def black_scholes(price, strike, t, rate, vol, call, put):
mr = -rate
sig_sig_two = vol * vol * 2
P = price
S = strike
T = t
a = np.log(P / S)
b = T * mr
z = T * sig_sig_two
c = 0.25 * z
y = 1./np.sqrt(z)
w1 = (a - b + c) * y
w2 = (a - b - c) * y
d1 = 0.5 + 0.5 * np.erf(w1)
d2 = 0.5 + 0.5 * np.erf(w2)
Se = np.exp(b) * S
r = P * d1 - Se * d2
call[:] = r # temporary `r` is necessary for faster `put` computation
put[:] = r - P + Se
def test_erf_fallback():
a = numpy.linspace(2.0, 3.0, num=10)
expected = numpy.empty_like(a)
for idx, val in enumerate(a):
expected[idx] = math.erf(val)
result = dpnp.erf(a)
numpy.testing.assert_array_equal(result, expected)
def test_strides_erf(dtype, shape):
a = numpy.arange(numpy.prod(shape), dtype=dtype).reshape(shape)
b = a[::2]
dpa = dpnp.reshape(dpnp.arange(numpy.prod(shape), dtype=dtype), shape)
dpb = dpa[::2]
result = dpnp.erf(dpb)
expected = numpy.empty_like(b)
for idx, val in enumerate(b):
expected[idx] = math.erf(val)
numpy.testing.assert_allclose(result, expected)
def black_scholes(price, strike, t, mrs, vol_vol_twos, quarters, ones, halfs,
call, put):
P = price
S = strike
T = t
a = np.log(P / S)
b = T * mrs
z = T * vol_vol_twos
c = quarters * z
y = ones / np.sqrt(z)
w1 = (a - b + c) * y
w2 = (a - b - c) * y
d1 = halfs + halfs * np.erf(w1)
d2 = halfs + halfs * np.erf(w2)
Se = np.exp(b) * S
r = P * d1 - Se * d2
call[:] = r # temporary `r` is necessary for faster `put` computation
put[:] = r - P + Se