| "execution_count": 20, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "math.sqrt(a[5])" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 21, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "3.1622776601683795" | |
| ] | |
| }, | |
| "execution_count": 21, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "np.sqrt(10)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 22, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "CPU times: user 10.7 s, sys: 244 ms, total: 10.9 s\n", | |
| "Wall time: 11.1 s\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "%time res = [np.sqrt(n) for n in range(10000000)]" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 23, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "CPU times: user 1.53 s, sys: 191 ms, total: 1.72 s\n", | |
| "Wall time: 1.73 s\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "%time res = [math.sqrt(n) for n in range(10000000)]" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 24, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "CPU times: user 156 ms, sys: 125 ms, total: 281 ms\n", | |
| "Wall time: 280 ms\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "%time res = np.sqrt(np.arange(10000000))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 25, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "CPU times: user 1.24 s, sys: 12.5 ms, total: 1.25 s\n", | |
| "Wall time: 1.26 s\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "%%time\n", | |
| "s = 0\n", | |
| "for n in range(10000000):\n", | |
| " s += n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 26, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "49999995000000" | |
| ] | |
| }, | |
| "execution_count": 26, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "s" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 27, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "CPU times: user 26.4 ms, sys: 36.9 ms, total: 63.3 ms\n", | |
| "Wall time: 62.5 ms\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "%time s = np.sum(np.arange(10000000))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 28, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "49999995000000" | |
| ] | |
| }, | |
| "execution_count": 28, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "s" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 29, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "CPU times: user 1.22 s, sys: 12.1 ms, total: 1.23 s\n", | |
| "Wall time: 1.24 s\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "%%time\n", | |
| "s = 0\n", | |
| "N = range(10000000)\n", | |
| "for n in N:\n", | |
| " s += n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 30, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "import sys" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 31, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "48" | |
| ] | |
| }, | |
| "execution_count": 31, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "sys.getsizeof(N)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 32, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "49999995000000" | |
| ] | |
| }, | |
| "execution_count": 32, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "s" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 33, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "CPU times: user 20.8 ms, sys: 10 ms, total: 30.8 ms\n", | |
| "Wall time: 29.2 ms\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "%%time\n", | |
| "N = np.arange(10000000)\n", | |
| "s = np.sum(N)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 34, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "49999995000000" | |
| ] | |
| }, | |
| "execution_count": 34, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "s" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 35, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "80000000" | |
| ] | |
| }, | |
| "execution_count": 35, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "N.nbytes" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Dynamic Compiling" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 36, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# !conda install -y numba" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 37, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "import numba as nb" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 38, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "def calculate_sum(N):\n", | |
| " s = 0\n", | |
| " g = range(N)\n", | |
| " for n in g:\n", | |
| " s += n\n", | |
| " return s" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 39, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "49999995000000\n", | |
| "CPU times: user 721 ms, sys: 11.4 ms, total: 732 ms\n", | |
| "Wall time: 779 ms\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "%%time\n", | |
| "s = calculate_sum(10000000)\n", | |
| "print(s)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 40, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "calculate_sum_nb = nb.jit(calculate_sum)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 41, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "49999995000000\n", | |
| "CPU times: user 95.9 ms, sys: 9.98 ms, total: 106 ms\n", | |
| "Wall time: 108 ms\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "%%time\n", | |
| "s = calculate_sum_nb(10000000)\n", | |
| "print(s)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 42, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "49999995000000\n", | |
| "CPU times: user 598 µs, sys: 852 µs, total: 1.45 ms\n", | |
| "Wall time: 1.02 ms\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "%%time\n", | |
| "s = calculate_sum_nb(10000000)\n", | |
| "print(s)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 43, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" | |
| ] | |
| }, | |
| "execution_count": 43, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "g = 10 ** 100\n", | |
| "g" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 44, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "333" | |
| ] | |
| }, | |
| "execution_count": 44, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "g.bit_length()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Working with Random Numbers" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 45, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "0.274925264690843" | |
| ] | |
| }, | |
| "execution_count": 45, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "np.random.random()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 46, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array([ 0.84766882, 0.07038037, 0.8078534 , 0.3994468 , 0.02690323,\n", | |
| " 0.20180815, 0.99278682, 0.27236966, 0.10977992, 0.26614816])" | |
| ] | |
| }, | |
| "execution_count": 46, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "np.random.random(10)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 47, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array([[ 0.2147967 , 0.34640817, 0.15251117, 0.72465723, 0.1109021 ],\n", | |
| " [ 0.36264475, 0.31540696, 0.50985658, 0.26918757, 0.99755769],\n", | |
| " [ 0.32147805, 0.797915 , 0.60654738, 0.26924871, 0.83212849],\n", | |
| " [ 0.24037098, 0.56995854, 0.0415754 , 0.8300432 , 0.05628744],\n", | |
| " [ 0.56273511, 0.68090745, 0.66763097, 0.45292436, 0.6870939 ]])" | |
| ] | |
| }, | |
| "execution_count": 47, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "np.random.random((5, 5))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 48, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "rn = np.random.random((1000, 2))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 49, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array([[ 0.46271545, 0.99327145],\n", | |
| " [ 0.47759658, 0.53334094],\n", | |
| " [ 0.66102529, 0.41721354],\n", | |
| " [ 0.52940254, 0.42966526],\n", | |
| " [ 0.31873786, 0.43665211],\n", | |
| " [ 0.20808885, 0.30438634],\n", | |
| " [ 0.4945814 , 0.32229595],\n", | |
| " [ 0.69679088, 0.23451341],\n", | |
| " [ 0.78259816, 0.4048634 ],\n", | |
| " [ 0.06057083, 0.87552202]])" | |
| ] | |
| }, | |
| "execution_count": 49, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "rn[:10]" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 50, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "(1000, 2)" | |
| ] | |
| }, | |
| "execution_count": 50, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "rn.shape" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 51, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "from pylab import plt\n", | |
| "plt.style.use('seaborn')\n", | |
| "%matplotlib inline" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 52, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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X6t+ITZycRHfXlPAtZPpG2vZ2OsBrr/l1TCgcvSNq02u0+KmcE4VmEzh/3viWSCvGK4Dt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\n2IliGIZhGIZRgJ0ohmEYhmEYBf5/pT4EDq8eQ+kAAAAASUVORK5CYII=\n", | |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x112ca0400>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "plt.figure(figsize=(10, 6))\n", | |
| "plt.plot(rn[:, 0], rn[:, 1], 'r.');" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 53, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "sn = np.random.standard_normal((1000, 2))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 54, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array([[-0.32995016, -0.77809234],\n", | |
| " [ 0.22285595, 1.63106726],\n", | |
| " [ 1.13396848, 0.66732563],\n", | |
| " [-0.99927244, -0.02772084],\n", | |
| " [-1.11198746, 0.7320291 ]])" | |
| ] | |
| }, | |
| "execution_count": 54, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "sn[:5]" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 55, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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P3Y/aQw+3NLHWrAUGBrA0Ng7p+R9r5zh7xgwz+h0zjhHi5V10jW+axpXlWENv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\n", | |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x112ca00b8>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "plt.figure(figsize=(10, 6))\n", | |
| "plt.plot(sn[:, 0], sn[:, 1], 'r.');" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 56, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "-0.0027694062138300841" | |
| ] | |
| }, | |
| "execution_count": 56, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "sn.mean()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 57, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "1.0038321493074167" | |
| ] | |
| }, | |
| "execution_count": 57, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "sn.std()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 58, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "sn -= sn.mean()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 59, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "sn /= sn.std()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 60, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "-8.8817841970012525e-18" | |
| ] | |
| }, | |
| "execution_count": 60, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "sn.mean()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 61, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "1.0" | |
| ] | |
| }, | |
| "execution_count": 61, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "sn.std()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 62, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "(1000, 2)" | |
| ] | |
| }, | |
| "execution_count": 62, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "sn.shape" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 63, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "(2000,)" | |
| ] | |
| }, | |
| "execution_count": 63, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "sn.flatten().shape" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 64, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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AWHYzB6qqOi/JLyT5+uTQrUlu7u5PVtXPJ7khyYfHS4T5cPsDAM6VkUt+70ny80n++2T/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\nDBKoAAAGCVQAAIMEKgCAQf8XI4JiOk8UC0YAAAAASUVORK5CYII=\n", | |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x113103dd8>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "plt.figure(figsize=(10, 6))\n", | |
| "plt.hist(sn.flatten(), bins=35);" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 65, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "(1000, 2)" | |
| ] | |
| }, | |
| "execution_count": 65, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "sn.cumsum(axis=0).shape" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 66, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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hDl8XedYc3EEPFr05IcozHug0fcfc3rhbraVanFXOlSWbmZcxe/TH1ur44MLbeN+CmzH0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\nIiIap/8fYq0VmzgaUC0AAAAASUVORK5CYII=\n", | |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x11319a080>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "plt.figure(figsize=(10, 6))\n", | |
| "plt.plot(sn.cumsum(axis=0));" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Static Monte Carlo Simulation " | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Difference equation for **geometric Brownian motion** (two dates only):\n", | |
| "\n", | |
| "$$\n", | |
| "S_T = S_0 \\exp \\left( \\left(r - \\frac{\\sigma^2}{2} \\right) T + \\sigma \\sqrt{T} z \\right)\n", | |
| "$$\n", | |
| "\n", | |
| "$S_T$ is the stock price at the future time $T$, $r$ is the risk-free short rate, $\\sigma$ the volatility factor and $z$ is a standard-normally distributed random variate." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 67, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "S0 = 100.\n", | |
| "r = 0.05\n", | |
| "sigma = 0.2\n", | |
| "T = 1.0" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 68, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "z = np.random.standard_normal(50000)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 69, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "CPU times: user 1.81 ms, sys: 1.95 ms, total: 3.76 ms\n", | |
| "Wall time: 2.04 ms\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "%time ST = S0 * np.exp((r - 0.5 * sigma ** 2) * T + sigma * math.sqrt(T) * z)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 70, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array([ 141.82347506, 83.49021236, 80.50175843, 143.65615362,\n", | |
| " 109.2976402 , 117.04141817, 101.90590852, 101.33439737,\n", | |
| " 76.01764776, 84.03648293])" | |
| ] | |
| }, | |
| "execution_count": 70, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "ST[:10]" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 71, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "105.01019651250633" | |
| ] | |
| }, | |
| "execution_count": 71, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "ST.mean()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 72, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "105.12710963760242" | |
| ] | |
| }, | |
| "execution_count": 72, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "S0 * math.exp(r * T)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 73, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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e5eX98x4CsMW2633t/DFLPWapx6xFqcdmvl24+p6q/UmeTPLUdHlt+3p9z+jYsac3MaTF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\n", | |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x11319a748>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "plt.figure(figsize=(10, 6))\n", | |
| "plt.hist(ST, bins=35)\n", | |
| "plt.axvline(S0 * math.exp(r * T), color='r');" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Pricing European Options" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 74, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "K = 105." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 75, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "CPU times: user 362 µs, sys: 85 µs, total: 447 µs\n", | |
| "Wall time: 293 µs\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "%time h = np.maximum(ST - K, 0)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 76, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "C0 = math.exp(-r * T) * h.mean()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 77, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "7.9708430619562982" | |
| ] | |
| }, | |
| "execution_count": 77, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "C0" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 78, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "CPU times: user 626 µs, sys: 328 µs, total: 954 µs\n", | |
| "Wall time: 585 µs\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "%time h = np.maximum(K - ST, 0)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 79, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "P0 = math.exp(-r * T) * h.mean()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 80, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "7.9611438392329985" | |
| ] | |
| }, | |
| "execution_count": 80, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "P0" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Dynamic Monte Carlo Simulation" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Difference equation for **geometric Brownian motion** (multiple dates):\n", | |
| "\n", | |
| "$$\n", | |
| "S_{t} = S_{t - \\Delta t} \\exp \\left( \\left(r - \\frac{\\sigma^2}{2} \\right) \\Delta t + \\sigma \\sqrt{\\Delta t} z \\right)\n", | |
| "$$\n", | |
| "\n", | |
| "$S_t$ is the stock price at some point in time $t \\in \\{\\Delta t, 2\\Delta t, ..., T\\}$, $r$ is the risk-free short rate, $\\sigma$ the volatility factor and $z$ is a standard-normally distributed random variate." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 81, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "S0 = 36.\n", | |
| "r = 0.06\n", | |
| "sigma = 0.2\n", | |
| "T = 1.0" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 82, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "M = 50\n", | |
| "dt = T / M\n", | |
| "I = 50000" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 83, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "rn = np.random.standard_normal((M + 1, I))\n", | |
| "rn -= rn.mean()\n", | |
| "rn /= rn.std()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 84, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "S = np.zeros_like(rn)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 85, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "(51, 50000)" | |
| ] | |
| }, | |
| "execution_count": 85, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "S.shape" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 86, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "S[0] = S0" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 87, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "CPU times: user 37.2 ms, sys: 1.4 ms, total: 38.6 ms\n", | |
| "Wall time: 40.5 ms\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "%%time\n", | |
| "for t in range(1, M + 1):\n", | |
| " S[t] = S[t - 1] * np.exp((r - 0.5 * sigma ** 2) * dt +\n", | |
| " sigma * math.sqrt(dt) * rn[t])" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 88, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array([[ 36. , 36. ],\n", | |
| " [ 35.81792219, 34.11253025],\n", | |
| " [ 36.01497877, 33.88574314],\n", | |
| " [ 38.13475829, 34.17239717],\n", | |
| " [ 37.0167213 , 33.84742317],\n", | |
| " [ 36.34741172, 33.77539808],\n", | |
| " [ 37.90933671, 34.29205614],\n", | |
| " [ 36.22572683, 35.65718066],\n", | |
| " [ 34.17594619, 35.73370101],\n", | |
| " [ 35.7834213 , 34.95090449]])" | |
| ] | |
| }, | |
| "execution_count": 88, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "S[:10, :2]" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 89, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "38.226890393253484" | |
| ] | |
| }, | |
| "execution_count": 89, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "S[-1].mean()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 90, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
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m8+DbmHQmLm/ZxF+u+yPuXDpWM6vUgbcYmqbx1tA2jDoj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whzdsokubwNCci6nscLCvfpAd1QNsOdjL3rpB6jpstPQ66B3xMOLw4fYGCYVF5DIBhVx2rPaa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\n0ZRQmjqMbN5eQFldF6H+btw3AjWNRookSbxV8gG7avYRoQkl2S+RHeWf4e/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SjT/O/PVp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| |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x11807f550>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "plt.figure(figsize=(10, 6))\n", | |
| "plt.plot(S[:, :15])\n", | |
| "plt.plot(S.mean(axis=1), 'r--', lw=3);" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 91, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "K = 40." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 92, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "h = np.maximum(K - S[-1], 0)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 93, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "P0 = math.exp(-r * T) * h.mean()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 94, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "3.838386477437405" | |
| ] | |
| }, | |
| "execution_count": 94, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "P0" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## American Option Valuation " | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 95, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "h = np.maximum(K - S, 0)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 96, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "(51, 50000)" | |
| ] | |
| }, | |
| "execution_count": 96, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "h.shape" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 97, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "V = h[-1].copy()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 98, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "df = math.exp(-r * dt)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 99, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "0.9988007197120864" | |
| ] | |
| }, | |
| "execution_count": 99, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "df" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 100, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "CPU times: user 761 ms, sys: 13.9 ms, total: 775 ms\n", | |
| "Wall time: 408 ms\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "%%time\n", | |
| "V = h[-1].copy()\n", | |
| "for t in range(M - 1, 0, -1):\n", | |
| " reg = np.polyfit(S[t], V * df, 5)\n", | |
| " C = np.polyval(reg, S[t])\n", | |
| " V = np.where(h[t] > C, h[t], V * df)\n", | |
| "V0 = V.mean() * df" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 101, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "4.465561761140453" | |
| ] | |
| }, | |
| "execution_count": 101, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "V0" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "<img src='http://hilpisch.com/tpq_logo.png' width=\"300px\" align=\"right\">" | |
| ] | |
| } | |
| ], | |
| "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": "3.6.3" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 2 | |
| } |
(Sorry about that, but we can’t show files that are this big right now.)
(Sorry about that, but we can’t show files that are this big right now.)
