案例研究：S&P 500 價格模擬

Manipulating Time Series Data in Python

Stefan Jansen

Founder & Lead Data Scientist at Applied Artificial Intelligence

隨機漫步與模擬

每日股價報酬難以預測
多數模型假設其具隨機性
Numpy 可產生隨機數
由隨機報酬轉為價格：用 .cumprod()
兩個例子：
- 產生隨機報酬
- 隨機抽樣實際 S&P 500 報酬

產生隨機數

from numpy.random import normal, seed

from scipy.stats import norm

seed(42)

random_returns = normal(loc=0, scale=0.01, size=1000)

sns.distplot(random_returns, fit=norm, kde=False)

ch3_3_v2 - Case Study - SP500 Simulation.011.png

建立隨機價格路徑

return_series = pd.Series(random_returns)

random_prices = return_series.add(1).cumprod().sub(1)

random_prices.mul(100).plot()

ch3_3_v2 - Case Study - SP500 Simulation.013.png

S&P 500 價格與報酬

data = pd.read_csv('sp500.csv', parse_dates=['date'], index_col='date')

data['returns'] = data.SP500.pct_change()

data.plot(subplots=True)

ch3_3_v2 - Case Study - SP500 Simulation.015.png

S&P 報酬分佈

sns.distplot(data.returns.dropna().mul(100), fit=norm)

ch3_3_v2 - Case Study - SP500 Simulation.017.png

產生隨機 S&P 500 報酬

from numpy.random import choice

sample = data.returns.dropna()

n_obs = data.returns.count()

random_walk = choice(sample, size=n_obs)

random_walk = pd.Series(random_walk, index=sample.index)

random_walk.head()

DATE
2007-05-29   -0.008357
2007-05-30    0.003702
2007-05-31   -0.013990
2007-06-01    0.008096
2007-06-04    0.013120

隨機 S&P 500 價格（1）

start = data.SP500.first('D')

DATE
2007-05-25    1515.73
Name: SP500, dtype: float64

sp500_random = start.append(random_walk.add(1))

sp500_random.head())

DATE
2007-05-25    1515.730000
2007-05-29       0.998290
2007-05-30       0.995190
2007-05-31       0.997787
2007-06-01       0.983853
dtype: float64

隨機 S&P 500 價格（2）

data['SP500_random'] = sp500_random.cumprod()

data[['SP500', 'SP500_random']].plot()

ch3_3_v2 - Case Study - SP500 Simulation.023.png

一起來練習吧！

Manipulating Time Series Data in Python