请基于Python 写一个指数期权多空 call spread或put spread的 尾部风险对冲策略

以下是一个简单的指数期权多空 call spread或put spread的尾部风险对冲策略：

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import yfinance as yf

# 获取标的资产价格数据
ticker = '^GSPC' # 标普500指数
data = yf.download(ticker, start='2015-01-01', end='2021-12-31')

# 计算历史波动率
data['log_returns'] = np.log(data['Adj Close']/data['Adj Close'].shift(1))
data['volatility'] = data['log_returns'].rolling(window=252).std() * np.sqrt(252)

# 模拟期权价格
S = data['Adj Close'].iloc[-1] # 标的资产当前价格
K1 = 3000 # 买入期权执行价格
K2 = 3100 # 卖出期权执行价格
T = 30/365 # 期权到期时间，以年为单位
r = 0.025 # 无风险利率

# 计算期权价格
def option_price(S, K, T, r, sigma, option_type):
    d1 = (np.log(S/K) + (r + 0.5*sigma**2)*T) / (sigma*np.sqrt(T))
    d2 = d1 - sigma*np.sqrt(T)
    if option_type == 'call':
        price = S*norm.cdf(d1) - K*np.exp(-r*T)*norm.cdf(d2)
    elif option_type == 'put':
        price = K*np.exp(-r*T)*norm.cdf(-d2) - S*norm.cdf(-d1)
    return price

sigma1 = data['volatility'].iloc[-1] # 买入期权波动率
sigma2 = data['volatility'].iloc[-1] + 0.05 # 卖出期权波动率
call_price1 = option_price(S, K1, T, r, sigma1, 'call') # 买入 call 期权价格
call_price2 = option_price(S, K2, T, r, sigma2, 'call') # 卖出 call 期权价格
put_price1 = option_price(S, K1, T, r, sigma1, 'put') # 买入 put 期权价格
put_price2 = option_price(S, K2, T, r, sigma2, 'put') # 卖出 put 期权价格

# 计算总成本和总收益
call_spread_cost = call_price1 - call_price2 # call spread 成本
put_spread_cost = put_price2 - put_price1 # put spread 成本
total_cost = call_spread_cost + put_spread_cost # 总成本
call_spread_profit = max(0, min(S-K1, K2-K1) - call_spread_cost) # call spread 收益
put_spread_profit = max(0, min(K2-K1, K2-S) - put_spread_cost) # put spread 收益
total_profit = call_spread_profit + put_spread_profit - total_cost # 总收益

# 计算 delta 中性对冲策略
# 假设持有 1 unit 的 call spread 和 1 unit 的 put spread
call_delta = 0.5 # call spread 的 delta
put_delta = -0.5 # put spread 的 delta
portfolio_delta = call_delta + put_delta # 组合的 delta

# 计算需要卖出的标的资产数量
hedging_volume = portfolio_delta * 100 # 每个期权合约的标的资产数量为 100
hedging_cost = hedging_volume * S # 对冲成本为标的资产价格乘以数量

# 绘制收益图像
S_range = np.arange(2700, 3300, 10)
call_spread_payoff = np.piecewise(S_range, [S_range < K1, (S_range >= K1) & (S_range <= K2), S_range > K2], [0, min(S_range-K1, K2-K1), K2-K1])
put_spread_payoff = np.piecewise(S_range, [S_range < K1, (S_range >= K1) & (S_range <= K2), S_range > K2], [K2-K1, max(K2-S_range, K2-K1), 0])
portfolio_payoff = call_spread_payoff + put_spread_payoff - total_cost
hedging_payoff = hedging_volume * (S_range - S) - hedging_cost
fig, ax = plt.subplots()
ax.spines['right'].set_visible(False)
ax.spines['top'].set_visible(False)
ax.plot(S_range, portfolio_payoff, linestyle='--', label='portfolio payoff')
ax.plot(S_range, hedging_payoff, label='hedging payoff')
ax.set_xlabel('标的资产价格')
ax.set_ylabel('收益')
ax.legend()
plt.show()

该策略的基本思路是，通过买入低执行价格的 call 期权和买入高执行价格的 put 期权来建立期权多空 spread，以期望在标的资产价格波动率下降时获得收益。为了对冲组合的尾部风险，我们计算组合的 delta，并根据 delta 中性原则卖出标的资产来对冲组合的 delta。我们还计算了组合的总成本和总收益，并绘制了组合收益和对冲收益的图像，以便更好地理解策略的风险和收益。