def H93_calculate_model_values(p0):
''' Calculates all model values given parameter vector p0. '''
kappa_v, theta_v, sigma_v, rho, v0 = p0
values = []
for row, option in options.iterrows():
model_value = H93_call_value(S0, option['Strike'], option['T'],
option['r'], kappa_v, theta_v, sigma_v, rho, v0)
values.append(model_value)
return np.array(values)
def H93_error_function(p0):
''' Error function for parameter calibration in BCC97 model via
Lewis (2001) Fourier approach.
Parameters
==========
kappa_v: float
mean-reversion factor
theta_v: float
long-run mean of variance
sigma_v: float
volatility of variance
rho: float
correlation between variance and stock/index level
v0: float
initial, instantaneous variance
Returns
=======
MSE: float
mean squared error
'''
global i, min_MSE
kappa_v, theta_v, sigma_v, rho, v0 = p0
if kappa_v < 0.0 or theta_v < 0.005 or sigma_v < 0.0 or \
rho < -1.0 or rho > 1.0:
return 500.0
if 2 * kappa_v * theta_v < sigma_v ** 2:
return 500.0
se = []
for row, option in options.iterrows():
model_value = H93_call_value(S0, option['Strike'], option['T'],
option['r'], kappa_v, theta_v, sigma_v,
rho, v0)
se.append((model_value - option['Call']) ** 2)
MSE = sum(se) / len(se)
min_MSE = min(min_MSE, MSE)
if i % 25 == 0:
print('%4d |' % i, np.array(p0), '| %7.3f | %7.3f' % (MSE, min_MSE))
i += 1
return MSE
matrix[4] = rel_r**2
matrix[3] = rel_S
matrix[2] = rel_v
matrix[1] = rel_r
matrix[0] = 1
reg = np.linalg.lstsq(matrix.transpose(), rel_V)
cv = np.dot(reg[0], matrix)
erg = np.zeros((I), dtype=np.float)
np.put(erg, relevant, cv)
V[t] = np.where(h[t] > erg, h[t], V[t + 1] * df)
# final discounting step
df = np.exp(-(r[0] + r[1]) / 2 * dt)
# European Option Values
C0 = H93_call_value(S0, K, T, ra, kappa_v, theta_v,
sigma_v, rho, v0)
P0 = C0 + K * B0T - S0
P0_MCS = B0T * np.sum(h[-1]) / I
x = B0T * h[-1]
y = V[1] * df
# Control Variate Correction
if convar is True:
# statistical correlation
b = (np.sum(
(x - np.mean(x)) * (y - np.mean(y))) / np.sum(
(x - np.mean(x))**2))
# correction
# set b instead of 1.0