我正在尝试使用python设置一个Vasicek校准例程。我认为最好使用scipy.optimize,但我正在为如何编写它而苦苦挣扎。我有下面的整体表格。
有人用python实现过Vasicek校准吗?初始数据-下表。
2.0> = <0.975,0.949,0.900,0.8519,0.8056>
更新:给定公式:B= (1 -tau(-kappatau))/ kappa A= np.exp((theta-(sigma__2)/(2(kappa2))) * (B-tau) - (sigma2)/(4*kappa)_(B__2)) Vasicek = A_np.exp(-r0 * B)
有什么python函数可以迭代地求解'kappa‘,从而使变量Vasicek命中某个值?
def py_exact_zcb_Vas_Table(theta, kappa, sigma, tau, zeroBond, r0 = 0):
length = len(tau)
B = np.zeros(length)
A = np.zeros(length)
Vasicek = np.zeros(length)
kappa_calib = np.zeros(length)
theta_calib = np.zeros(length)
Vasci_calib = np.zeros(length)
for i in range(0, length, 1):
B[i] = (1 - np.exp(-kappa*tau[i])) / kappa
A[i] = np.exp((theta-(sigma[i]**2)/(2*(kappa**2))) * (B[i]-tau[i]) - (sigma[i]**2)/(4*kappa)*(B[i]**2))
Vasicek[i] = A[i]*np.exp(-r0 * B[i])
#do while (zeroBond[i] - Vasci_calib[i]) <> 0:
# change kappa[i] such that I match Vasci_calib[i] with zeroBond[i]
return pd.DataFrame({'B':B, 'A':A, 'Vasicek':Vasicek, 'kappa':kapp_calib})
发布于 2018-07-17 04:59:53
您可以使用scipy.optimize.minimize_scalar
函数来查找求解方程Vasicek(kappa) = target_value
的kappa
,给定参数(tau, sigma, theta, r0)
import numpy as np
from scipy.optimize import minimize_scalar
def compute_Vasicek(kappa, tau, sigma, theta, r0):
B = (1 - np.exp(-kappa*tau)) / kappa
A = np.exp((theta-(sigma**2)/(2*(kappa**2))) * (B-tau) - (sigma**2)/(4*kappa)*(B**2))
vasicek = A*np.exp(-r0 * B)
return vasicek
def objectif_function(kappa, *args):
return (compute_Vasicek(kappa, *args[1:]) - args[0])**2
# Minimization:
targeted_Vasicek = 10
tau, sigma, theta, r0 = 4, 205, 5, 0
result = minimize_scalar(objectif_function, args=(targeted_Vasicek, tau, sigma, theta, r0), bounds=(0, 100), method='bounded')
print(result)
也许Brent
方法可以在您的情况下工作,使用非随机值作为参数...
然后,您可以这样做:
kappa_calib = result.x
vasci_calib = compute_Vasicek(kappa_calib, tau, sigma, theta, r0)
并将最小化部分包装在另一个函数中,因此可以从循环内部调用它
https://stackoverflow.com/questions/51290578
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