期權 Pair trading 策略

Pair trading 策略 - 期權

0. 引庫

import pandas as pd
import numpy as np
import tushare as ts
import seaborn
from matplotlib import pyplot as plt
plt.style.use('seaborn')
%matplotlib inline
stocks_pair = ['cu', 'zn']

1. 數據準備

# 加載數據
data1 = pd.read_csv('cu.csv')[['date','close']]
data2 = pd.read_csv('zn.csv')['close']
# 按行拼接收盤價
data = pd.concat([data1, data2], axis=1)
data.set_index('date',inplace = True)
# 重命名列（'cu'、'zn'）
data.columns = stocks_pair
data.head()

	cu	zn
date
2016/10/18	37300	18080
2016/10/19	37260	18200
2016/10/20	37270	18255
2016/10/21	37150	18245
2016/10/24	37320	18175

data.plot(figsize= (8,6));

2. 策略開發思路

data.corr()  # 協方差矩陣

	cu	zn
cu	1.000000	0.941114
zn	0.941114	1.000000

# 數據可視化，看相關關係
plt.figure(figsize =(8,6))
plt.title('Stock Correlation')
plt.plot(data['cu'], data['zn'], '.');
plt.xlabel('cu')
plt.ylabel('zn')
data.dropna(inplace = True)

# 對兩股票價格做線性迴歸（白噪聲項符合正態分佈）
[slope, intercept] = np.polyfit(data.iloc[:,0], data.iloc[:,1], 1).round(2)      
slope,intercept

(0.48, 266.73)

(y-266.73-0.48x) 符合Stationary

# 算出 (y-266.73-0.48x) 一列
data['spread'] = data.iloc[:,1] - (data.iloc[:,0]*slope + intercept)
data.head()

	cu	zn	spread
date
2016/10/18	37300	18080	-90.73
2016/10/19	37260	18200	48.47
2016/10/20	37270	18255	98.67
2016/10/21	37150	18245	146.27
2016/10/24	37320	18175	-5.33

data['spread'].plot(figsize = (8,6),title = 'Price Spread');

# 對 spread 進行標準化
data['zscore'] = (data['spread'] - data['spread'].mean())/data['spread'].std()
data.head()

	cu	zn	spread	zscore
date
2016/10/18	37300	18080	-90.73	-0.018872
2016/10/19	37260	18200	48.47	0.192004
2016/10/20	37270	18255	98.67	0.268053
2016/10/21	37150	18245	146.27	0.340163
2016/10/24	37320	18175	-5.33	0.110502

# 可視化標準化後的值
data['zscore'].plot(figsize = (10,8),title = 'Z-score')
plt.axhline(1.5)
plt.axhline(0)
plt.axhline(-1.5)

產生交易信號

data['position_1'] = np.where(data['zscore'] > 1.5, 1, np.nan)
data['position_1'] = np.where(data['zscore'] < -1.5, -1, data['position_1'])
data['position_1'] = np.where(abs(data['zscore']) < 0.5, 0, data['position_1'])

data['position_1'] = data['position_1'].fillna(method = 'ffill')
data['position_1'].plot(ylim=[-1.1, 1.1], figsize=(10, 6),title = 'Trading Signal_Uptrade');

data['position_2'] = -np.sign(data['position_1'])
data['position_2'].plot(ylim=[-1.1, 1.1], figsize=(10, 6),title = 'Trading Signal_Downtrade');

3. 計算策略年化收益並可視化

# 算離散收益率
data['returns_1'] = np.log(data['cu'] / data['cu'].shift(1))
data['returns_2'] = np.log(data['zn'] / data['zn'].shift(1))

# 算策略列
data['strategy'] = 0.5*(data['position_1'].shift(1) * data['returns_1']) + 0.5*(data['position_2'].shift(1) * data['returns_2'])
# 計算累積收益率
data[['returns_1','returns_2','strategy']].dropna().cumsum().apply(np.exp).tail(1)

	returns_1	returns_2	strategy
date
2018/6/6	1.410724	1.378042	1.35536

# 畫出累積收益率
data[['returns_1','returns_2','strategy']].dropna().cumsum().apply(np.exp).plot(figsize=(10, 8),title = 'Strategy_Backtesting');

# 計算年化收益率
data[['returns_1','returns_2','strategy']].dropna().mean() * 252

returns_1    0.216785
returns_2    0.202018
strategy     0.191562
dtype: float64

# 計算年化風險
data[['returns_1','returns_2','strategy']].dropna().std() * 252 ** 0.5

returns_1    0.158409
returns_2    0.210702
strategy     0.054305
dtype: float64

# 策略累積收益率
data['cumret'] = data['strategy'].dropna().cumsum().apply(np.exp)
# 策略累積最大值
data['cummax'] = data['cumret'].cummax()
# 算回撤序列
drawdown = (data['cummax'] - data['cumret'])
# 算最大回撤
drawdown.max()

0.026175344283502433

小結

策略的思考

1. 對多隻ETF進行配對交易，是很多實盤量化基金的交易策略；

策略的風險和問題：

1. Spread不迴歸的風險，當市場結構發生重大改變時，用過去歷史迴歸出來的Spread會發生不迴歸的重大風險；

2. 中國市場做空受到限制，策略中有部分做空的收益是無法獲得的；

3. 迴歸係數需要Rebalancing；

4. 策略沒有考慮交易成本和其他成本；