Gist with additional files from For Python Quants Bootcamp, May 2017, New York City

00_bc_day_1_section_02

3 + 4
3 * 4
3 / 4
type(3)
type(4)
3 ** 4
sqrt(3)
3 ** 0.5
import math
math.sqrt(3)
print("Python.")
a = 3
b = 0.75
c = 'Python.'
d = "He said:'I am late.'"
d
d = "He said:"I am late.""
d = 'He said:"I am late."'
d
a
print(a)
a
b
a * b
a ** b
d
2 * d
d + d
d + d * 2
d / d
d / 2
d
d[0]
d[1]
len(d)
d[20]
d[19]
d[-1]
d[-2]
d[-20]
d[-21]
d[2]
d[:2]
d[:2] + d[2:]
d[2:]
d[2:7]
d[2:7:2]
d[::2]
d[::-1]
range(10)
type(range(10))
for i in range(10):
    print('For Python Quants')
for i in range(10):
    print(i)
for i in range(10):
    print(i ** 2)
%magic
%lsmagic
%hist
%hist?
%history?
len?
for i in range(10):
    print(d[i])
for c in d:
    print(c)
for _ in d:
    print(_)
c
for _ in d:
    print(_, end='')
for _ in d:
    print(_, end='|')
for x in range(10):
    print(x)
for x in range(10):
    print(x ** 2)
l = [x for x in range(10)]
l
l = [x ** 2 for x in range(10)]
l
type(l)
l2 = [x ** 2 for x in range(10) if x > 2]
l2
l2 = [x ** 2 for x in range(10) if (x > 2) and (x < 8)]
l2
l[0]
l[:5]
l[5:]
l[::-1]
l = [x ** 2 for x in range(10)]
10 % 2
11 % 2
l = [x ** 2 for x in range(10) if x % 2 == 0]
l
l = [x for x in range(20) if x % 2 == 0]
l
for x in range(20):
    for y in range(10, 50):
        if x % 2 == 0:
            # then do something
            pass
def f(x):
    return x ** 2
f
f(10)
f(10.5)
l = [f(x) for x in range(20) if x % 2 == 0]
l
l3 = [5, 'fpq', a, l]
l3
l3.append('this is new')
l3
l3.append(f)
l3
l3[-1](5)
l.append('new')
l
l3
l
l3
def is_prime(I):
    for i in range(2, I):
        if I % i == 0:
            return False
    return True
is_prime(8)
is_prime(10)
is_prime(11)
is_prime(13)
l = [is_prime(x) for x in range(2, 101)]
l
l = [is_prime(x) for x in range(2, 20)]
l
class MyClass(object):
    pass
class my_class(object):
    pass
int(Ture)
int(True)
int(False)
while True:
    print('hi')
while 2:
    print('hi')
2 == 2
True == 2
True == 1
def is_prime_2(I):
    for i in range(2, I ** 0.5):
        if I % i == 0:
            return False
    return True
is_prime_2(10)
def is_prime_2(I):
    for i in range(2, int(I ** 0.5)):
        if I % i == 0:
            return False
    return True
int(2.3)
int(2.7)
def is_prime_2(I):
    for i in range(2, int(I ** 0.5) + 1):
        if I % i == 0:
            return False
    return True
is_prime_2(10)
is_prime_2(11)
%ed
p1 = int(1e8 + 1)
p2 = int(1e8 + 3)
p1
p2
is_prime(p1)
is_prime(p2)
p2 = 2** 17 − 1
p2 = 2 ** 17 - 1
p2
p2 = 2 ** 31 - 1
p2
%time is_prime(p1)
%time is_prime(p2)
p2 = 2 ** 17 - 1
%time is_prime(p2)
%time is_prime_2(p2)
%time is_prime_2(int(2**31 - 1))
def is_prime_3(I):
    if I % 2 == 0:
        return False
    for i in range(3, int(I ** 0.5) + 1, 2):
        if I % i == 0:
            return False
    return True
%time is_prime_3(int(2**31 - 1))
%ed is_prime_3
%ed -p
from math import sqrt
sqrt(4)
ls
cd ..
ls
cd bc
!mkdir bc
cd bc/
%hist -f bc_day_1_section_02

01_bc_day_1_03_04.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" width=\"350px\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Finance with Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a class about _Python_ for **Finance**.\n",
    "\n",
    "$$\n",
    "\\frac{dS_t}{S_t} = r dt + \\sigma dZ_t\n",
    "$$\n",
    "\n",
    "This is Latex $S_t$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3 + 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3 * 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Financial Market"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "B0 = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "S0 = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "B = np.array([11, 11])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "S = np.array([20, 5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([11, 11])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int64')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([22, 22])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B * 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[11, 11, 11, 11]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[11, 11] * 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12.5"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "C = np.maximum(S - 15, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 0])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def ret(x0, x):\n",
    "    return x.mean() / x0 - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.10000000000000009"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ret(B0, B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.25"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ret(S0, S)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "C0 = C.mean() / (1 + 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.2727272727272725"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "i = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 23.5,  10. ])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0.5 * B + 0.9 * S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "M0 = np.array([B0, S0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10, 10])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "M = np.array([B, S]).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[11, 20],\n",
       "       [11,  5]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "phi = np.linalg.solve(M, C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.15151515,  0.33333333])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "phi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5.,  0.])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(M, phi).round(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "C0r = np.dot(M0, phi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8181818181818181"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C0r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.2727272727272725"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "C0 = C.mean() / (1 + 0.25) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.375"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ret(C0r, C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8181818181818181"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C.mean() / (1 + 0.375)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Deriving the Martingale Measure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.optimize import minimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "bnds = ((0, 1), (0, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def E(Q):\n",
    "    return np.dot(S, Q) - S0 * (1 + i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def E(Q):\n",
    "    return (np.dot(S, Q) - S0 * (1 + i)) ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Q = np.array([0.45, 0.55])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5625"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E(Q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cons = (\n",
    "    {'type': 'eq', 'fun': lambda Q: Q.sum() - 1} #,\n",
    "    # {'type': 'eq', 'fun': lambda Q: E(Q)}\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "res = minimize(E, (0.5, 0.5), bounds=bnds,\n",
    "               constraints=cons)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     fun: 1.2556709968339189e-14\n",
       "     jac: array([  1.47819541e-06,  -7.48038236e-07])\n",
       " message: 'Optimization terminated successfully.'\n",
       "    nfev: 9\n",
       "     nit: 2\n",
       "    njev: 2\n",
       "  status: 0\n",
       " success: True\n",
       "       x: array([ 0.39999999,  0.60000001])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q = res['x']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2556709968339189e-14"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E(Q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11.0"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S0 * 1.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.999999887943273"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(S, Q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "C0m = np.dot(C, Q) / (1 + i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8181817842252341"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C0m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8181818181818181"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C0r"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Incomplete Market"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "B = np.array([11, 11, 11])\n",
    "S = np.array([20, 10, 5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10, 10])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "M = np.array((B, S)).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[11, 20],\n",
       "       [11, 10],\n",
       "       [11,  5]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "C = np.maximum(S - 15, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 0, 0])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "lsq = np.linalg.lstsq(M, C)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.64285714,  1.07142857, -0.71428571])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(M, lsq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2987012987012982"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(M0, lsq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.35714286,  1.07142857, -0.71428571])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(M, lsq) - C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True], dtype=bool)"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "5 / 11 * B >= C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.545454545454545"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "5 / 11 * B0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 0, 0])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def costs(phi):\n",
    "    return np.dot(M0, phi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cons = ({'type': 'ineq', 'fun': lambda phi: np.dot(M, phi) - C})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "res = minimize(costs, (0.5, 0.5), constraints=cons)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     fun: 1.8181818181822074\n",
       "     jac: array([ 10.,  10.])\n",
       " message: 'Optimization terminated successfully.'\n",
       "    nfev: 8\n",
       "     nit: 2\n",
       "    njev: 2\n",
       "  status: 0\n",
       " success: True\n",
       "       x: array([-0.15151515,  0.33333333])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "phi = res['x']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.   ,  1.667,  0.   ])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(M, phi).round(3) - C"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mean Variance Portfolio Theory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# alt payoff\n",
    "B = np.array((5, 15, 11))\n",
    "M = np.array((B, S)).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5, 20],\n",
       "       [15, 10],\n",
       "       [11,  5]])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10, 10])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "R = M / M0 - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.5,  1. ],\n",
       "       [ 0.5,  0. ],\n",
       "       [ 0.1, -0.5]])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.10000000000000002"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.03333333,  0.16666667])"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R.mean(axis=0)\n",
    "# mean return per financial asset for equal probability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.25,  0.25, -0.2 ])"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R.mean(axis=1)\n",
    "# mean return per state for equal weight portfolio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.41096093,  0.62360956])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R.std(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def mu(phi):\n",
    "    return np.dot(R.mean(axis=0), phi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "def vol(phi):\n",
    "    return np.dot(phi, np.dot(np.cov(R.T, ddof=0), phi)) ** 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "phi = (0.5, 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.10000000000000001"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu(phi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.21213203435596423"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vol(phi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "phi = (0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.16666666666666666"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu(phi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.62360956446232352"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vol(phi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "phi = (1, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.033333333333333361"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu(phi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.41096093353126506"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vol(phi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "s = np.linspace(-1, 2, 25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.   , -0.875, -0.75 , -0.625, -0.5  , -0.375, -0.25 , -0.125,\n",
       "        0.   ,  0.125,  0.25 ,  0.375,  0.5  ,  0.625,  0.75 ,  0.875,\n",
       "        1.   ,  1.125,  1.25 ,  1.375,  1.5  ,  1.625,  1.75 ,  1.875,  2.   ])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pos = [(1-s, s) for s in np.linspace(-1, 2, 50)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(2.0, -1.0),\n",
       " (1.9387755102040818, -0.93877551020408168),\n",
       " (1.8775510204081631, -0.87755102040816324),\n",
       " (1.8163265306122449, -0.81632653061224492),\n",
       " (1.7551020408163265, -0.75510204081632648),\n",
       " (1.693877551020408, -0.69387755102040816),\n",
       " (1.6326530612244898, -0.63265306122448983),\n",
       " (1.5714285714285714, -0.5714285714285714),\n",
       " (1.510204081632653, -0.51020408163265307),\n",
       " (1.4489795918367347, -0.44897959183673475)]"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pos[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mv = np.array([(vol(phi), mu(phi)) for phi in pos])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.34907376, -0.1       ],\n",
       "       [ 1.29040285, -0.09183673],\n",
       "       [ 1.23178439, -0.08367347],\n",
       "       [ 1.17322624, -0.0755102 ],\n",
       "       [ 1.11473789, -0.06734694]])"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mv[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from pylab import plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plt.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x119278400>]"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1191d9588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(mv[:, 0], mv[:, 1], 'ro')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" width=\"350px\">"
   ]
  }
 ],
 "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
}

02_bc_day_2_01_02_03.ipynb

bc_day_1_03_04.ipynb

bc_day_2_01_02_03.ipynb

bc_day_3.ipynb

bc_day_4.ipynb

tick_client.py

#
# Tick Data Client
# with ZeroMQ
#
import zmq
import datetime

context = zmq.Context()
socket = context.socket(zmq.SUB)
socket.connect('tcp://127.0.0.1:5555')
socket.setsockopt_string(zmq.SUBSCRIBE, '')

while True:
    msg = socket.recv_string()
    t = datetime.datetime.now()
    print(str(t) + ' | ' + msg)

tick_plot.py

#
# Tick Data Client
# with ZeroMQ
#
import zmq
import datetime
import plotly.plotly as ply
import plotly.tools as tls
from plotly.graph_objs import *

stream_ids = tls.get_credentials_file()['stream_ids']

# socket
context = zmq.Context()
socket = context.socket(zmq.SUB)
socket.connect('tcp://127.0.0.1:5555')
socket.setsockopt_string(zmq.SUBSCRIBE, '')

# plotting
s = Stream(maxpoints=100, token=stream_ids[0])
t = Scatter(x=[], y=[], name='tick data', mode='lines+markers', stream=s)
d = Data([t])
l = Layout(title='Bootcamp Tick Data')
f = Figure(data=d, layout=l)
ply.plot(f, filename='fpq_bootcamp', auto_open=True)

st = ply.Stream(stream_ids[0])
st.open()

while True:
    msg = socket.recv_string()
    t = datetime.datetime.now()
    sym, value = msg.split()
    print(str(t) + ' | ' + msg)
    st.write({'x': t, 'y': float(value)})

tick_server.py

#
# Tick Data Server
# with ZeroMQ
#
import zmq
import time
import random

context = zmq.Context()
socket = context.socket(zmq.PUB)
socket.bind('tcp://127.0.0.1:5555')

AMZN = 100.

while True:
    AMZN += random.gauss(0, 1) * 0.5
    msg = 'AMZN %s' % AMZN
    socket.send_string(msg)
    print(msg)
    time.sleep(random.random() * 2)

tpqoa.py

#
# tpqoa is a wrapper class for the
# Oanda v20 API (RESTful & streaming)
# (c) Dr. Yves J. Hilpisch
# The Python Quants GmbH
#
import v20
import pandas as pd
import datetime as dt
import configparser

class tpqoa(object):
    ''' tpqoa is a Python wrapper class for the Oanda v20 API. '''

    def __init__(self, conf_file):
        ''' Init function expecting a configuration file with
        the following content:

        [oanda_v20]
        account_id = XYZ-ABC-...
        access_token = ZYXCAB...

        Parameters
        ==========
        conf_file: string
            path to and filename of the configuration file, e.g. '/home/me/oanda.cfg'
        '''
        self.config = configparser.ConfigParser()
        self.config.read(conf_file)
        self.access_token = self.config['oanda_v20']['access_token']
        self.account_id = self.config['oanda_v20']['account_id']
        self.ctx = v20.Context(
            hostname='api-fxpractice.oanda.com',
            port=443,
            ssl=True,
            application='sample_code',
            token=self.access_token,
            datetime_format='RFC3339')
        self.ctx_stream = v20.Context(
            hostname='stream-fxpractice.oanda.com',
            port=443,
            ssl=True,
            application='sample_code',
            token=self.access_token,
            datetime_format='RFC3339'
        )
        self.suffix = '.000000000Z'

    def get_instruments(self):
        ''' Retrieves and returns all instruments for the given account. '''
        resp = self.ctx.account.instruments(self.account_id)
        instruments = resp.get('instruments')
        instruments = [ins.dict() for ins in instruments]
        instruments = [(ins['displayName'], ins['name'])
                      for ins in instruments]
        return instruments

    def transform_datetime(self, dt):
        ''' Transforms Python datetime object to string. '''
        if isinstance(dt, str):
            dt = pd.Timestamp(dt).to_pydatetime()
        return dt.isoformat('T') + self.suffix

    def get_history(self, instrument, start, end,
                    granularity, price):
        ''' Retrieves historical data for instrument.

        Parameters
        ==========
        instrument: string
            valid instrument name
        start, end: datetime, str
            Python datetime or string objects for start and end
        granularity: string
            a string like 'S5', 'M1' or 'D'
        price: string
            one of 'A' (ask) or 'B' (bid)

        Returns
        =======
        data: pd.DataFrame
            pandas DataFrame object with data
        '''
        start = self.transform_datetime(start)
        end = self.transform_datetime(end)
        raw = self.ctx.instrument.candles(
            instrument=instrument,
            fromTime=start, toTime=end,
            granularity=granularity, price=price)
        raw = raw.get('candles')
        raw = [cs.dict() for cs in raw]
        for cs in raw:
            cs.update(cs['ask'])
            del cs['ask']
        if len(raw) == 0:
            return 'No data available.'
        data = pd.DataFrame(raw)
        data['time'] = pd.to_datetime(data['time'])
        data = data.set_index('time')
        data.index = pd.DatetimeIndex(data.index)
        for col in list('ohlc'):
            data[col] = data[col].astype(float)
        return data

    def create_order(self, instrument, units):
        ''' Places order with Oanda.

        Parameters
        ==========
        instrument: string
            valid instrument name
        units: int
            number of units of instrument to be bought (positive int, eg 'units=50')
            or to be sold (negative int, eg 'units=-100')
        '''
        request = self.ctx.order.market(
            self.account_id,
            instrument=instrument,
            units=units,
        )
        order = request.get('orderFillTransaction')
        print('\n\n', order.dict(), '\n')

    def stream_data(self, instrument, stop=None):
        ''' Starts a real-time data stream.

        Parameters
        ==========
        instrument: string
            valid instrument name
        '''
        self.stream_instrument = instrument
        self.ticks = 0
        response = self.ctx_stream.pricing.stream(
            self.account_id, snapshot=True,
            instruments=instrument)
        for msg_type, msg in response.parts():
            # print(msg_type, msg)
            if msg_type == 'pricing.Price':
                self.ticks +=1
                self.on_success(msg.time,
                                float(msg.bids[0].price),
                                float(msg.asks[0].price))
                if stop is not None:
                    if self.ticks >= stop:
                        break

    def on_success(self, time, bid, ask):
        ''' Method called when new data is retrieved. '''
        print(time, bid, ask)

    def get_account_summary(self, detailed=False):
        ''' Returns summary data for Oanda account.'''
        if detailed is True:
            response = self.ctx.account.get(self.account_id)
        else:
            response = self.ctx.account.summary(self.account_id)
        raw = response.get('account')
        return raw.dict()

    def get_transactions(self, tid=0):
        ''' Retrieves and returns transactions data. '''
        response = self.ctx.transaction.since(self.account_id, id=tid)
        transactions = response.get('transactions')
        transactions = [t.dict() for t in transactions]
        return transactions

    def print_transactions(self, tid=0):
        ''' Prints basic transactions data. '''
        transactions = self.get_transactions(tid)
        for trans in transactions:
             templ = '%5s | %s | %9s | %12s'
             print(templ % (trans['id'],
                            trans['time'],
                            trans['instrument'],
                            trans['units']))