VaR模型 - 用历史模拟法计算VaR
Contents
VaR模型 - 用历史模拟法计算VaR¶
前言¶
VaR模型有多种的计算方法,比较常见的有历史模拟法、方差-协方差法 和 蒙特.卡洛模拟法 ,本文将介绍历史模拟法并计算VaR。
其实用历史模拟法计算VaR的整体思路是,先计算出某只股票某段时间的整体回报率和波动, 然后根据置信区间的百分比,如10%、5%或 1% 来确定最大损失值。
import tushare as ts
import pandas as pd
import numpy as np
import scipy.stats
import matplotlib.pyplot as plt
plt.style.use('seaborn-white')
plt.rcParams['font.sans-serif'] = ['SimHei']
plt.rcParams['axes.unicode_minus'] = False
pro = ts.pro_api('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx') #这里需要填写你注册好的Tushare的TOKEN凭证
通过调用tushare获取股票600377(宁沪高速)的股票数据,这里不设置日期,那么默认获取Tushare提供的历史数据。
ticker_data = pro.daily(ts_code='600377.SH')
print('数据量:',len(ticker_data))
ticker_data.head(5)
数据量: 5000
ts_code | trade_date | open | high | low | close | pre_close | change | pct_chg | vol | amount | |
---|---|---|---|---|---|---|---|---|---|---|---|
0 | 600377.SH | 20220527 | 8.31 | 8.33 | 8.24 | 8.31 | 8.31 | 0.00 | 0.0000 | 56267.33 | 46660.525 |
1 | 600377.SH | 20220526 | 8.20 | 8.32 | 8.18 | 8.31 | 8.20 | 0.11 | 1.3415 | 65676.90 | 54313.733 |
2 | 600377.SH | 20220525 | 8.08 | 8.22 | 8.05 | 8.20 | 8.09 | 0.11 | 1.3597 | 60573.68 | 49462.806 |
3 | 600377.SH | 20220524 | 8.27 | 8.32 | 8.08 | 8.09 | 8.27 | -0.18 | -2.1765 | 48194.94 | 39510.515 |
4 | 600377.SH | 20220523 | 8.23 | 8.28 | 8.18 | 8.27 | 8.21 | 0.06 | 0.7308 | 56377.31 | 46416.005 |
从上面可以看出,序号并不是以时间作为单位的。那么我们首先需要将trade_date转为datetime格式,然后设置为序号以便于画图。
ticker_data['trade_date'] = pd.to_datetime(ticker_data['trade_date'],format='%Y%m%d')
ticker_data.set_index('trade_date', inplace=True)
returns = ticker_data["close"].pct_change().dropna()
plt.figure(figsize=(15, 5))
plt.title("股票代码:600377 - 宁沪高速", weight='bold')
ticker_data['close'].plot()
<AxesSubplot:title={'center':'股票代码:600377 - 宁沪高速'}, xlabel='trade_date'>
/opt/hostedtoolcache/Python/3.8.12/x64/lib/python3.8/site-packages/IPython/core/pylabtools.py:151: UserWarning: Glyph 32929 (\N{CJK UNIFIED IDEOGRAPH-80A1}) missing from current font.
fig.canvas.print_figure(bytes_io, **kw)
/opt/hostedtoolcache/Python/3.8.12/x64/lib/python3.8/site-packages/IPython/core/pylabtools.py:151: UserWarning: Glyph 31080 (\N{CJK UNIFIED IDEOGRAPH-7968}) missing from current font.
fig.canvas.print_figure(bytes_io, **kw)
/opt/hostedtoolcache/Python/3.8.12/x64/lib/python3.8/site-packages/IPython/core/pylabtools.py:151: UserWarning: Glyph 20195 (\N{CJK UNIFIED IDEOGRAPH-4EE3}) missing from current font.
fig.canvas.print_figure(bytes_io, **kw)
/opt/hostedtoolcache/Python/3.8.12/x64/lib/python3.8/site-packages/IPython/core/pylabtools.py:151: UserWarning: Glyph 30721 (\N{CJK UNIFIED IDEOGRAPH-7801}) missing from current font.
fig.canvas.print_figure(bytes_io, **kw)
/opt/hostedtoolcache/Python/3.8.12/x64/lib/python3.8/site-packages/IPython/core/pylabtools.py:151: UserWarning: Glyph 23425 (\N{CJK UNIFIED IDEOGRAPH-5B81}) missing from current font.
fig.canvas.print_figure(bytes_io, **kw)
/opt/hostedtoolcache/Python/3.8.12/x64/lib/python3.8/site-packages/IPython/core/pylabtools.py:151: UserWarning: Glyph 27818 (\N{CJK UNIFIED IDEOGRAPH-6CAA}) missing from current font.
fig.canvas.print_figure(bytes_io, **kw)
/opt/hostedtoolcache/Python/3.8.12/x64/lib/python3.8/site-packages/IPython/core/pylabtools.py:151: UserWarning: Glyph 39640 (\N{CJK UNIFIED IDEOGRAPH-9AD8}) missing from current font.
fig.canvas.print_figure(bytes_io, **kw)
/opt/hostedtoolcache/Python/3.8.12/x64/lib/python3.8/site-packages/IPython/core/pylabtools.py:151: UserWarning: Glyph 36895 (\N{CJK UNIFIED IDEOGRAPH-901F}) missing from current font.
fig.canvas.print_figure(bytes_io, **kw)

下面将画出每日收盘价的百分比变化图:
plt.figure(figsize=(15, 5))
ticker_data["close"].pct_change().plot()
plt.title("股票代码:600377 - 宁沪高速", weight='bold');
/opt/hostedtoolcache/Python/3.8.12/x64/lib/python3.8/site-packages/IPython/core/pylabtools.py:151: UserWarning: Glyph 32929 (\N{CJK UNIFIED IDEOGRAPH-80A1}) missing from current font.
fig.canvas.print_figure(bytes_io, **kw)
/opt/hostedtoolcache/Python/3.8.12/x64/lib/python3.8/site-packages/IPython/core/pylabtools.py:151: UserWarning: Glyph 31080 (\N{CJK UNIFIED IDEOGRAPH-7968}) missing from current font.
fig.canvas.print_figure(bytes_io, **kw)
/opt/hostedtoolcache/Python/3.8.12/x64/lib/python3.8/site-packages/IPython/core/pylabtools.py:151: UserWarning: Glyph 20195 (\N{CJK UNIFIED IDEOGRAPH-4EE3}) missing from current font.
fig.canvas.print_figure(bytes_io, **kw)
/opt/hostedtoolcache/Python/3.8.12/x64/lib/python3.8/site-packages/IPython/core/pylabtools.py:151: UserWarning: Glyph 30721 (\N{CJK UNIFIED IDEOGRAPH-7801}) missing from current font.
fig.canvas.print_figure(bytes_io, **kw)
/opt/hostedtoolcache/Python/3.8.12/x64/lib/python3.8/site-packages/IPython/core/pylabtools.py:151: UserWarning: Glyph 23425 (\N{CJK UNIFIED IDEOGRAPH-5B81}) missing from current font.
fig.canvas.print_figure(bytes_io, **kw)
/opt/hostedtoolcache/Python/3.8.12/x64/lib/python3.8/site-packages/IPython/core/pylabtools.py:151: UserWarning: Glyph 27818 (\N{CJK UNIFIED IDEOGRAPH-6CAA}) missing from current font.
fig.canvas.print_figure(bytes_io, **kw)
/opt/hostedtoolcache/Python/3.8.12/x64/lib/python3.8/site-packages/IPython/core/pylabtools.py:151: UserWarning: Glyph 39640 (\N{CJK UNIFIED IDEOGRAPH-9AD8}) missing from current font.
fig.canvas.print_figure(bytes_io, **kw)
/opt/hostedtoolcache/Python/3.8.12/x64/lib/python3.8/site-packages/IPython/core/pylabtools.py:151: UserWarning: Glyph 36895 (\N{CJK UNIFIED IDEOGRAPH-901F}) missing from current font.
fig.canvas.print_figure(bytes_io, **kw)

从上面可以看出,由于A股市场的每日涨跌幅限制,可以看到宁沪高速最大的涨跌幅为10%, 但其中有一个数据是超出10%(介于2016年至2017年坐标轴之间),估计是高开涨停。上图也可以理解为股票收益的波动图.
历史模拟法计算VaR¶
在险百分比¶
#### 计算百分比VaR对应的在险百分比
VaR_90 = returns.quantile(0.1)
VaR_95 = returns.quantile(0.05)
VaR_99 = returns.quantile(0.01)
VaR_9999 = returns.quantile(0.001)
h_VaR = {'90%':VaR_90, '95%':VaR_95,'99%':VaR_99,'99.99%':VaR_9999}
pd.DataFrame.from_dict(h_VaR, orient='index',columns=['在险损失(VaR)'])
在险损失(VaR) | |
---|---|
90% | -0.018562 |
95% | -0.026998 |
99% | -0.051330 |
99.99% | -0.090807 |
在险绝对金额¶
假设你的投资金额为100万,那么用绝对值来算,那么:
invest =100
VaR_90 = returns.quantile(0.1)*invest
VaR_95 = returns.quantile(0.05)*invest
VaR_99 = returns.quantile(0.01)*invest
VaR_9999 = returns.quantile(0.001)*invest
h_VaR = {'90%':VaR_90, '95%':VaR_95,'99%':VaR_99,'99.99%':VaR_9999}
pd.DataFrame.from_dict(h_VaR, orient='index',columns=['在险损失(金额)'])
在险损失(金额) | |
---|---|
90% | -1.856195 |
95% | -2.699795 |
99% | -5.132995 |
99.99% | -9.080738 |
解释
假设你投资了100万股票600377(宁沪高速),你单日的投资损失有90%的机率会少于1.85万;你单日的投资损失有95%的机率会少于2.70万;你单日的投资损失有99%的机率会少于5.13万;你单日的投资损失有99.99%的机率会少于9.08万。
# 假设置信区间为95%
varg = np.percentile(returns, 5)
#柱状图
plt.figure(figsize=(15, 5))
plt.hist(returns,bins=50, density=True)
plt.xlabel('回报率')
plt.ylabel('频率')
plt.title(r'收益柱状图', fontsize=18, fontweight='bold')
plt.axvline(x=varg, color='r', linestyle='--', label='95% 置信区间 VaR: ' + "{0:.2f}%".format(varg * 100))
plt.legend(loc='upper right')
plt.show()
print ("你单日的最大投资损失有95%的机率会少于" + "{0:.2f}%".format(np.percentile(returns, 5) * 100))
print(" 占" + str(len(returns)) + " 天中的" + "{0:.2f}".format(.05*len(returns)) + "天")
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fig.canvas.print_figure(bytes_io, **kw)
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fig.canvas.print_figure(bytes_io, **kw)
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fig.canvas.print_figure(bytes_io, **kw)
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fig.canvas.print_figure(bytes_io, **kw)
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fig.canvas.print_figure(bytes_io, **kw)
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fig.canvas.print_figure(bytes_io, **kw)
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fig.canvas.print_figure(bytes_io, **kw)
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fig.canvas.print_figure(bytes_io, **kw)
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fig.canvas.print_figure(bytes_io, **kw)
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fig.canvas.print_figure(bytes_io, **kw)
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fig.canvas.print_figure(bytes_io, **kw)
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fig.canvas.print_figure(bytes_io, **kw)
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fig.canvas.print_figure(bytes_io, **kw)

你单日的最大投资损失有95%的机率会少于-2.70%
占4999 天中的249.95天