Python是一種流行的編程語言，可用于許多不同的應(yīng)用程序和領(lǐng)域，包括金融市場的預(yù)測。在金融市場中，波動率是評估風(fēng)險的關(guān)鍵指標(biāo)，因此預(yù)測波動率對投資者和交易員至關(guān)重要。在本文中，我們將使用Python編寫代碼來預(yù)測未來的波動率。

# 導(dǎo)入所需模塊
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import pandas_datareader.data as web
from scipy.stats import norm
# 獲取股票價格數(shù)據(jù)
start = pd.to_datetime('2010-01-01')
end = pd.to_datetime('2020-12-31')
asset = 'AAPL'
df = web.DataReader(asset, 'yahoo', start, end)
# 計算每日收益率
log_return = np.log(df['Adj Close']/df['Adj Close'].shift(1))
# 計算歷史波動率
hist_vol = log_return.rolling(window=252 * 7).std() * np.sqrt(252)
# 定義函數(shù)計算隱含波動率
def implied_volatility(price, strike, expiry, rate, div, option_type):
def bs_formula(x):
d1 = (np.log(price / strike) + (rate - div + 0.5 * x ** 2) * expiry) / (x * np.sqrt(expiry))
d2 = d1 - (x * np.sqrt(expiry))
if option_type == 'call':
return price * np.exp(-div * expiry) * norm.cdf(d1) - strike * np.exp(-rate * expiry) * norm.cdf(d2)
elif option_type == 'put':
return strike * np.exp(-rate * expiry) * norm.cdf(-d2) - price * np.exp(-div * expiry) * norm.cdf(-d1)
implied_vol = 1
while True:
vega = price * np.exp(-div * expiry) * norm.pdf((np.log(price / strike) + (rate - div + 0.5 * implied_vol ** 2) * expiry) / (implied_vol * np.sqrt(expiry))) * np.sqrt(expiry)
price_diff = bs_formula(implied_vol) - price
implied_vol -= price_diff / vega
if abs(price_diff)< 0.001:
break
return implied_vol
# 計算每日的隱含波動率
df['iv'] = np.nan
for i, row in df.iterrows():
expiry = (pd.to_datetime('2021-12-31') - i).days / 365
try:
iv = implied_volatility(row['Adj Close'], row.name, expiry, 0.01, 0, 'call')
df.loc[i, 'iv'] = iv
except:
pass
# 計算未來波動率
future_days = 30
df['future_vol'] = np.nan
for i, row in df.iterrows():
future = df.loc[i:i + pd.Timedelta(days=future_days), 'iv']
if len(future) == future_days + 1:
future = future.dropna()
weights = norm.pdf(np.arange(len(future))) / sum(norm.pdf(np.arange(len(future))))
df.loc[i + pd.Timedelta(days=future_days), 'future_vol'] = np.sqrt(252) * np.sqrt(sum(weights * (future ** 2)))

上述代碼使用pandas_datareader模塊從Yahoo Finance獲取了蘋果股票價格數(shù)據(jù)，并計算了歷史波動率。通過定義函數(shù)計算隱含波動率，并使用for循環(huán)計算了每日的隱含波動率。最后，計算了未來30天的波動率。

通過分析歷史數(shù)據(jù)和計算出的未來波動率，投資者和交易員可以根據(jù)自己的風(fēng)險偏好做出相應(yīng)的投資策略。