请写出用MCCM法去估计CEV期权定价模型的参数的python代码
时间: 2024-05-13 22:16:58 浏览: 10
以下是使用MCCM法估计CEV期权定价模型的参数的Python代码示例:
```python
import numpy as np
from scipy.stats import norm
# 定义CEV期权定价函数
def cev_option_price(S, K, r, sigma, T, beta, option_type='call'):
if option_type == 'call':
d1 = (np.log(S / K) + (r + (beta / 2) * sigma ** 2) * T) / (sigma * np.sqrt(T))
d2 = d1 - sigma * np.sqrt(T)
price = S * norm.cdf(d1) - K * np.exp(-r * T) * norm.cdf(d2)
else:
d1 = (np.log(S / K) + (r + (beta / 2) * sigma ** 2) * T) / (sigma * np.sqrt(T))
d2 = d1 - sigma * np.sqrt(T)
price = K * np.exp(-r * T) * norm.cdf(-d2) - S * norm.cdf(-d1)
return price
# 定义MCCM法估计CEV模型参数的函数
def mccm_cev_option_params(S, K, r, T, option_price, beta_list, sigma_list, N, M):
# 初始化参数
n_beta = len(beta_list)
n_sigma = len(sigma_list)
e = np.zeros((n_beta, n_sigma))
theta = np.zeros((n_beta, n_sigma))
# 使用Monte Carlo模拟生成随机数
np.random.seed(123)
Z = np.random.normal(size=(N, M))
# 计算随机数的累计和
cumsum_Z = np.cumsum(Z, axis=1)
# 计算CEV期权定价模型参数的估计值
for i in range(n_beta):
for j in range(n_sigma):
for k in range(M):
S_T = S * np.exp((r - beta_list[i] * sigma_list[j] ** 2 / 2) * T + sigma_list[j] * np.sqrt(T) * cumsum_Z[-1, k])
option_price_mc = cev_option_price(S, K, r, sigma_list[j], T, beta_list[i])
e[i, j] += (option_price_mc - option_price) ** 2
theta[i, j] += (np.sum(S_T) / M - S) ** 2
e[i, j] = np.sqrt(e[i, j] / N)
theta[i, j] = np.sqrt(theta[i, j] / M)
# 计算最小距离估计值
min_dist = np.inf
for i in range(n_beta):
for j in range(n_sigma):
dist = np.sqrt(e[i, j] ** 2 + theta[i, j] ** 2)
if dist < min_dist:
min_dist = dist
beta_hat = beta_list[i]
sigma_hat = sigma_list[j]
return beta_hat, sigma_hat
# 测试代码
S = 100
K = 100
r = 0.05
sigma = 0.2
T = 1
beta_list = [0.5, 1, 1.5]
sigma_list = [0.1, 0.2, 0.3]
N = 1000
M = 1000
option_price = cev_option_price(S, K, r, sigma, T, beta=1.2)
beta_hat, sigma_hat = mccm_cev_option_params(S, K, r, T, option_price, beta_list, sigma_list, N, M)
print('beta_hat:', beta_hat)
print('sigma_hat:', sigma_hat)
```