请写出用GMM法去估计CEV期权定价模型的参数的python代码

以下是使用GMM方法估计CEV期权定价模型参数的Python代码：

import numpy as np
from scipy.stats import norm

def cev_option_price(S, K, T, r, sigma, beta):
    # 计算CEV期权的价格
    d1 = (np.log(S / K) + (r + (sigma ** 2) / (2 * beta)) * T) / (sigma * np.sqrt(T * beta))
    d2 = d1 - sigma * np.sqrt(T * beta)
    call_price = S * norm.cdf(d1) - K * np.exp(-r * T) * norm.cdf(d2)
    return call_price

def moment_conditions(theta, S, K, T, r, call_prices):
    # 定义矩条件
    sigma, beta = theta
    option_prices = np.zeros_like(call_prices)
    for i in range(len(S)):
        option_prices[i] = cev_option_price(S[i], K[i], T[i], r, sigma, beta)
    # 计算误差
    errors = call_prices - option_prices
    # 计算矩条件
    m1 = np.mean(errors)
    m2 = np.mean(errors * S)
    m3 = np.mean(errors * (S ** 2))
    # 返回矩条件
    return np.array([m1, m2, m3])

def gmm_estimate(S, K, T, r, call_prices, theta_0, W):
    # 初始参数
    theta = theta_0
    # 迭代次数
    max_iter = 100
    tol = 1e-6
    for i in range(max_iter):
        # 计算矩条件
        moments = moment_conditions(theta, S, K, T, r, call_prices)
        # 计算GMM估计
        gmm = np.dot(moments, W * moments)
        # 计算Jacobi矩阵
        jacobi = np.zeros((3, 2))
        jacobi[0, 0] = -1
        jacobi[1, 0] = -np.mean(S)
        jacobi[2, 0] = -np.mean(S ** 2)
        jacobi[:, 1] = np.array([-np.mean(call_prices * S ** 2 / (sigma ** 3)), 
                                 -np.mean(call_prices * S ** 3 / (sigma ** 3) * (beta * np.log(S / K) + r + (beta * sigma ** 2) / 2)),
                                 -np.mean(call_prices * S ** 4 / (sigma ** 3) * (beta * np.log(S / K) + r + (beta * sigma ** 2) / 2) ** 2)])
        # 更新参数
        theta_new = theta - np.dot(np.linalg.inv(np.dot(jacobi.T, np.dot(W, jacobi))), np.dot(jacobi.T, np.dot(W, moments)))
        # 判断是否收敛
        if np.max(np.abs(theta_new - theta)) < tol:
            break
        theta = theta_new
    return theta

# 测试代码
S = np.array([100, 110, 120, 130, 140])
K = np.array([100, 100, 100, 100, 100])
T = np.array([1, 1, 1, 1, 1])
r = 0.05
sigma = 0.2
beta = 0.5
call_prices = np.array([18.931, 15.385, 12.213, 9.372, 6.818])
theta_0 = np.array([0.2, 0.5])
W = np.eye(3)
theta_hat = gmm_estimate(S, K, T, r, call_prices, theta_0, W)
print('sigma_hat =', theta_hat[0])
print('beta_hat =', theta_hat[1])