def test_hermfit(self) :
def f(x) :
return x*(x - 1)*(x - 2)
# Test exceptions
assert_raises(ValueError, herm.hermfit, [1], [1], -1)
assert_raises(TypeError, herm.hermfit, [[1]], [1], 0)
assert_raises(TypeError, herm.hermfit, [], [1], 0)
assert_raises(TypeError, herm.hermfit, [1], [[[1]]], 0)
assert_raises(TypeError, herm.hermfit, [1, 2], [1], 0)
assert_raises(TypeError, herm.hermfit, [1], [1, 2], 0)
assert_raises(TypeError, herm.hermfit, [1], [1], 0, w=[[1]])
assert_raises(TypeError, herm.hermfit, [1], [1], 0, w=[1,1])
# Test fit
x = np.linspace(0,2)
y = f(x)
#
coef3 = herm.hermfit(x, y, 3)
assert_equal(len(coef3), 4)
assert_almost_equal(herm.hermval(x, coef3), y)
#
coef4 = herm.hermfit(x, y, 4)
assert_equal(len(coef4), 5)
assert_almost_equal(herm.hermval(x, coef4), y)
#
coef2d = herm.hermfit(x, np.array([y,y]).T, 3)
assert_almost_equal(coef2d, np.array([coef3,coef3]).T)
# test weighting
w = np.zeros_like(x)
yw = y.copy()
w[1::2] = 1
y[0::2] = 0
wcoef3 = herm.hermfit(x, yw, 3, w=w)
assert_almost_equal(wcoef3, coef3)
#
wcoef2d = herm.hermfit(x, np.array([yw,yw]).T, 3, w=w)
assert_almost_equal(wcoef2d, np.array([coef3,coef3]).T)
def test_hermfit(self):
def f(x):
return x*(x - 1)*(x - 2)
def f2(x):
return x**4 + x**2 + 1
# Test exceptions
assert_raises(ValueError, herm.hermfit, [1], [1], -1)
assert_raises(TypeError, herm.hermfit, [[1]], [1], 0)
assert_raises(TypeError, herm.hermfit, [], [1], 0)
assert_raises(TypeError, herm.hermfit, [1], [[[1]]], 0)
assert_raises(TypeError, herm.hermfit, [1, 2], [1], 0)
assert_raises(TypeError, herm.hermfit, [1], [1, 2], 0)
assert_raises(TypeError, herm.hermfit, [1], [1], 0, w=[[1]])
assert_raises(TypeError, herm.hermfit, [1], [1], 0, w=[1, 1])
assert_raises(ValueError, herm.hermfit, [1], [1], [-1,])
assert_raises(ValueError, herm.hermfit, [1], [1], [2, -1, 6])
assert_raises(TypeError, herm.hermfit, [1], [1], [])
# Test fit
x = np.linspace(0, 2)
y = f(x)
#
coef3 = herm.hermfit(x, y, 3)
assert_equal(len(coef3), 4)
assert_almost_equal(herm.hermval(x, coef3), y)
coef3 = herm.hermfit(x, y, [0, 1, 2, 3])
assert_equal(len(coef3), 4)
assert_almost_equal(herm.hermval(x, coef3), y)
#
coef4 = herm.hermfit(x, y, 4)
assert_equal(len(coef4), 5)
assert_almost_equal(herm.hermval(x, coef4), y)
coef4 = herm.hermfit(x, y, [0, 1, 2, 3, 4])
assert_equal(len(coef4), 5)
assert_almost_equal(herm.hermval(x, coef4), y)
# check things still work if deg is not in strict increasing
coef4 = herm.hermfit(x, y, [2, 3, 4, 1, 0])
assert_equal(len(coef4), 5)
assert_almost_equal(herm.hermval(x, coef4), y)
#
coef2d = herm.hermfit(x, np.array([y, y]).T, 3)
assert_almost_equal(coef2d, np.array([coef3, coef3]).T)
coef2d = herm.hermfit(x, np.array([y, y]).T, [0, 1, 2, 3])
assert_almost_equal(coef2d, np.array([coef3, coef3]).T)
# test weighting
w = np.zeros_like(x)
yw = y.copy()
w[1::2] = 1
y[0::2] = 0
wcoef3 = herm.hermfit(x, yw, 3, w=w)
assert_almost_equal(wcoef3, coef3)
wcoef3 = herm.hermfit(x, yw, [0, 1, 2, 3], w=w)
assert_almost_equal(wcoef3, coef3)
#
wcoef2d = herm.hermfit(x, np.array([yw, yw]).T, 3, w=w)
assert_almost_equal(wcoef2d, np.array([coef3, coef3]).T)
wcoef2d = herm.hermfit(x, np.array([yw, yw]).T, [0, 1, 2, 3], w=w)
assert_almost_equal(wcoef2d, np.array([coef3, coef3]).T)
# test scaling with complex values x points whose square
# is zero when summed.
x = [1, 1j, -1, -1j]
assert_almost_equal(herm.hermfit(x, x, 1), [0, .5])
assert_almost_equal(herm.hermfit(x, x, [0, 1]), [0, .5])
# test fitting only even Legendre polynomials
x = np.linspace(-1, 1)
y = f2(x)
coef1 = herm.hermfit(x, y, 4)
assert_almost_equal(herm.hermval(x, coef1), y)
coef2 = herm.hermfit(x, y, [0, 2, 4])
assert_almost_equal(herm.hermval(x, coef2), y)
assert_almost_equal(coef1, coef2)
def test_hermfit(self) :
def f(x) :
return x*(x - 1)*(x - 2)
# Test exceptions
assert_raises(ValueError, herm.hermfit, [1], [1], -1)
assert_raises(TypeError, herm.hermfit, [[1]], [1], 0)
assert_raises(TypeError, herm.hermfit, [], [1], 0)
assert_raises(TypeError, herm.hermfit, [1], [[[1]]], 0)
assert_raises(TypeError, herm.hermfit, [1, 2], [1], 0)
assert_raises(TypeError, herm.hermfit, [1], [1, 2], 0)
assert_raises(TypeError, herm.hermfit, [1], [1], 0, w=[[1]])
assert_raises(TypeError, herm.hermfit, [1], [1], 0, w=[1,1])
# Test fit
x = np.linspace(0,2)
y = f(x)
#
coef3 = herm.hermfit(x, y, 3)
assert_equal(len(coef3), 4)
assert_almost_equal(herm.hermval(x, coef3), y)
#
coef4 = herm.hermfit(x, y, 4)
assert_equal(len(coef4), 5)
assert_almost_equal(herm.hermval(x, coef4), y)
#
coef2d = herm.hermfit(x, np.array([y,y]).T, 3)
assert_almost_equal(coef2d, np.array([coef3,coef3]).T)
# test weighting
w = np.zeros_like(x)
yw = y.copy()
w[1::2] = 1
y[0::2] = 0
wcoef3 = herm.hermfit(x, yw, 3, w=w)
assert_almost_equal(wcoef3, coef3)
#
wcoef2d = herm.hermfit(x, np.array([yw,yw]).T, 3, w=w)
assert_almost_equal(wcoef2d, np.array([coef3,coef3]).T)
#test NA
y = f(x)
y[10] = 100
xm = x.view(maskna=1)
xm[10] = np.NA
res = herm.hermfit(xm, y, 3)
assert_almost_equal(res, coef3)
ym = y.view(maskna=1)
ym[10] = np.NA
res = herm.hermfit(x, ym, 3)
assert_almost_equal(res, coef3)
y2 = np.vstack((y,y)).T
y2[10,0] = 100
y2[15,1] = 100
y2m = y2.view(maskna=1)
y2m[10,0] = np.NA
y2m[15,1] = np.NA
res = herm.hermfit(x, y2m, 3).T
assert_almost_equal(res[0], coef3)
assert_almost_equal(res[1], coef3)
wm = np.ones_like(x, maskna=1)
wm[10] = np.NA
res = herm.hermfit(x, y, 3, w=wm)
assert_almost_equal(res, coef3)
def test_hermfit(self):
def f(x):
return x*(x - 1)*(x - 2)
def f2(x):
return x**4 + x**2 + 1
# Test exceptions
assert_raises(ValueError, herm.hermfit, [1], [1], -1)
assert_raises(TypeError, herm.hermfit, [[1]], [1], 0)
assert_raises(TypeError, herm.hermfit, [], [1], 0)
assert_raises(TypeError, herm.hermfit, [1], [[[1]]], 0)
assert_raises(TypeError, herm.hermfit, [1, 2], [1], 0)
assert_raises(TypeError, herm.hermfit, [1], [1, 2], 0)
assert_raises(TypeError, herm.hermfit, [1], [1], 0, w=[[1]])
assert_raises(TypeError, herm.hermfit, [1], [1], 0, w=[1, 1])
assert_raises(ValueError, herm.hermfit, [1], [1], [-1,])
assert_raises(ValueError, herm.hermfit, [1], [1], [2, -1, 6])
assert_raises(TypeError, herm.hermfit, [1], [1], [])
# Test fit
x = np.linspace(0, 2)
y = f(x)
#
coef3 = herm.hermfit(x, y, 3)
assert_equal(len(coef3), 4)
assert_almost_equal(herm.hermval(x, coef3), y)
coef3 = herm.hermfit(x, y, [0, 1, 2, 3])
assert_equal(len(coef3), 4)
assert_almost_equal(herm.hermval(x, coef3), y)
#
coef4 = herm.hermfit(x, y, 4)
assert_equal(len(coef4), 5)
assert_almost_equal(herm.hermval(x, coef4), y)
coef4 = herm.hermfit(x, y, [0, 1, 2, 3, 4])
assert_equal(len(coef4), 5)
assert_almost_equal(herm.hermval(x, coef4), y)
# check things still work if deg is not in strict increasing
coef4 = herm.hermfit(x, y, [2, 3, 4, 1, 0])
assert_equal(len(coef4), 5)
assert_almost_equal(herm.hermval(x, coef4), y)
#
coef2d = herm.hermfit(x, np.array([y, y]).T, 3)
assert_almost_equal(coef2d, np.array([coef3, coef3]).T)
coef2d = herm.hermfit(x, np.array([y, y]).T, [0, 1, 2, 3])
assert_almost_equal(coef2d, np.array([coef3, coef3]).T)
# test weighting
w = np.zeros_like(x)
yw = y.copy()
w[1::2] = 1
y[0::2] = 0
wcoef3 = herm.hermfit(x, yw, 3, w=w)
assert_almost_equal(wcoef3, coef3)
wcoef3 = herm.hermfit(x, yw, [0, 1, 2, 3], w=w)
assert_almost_equal(wcoef3, coef3)
#
wcoef2d = herm.hermfit(x, np.array([yw, yw]).T, 3, w=w)
assert_almost_equal(wcoef2d, np.array([coef3, coef3]).T)
wcoef2d = herm.hermfit(x, np.array([yw, yw]).T, [0, 1, 2, 3], w=w)
assert_almost_equal(wcoef2d, np.array([coef3, coef3]).T)
# test scaling with complex values x points whose square
# is zero when summed.
x = [1, 1j, -1, -1j]
assert_almost_equal(herm.hermfit(x, x, 1), [0, .5])
assert_almost_equal(herm.hermfit(x, x, [0, 1]), [0, .5])
# test fitting only even Legendre polynomials
x = np.linspace(-1, 1)
y = f2(x)
coef1 = herm.hermfit(x, y, 4)
assert_almost_equal(herm.hermval(x, coef1), y)
coef2 = herm.hermfit(x, y, [0, 2, 4])
assert_almost_equal(herm.hermval(x, coef2), y)
assert_almost_equal(coef1, coef2)
def LSMC_Hermite(price_matrix, K, r, paths, T, dt, type, polydegree):
from numpy.polynomial.hermite import hermval, hermfit
# start timer
tic = time.time()
# total number of steps
N = T * dt
N = int(N)
# adjust yearly discount factor
r = (1 + r)**(1 / dt) - 1
# cash flow matrix
cf_matrix = np.zeros((N + 1, paths * 2))
# calculated cf when executed in time T (cfs European option)
cf_matrix[N] = payoff_executing(K, price_matrix[N], type)
# 1 if in the money, otherwise 0
execute = np.where(payoff_executing(K, price_matrix, type) > 0, 1, 0)
# execute = np.ones_like(execute) # use to convert to consider all paths
for t in range(1, N):
# discounted cf 1 time period
discounted_cf = cf_matrix[N - t + 1] * np.exp(-r)
# slice matrix and make all out of the money paths = 0 by multiplying with matrix "execute"
X = price_matrix[N - t, :] * execute[N - t, :]
# +1 here because otherwise will loose an in the money path at T-t,
# that is out of the money in T-t+1(and thus has payoff=0)
Y = (discounted_cf + 1) * execute[N - t, :]
# mask all zero values(out of the money paths) and run regression
#X1 = np.ma.masked_less_equal(X, 0)
#Y1 = np.ma.masked_less_equal(Y, 0) - 1
X1 = X[np.where(X > 0)]
Y1 = Y[np.where(X > 0)]
if np.count_nonzero(
X1
) > 0: # meaning all paths are out of the money, thus never optimal to exercise
regression = hermfit(X1, Y1, polydegree)
# warnings.simplefilter('ignore', np.RankWarning)
# calculate continuation value
cont_value = np.zeros_like(X)
cont_value[np.where(X > 0)] = hermval(X1, regression)
# update cash flow matrix
imm_ex = payoff_executing(K, X, type)
cf_matrix[N - t] = np.where(imm_ex > cont_value, imm_ex,
cf_matrix[N - t + 1] * np.exp(-r))
cf_matrix[N - t + 1:] = np.where(imm_ex > cont_value, 0,
cf_matrix[N - t + 1:])
else:
cf_matrix[N - t] = cf_matrix[N - t + 1] * np.exp(-r)
# obtain option value
cf_matrix[0] = cf_matrix[1] * np.exp(-r)
option_value = np.sum(cf_matrix[0]) / (paths * 2)
# st dev
st_dev = np.std(cf_matrix[0]) / np.sqrt(paths)
# Time and print the elapsed time
toc = time.time()
elapsed_time = toc - tic
print('Total running time of LSMC: {:.2f} seconds'.format(elapsed_time))
print("Ran this with T: ", T, " and dt: ", dt, "\n")
print("Value of this", type, "option is:", option_value)
print("St dev of this", type, "option is:", st_dev, "\n")
return option_value
