Commit d716f8a8 authored by Erik Tollerud's avatar Erik Tollerud Committed by Martín Gaitán

Add a pure-python version of the Black-Scholes function for comparison with the Cython equivalent

parent 4e9e533c
{
"metadata": {
"name": "",
"signature": "sha256:72d92961ad5ed0edc2b71d8b835c31c35d82d67c6f7f2360d56c2c708f1d9767"
"name": "Cython Magics",
"signature": "sha256:c357b93e9480d6347c6677862bf43750745cef4b30129c5bc53cb879a19d4074"
},
"nbformat": 3,
"nbformat_minor": 0,
......@@ -35,7 +35,7 @@
"cell_type": "code",
"collapsed": false,
"input": [
"%load_ext cython"
"%load_ext cythonmagic"
],
"language": "python",
"metadata": {},
......@@ -164,11 +164,11 @@
"from libc.math cimport exp, sqrt, pow, log, erf\n",
"\n",
"@cython.cdivision(True)\n",
"cdef double std_norm_cdf(double x) nogil:\n",
"cdef double std_norm_cdf_cy(double x) nogil:\n",
" return 0.5*(1+erf(x/sqrt(2.0)))\n",
"\n",
"@cython.cdivision(True)\n",
"def black_scholes(double s, double k, double t, double v,\n",
"def black_scholes_cy(double s, double k, double t, double v,\n",
" double rf, double div, double cp):\n",
" \"\"\"Price an option using the Black-Scholes model.\n",
" \n",
......@@ -184,8 +184,8 @@
" with nogil:\n",
" d1 = (log(s/k)+(rf-div+0.5*pow(v,2))*t)/(v*sqrt(t))\n",
" d2 = d1 - v*sqrt(t)\n",
" optprice = cp*s*exp(-div*t)*std_norm_cdf(cp*d1) - \\\n",
" cp*k*exp(-rf*t)*std_norm_cdf(cp*d2)\n",
" optprice = cp*s*exp(-div*t)*std_norm_cdf_cy(cp*d1) - \\\n",
" cp*k*exp(-rf*t)*std_norm_cdf_cy(cp*d2)\n",
" return optprice"
],
"language": "python",
......@@ -197,7 +197,7 @@
"cell_type": "code",
"collapsed": false,
"input": [
"black_scholes(100.0, 100.0, 1.0, 0.3, 0.03, 0.0, -1)"
"black_scholes_cy(100.0, 100.0, 1.0, 0.3, 0.03, 0.0, -1)"
],
"language": "python",
"metadata": {},
......@@ -213,11 +213,76 @@
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For comparison, the same code is implemented here in pure python."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import exp, sqrt, pow, log, erf\n",
"\n",
"def std_norm_cdf_py(x):\n",
" return 0.5*(1+erf(x/sqrt(2.0)))\n",
"\n",
"def black_scholes_py(s, k, t, v, rf, div, cp):\n",
" \"\"\"Price an option using the Black-Scholes model.\n",
" \n",
" s : initial stock price\n",
" k : strike price\n",
" t : expiration time\n",
" v : volatility\n",
" rf : risk-free rate\n",
" div : dividend\n",
" cp : +1/-1 for call/put\n",
" \"\"\"\n",
" d1 = (log(s/k)+(rf-div+0.5*pow(v,2))*t)/(v*sqrt(t))\n",
" d2 = d1 - v*sqrt(t)\n",
" optprice = cp*s*exp(-div*t)*std_norm_cdf_py(cp*d1) - \\\n",
" cp*k*exp(-rf*t)*std_norm_cdf_py(cp*d2)\n",
" return optprice"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 8
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"black_scholes_py(100.0, 100.0, 1.0, 0.3, 0.03, 0.0, -1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 9,
"text": [
"10.327861752731728"
]
}
],
"prompt_number": 9
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Below we see the runtime of the two functions: the Cython version is nearly a factor of 10 faster."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%timeit black_scholes(100.0, 100.0, 1.0, 0.3, 0.03, 0.0, -1)"
"%timeit black_scholes_cy(100.0, 100.0, 1.0, 0.3, 0.03, 0.0, -1)"
],
"language": "python",
"metadata": {},
......@@ -226,11 +291,30 @@
"output_type": "stream",
"stream": "stdout",
"text": [
"1000000 loops, best of 3: 821 ns per loop\n"
"1000000 loops, best of 3: 319 ns per loop\n"
]
}
],
"prompt_number": 8
"prompt_number": 10
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%timeit black_scholes_py(100.0, 100.0, 1.0, 0.3, 0.03, 0.0, -1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"100000 loops, best of 3: 2.28 \u00b5s per loop\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
......@@ -266,7 +350,7 @@
]
}
],
"prompt_number": 9
"prompt_number": 12
},
{
"cell_type": "markdown",
......
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