126 lines
3.5 KiB
Python
126 lines
3.5 KiB
Python
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import math
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import numpy as np
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import unittest
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from numba import njit
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from numba.extending import register_jitable
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from numba.tests.support import TestCase
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RISKFREE = 0.02
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VOLATILITY = 0.30
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A1 = 0.31938153
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A2 = -0.356563782
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A3 = 1.781477937
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A4 = -1.821255978
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A5 = 1.330274429
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RSQRT2PI = 0.39894228040143267793994605993438
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@register_jitable
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def cnd_array(d):
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K = 1.0 / (1.0 + 0.2316419 * np.abs(d))
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ret_val = (RSQRT2PI * np.exp(-0.5 * d * d) *
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(K * (A1 + K * (A2 + K * (A3 + K * (A4 + K * A5))))))
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return np.where(d > 0, 1.0 - ret_val, ret_val)
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@register_jitable
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def cnd(d):
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K = 1.0 / (1.0 + 0.2316419 * math.fabs(d))
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ret_val = (RSQRT2PI * math.exp(-0.5 * d * d) *
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(K * (A1 + K * (A2 + K * (A3 + K * (A4 + K * A5))))))
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if d > 0:
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ret_val = 1.0 - ret_val
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return ret_val
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@njit
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def blackscholes_arrayexpr(stockPrice, optionStrike, optionYears, Riskfree,
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Volatility):
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S = stockPrice
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X = optionStrike
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T = optionYears
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R = Riskfree
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V = Volatility
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sqrtT = np.sqrt(T)
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d1 = (np.log(S / X) + (R + 0.5 * V * V) * T) / (V * sqrtT)
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d2 = d1 - V * sqrtT
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cndd1 = cnd_array(d1)
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cndd2 = cnd_array(d2)
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expRT = np.exp(- R * T)
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callResult = (S * cndd1 - X * expRT * cndd2)
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putResult = (X * expRT * (1.0 - cndd2) - S * (1.0 - cndd1))
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return callResult, putResult
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@njit
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def blackscholes_scalar(callResult, putResult, stockPrice, optionStrike,
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optionYears, Riskfree, Volatility):
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S = stockPrice
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X = optionStrike
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T = optionYears
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R = Riskfree
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V = Volatility
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for i in range(len(S)):
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sqrtT = math.sqrt(T[i])
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d1 = (math.log(S[i] / X[i]) + (R + 0.5 * V * V) * T[i]) / (V * sqrtT)
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d2 = d1 - V * sqrtT
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cndd1 = cnd(d1)
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cndd2 = cnd(d2)
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expRT = math.exp((-1. * R) * T[i])
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callResult[i] = (S[i] * cndd1 - X[i] * expRT * cndd2)
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putResult[i] = (X[i] * expRT * (1.0 - cndd2) - S[i] * (1.0 - cndd1))
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def randfloat(rand_var, low, high):
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return (1.0 - rand_var) * low + rand_var * high
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class TestBlackScholes(TestCase):
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def test_array_expr(self):
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OPT_N = 400
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stockPrice = randfloat(self.random.random_sample(OPT_N), 5.0, 30.0)
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optionStrike = randfloat(self.random.random_sample(OPT_N), 1.0, 100.0)
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optionYears = randfloat(self.random.random_sample(OPT_N), 0.25, 10.0)
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args = stockPrice, optionStrike, optionYears, RISKFREE, VOLATILITY
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callResultGold, putResultGold = blackscholes_arrayexpr.py_func(*args)
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callResultNumba, putResultNumba = blackscholes_arrayexpr(*args)
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delta = np.abs(callResultGold - callResultNumba)
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self.assertAlmostEqual(delta.max(), 0)
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def test_scalar(self):
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OPT_N = 400
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callResultGold = np.zeros(OPT_N)
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putResultGold = np.zeros(OPT_N)
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callResultNumba = np.zeros(OPT_N)
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putResultNumba = np.zeros(OPT_N)
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stockPrice = randfloat(self.random.random_sample(OPT_N), 5.0, 30.0)
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optionStrike = randfloat(self.random.random_sample(OPT_N), 1.0, 100.0)
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optionYears = randfloat(self.random.random_sample(OPT_N), 0.25, 10.0)
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args = stockPrice, optionStrike, optionYears, RISKFREE, VOLATILITY
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blackscholes_scalar.py_func(callResultGold, putResultGold, *args)
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blackscholes_scalar(callResultNumba, putResultNumba, *args)
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delta = np.abs(callResultGold - callResultNumba)
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self.assertAlmostEqual(delta.max(), 0)
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if __name__ == "__main__":
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unittest.main()
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