September 2011Wilmott Journal 2011:74-81
Project: Rare Events
Authors：Dragos Bozdog, Ionut¸ Florescu, Khaldoun Khashanah, and Jim Wang
source：https://www.researchgate.net/publication/215958736_Rare_Events_Analysis_of_High-Frequency_Equity_Data
In this work we present a methodology to detect rare events which are defined as large price movements relative to the volume traded. We analyze the behavior of equity after the detection of these rare events. We provide methods to calibrate trading rules based on the detection of these events and illustrate for a particular trading rule. We apply the methodology to tick data for thousands of equities over a period of five days. In order to draw comprehensive conclusions, we group the equities into classes and calculate probabilities of price recovery after these rare events for each class. The methodology that we have developed is based on non-parametric statistics and makes no assumption about the distribution of the random variables in the study.
high-frequency trading, average daily volume, trading strategy
開發一種即時檢測罕見事件的方法，其中價格變動較大且股票交易量相對較小
分析這些罕見事件后的價格行為，研究價格回升的概率。如果進行交易，在檢測到的觀察中，預期回報是多少？
透過Rare Events Analysis for High-Frequency Equity Data論文所提供的方法
運用yfinance抓取股票的“收盤價”、“交易量”和“日期”，計算APPLE在一年內歷史股價，進行高頻罕見事件分析
-捉歷史股價的工具
!pip install yfinance
-抓取AAPL一年內的資料
import yfinance as yf
msft = yf.Ticker("AAPL")
# get stock info
msft.info
# get historical market data
hist = msft.history(period="1y")
hist
-設定V0
#hist[["Close", "Volume"]]
V0 = hist["Volume"].mean()
amt = list(hist[["Volume"]].iloc[:, 0])
data = hist[["Close", "Volume"]]
data.head()
-輸出Volume
data["Volume"].sum()
-
data.shape
-
print(data.iloc[0, 1])
print(data.iloc[-1, 1])
print(data.iloc[data.shape[0]-1, 1])
s_sum = 0
for i in range(0, data.shape[0]-1):
s_sum = s_sum + data.iloc[i, 1]
print(s_sum)
-
#for i in range(0, data.shape[0]):
# print( int(data.iloc[j, 0]), int(data.iloc[j, 1]))
#if(s_sum < V0):
print(data.iloc[251, 0]- data.iloc[0, 0])
from pandas.core.indexes.extension import deprecate_ndim_indexing
import pandas as pd
import numpy as np
#設定一個空的k及dp, 初值皆為NaN
k = np.empty(len(hist))
dp = np.empty(len(hist))
k[:] = np.nan
dp[:] = np.nan
#將Volumn存在volume中
volume = list(hist[["Volume"]].iloc[:, 0])
#================================
#任意設定一個V0值
#================================
V0 = np.mean(volume)
#找出每個索引值的k
for i in range(0, len(hist)):
t=np.nan
for j in range(i+1):
if sum(volume[j:i]) < V0:
t=j
break
k[i]=t
#找出每個索引值的dp
for i in range(0, len(hist)):
t=[]
for j in range(int(k[i]), i):
t.append(volume[i]-volume[j])
if len(t)==0:
dp[i] = np.nan
else:
dp[i] = max(t)
#印dp
dp
#將dp(list)轉成df_dp(DataFrame)
df_dp = pd.DataFrame(dp)
#平均數/標準誤
m = float(df_dp.mean())
se = float(df_dp.std() / len(hist)**0.5)
#推論x值(假設a=0.05)
print(m-1.96*se)
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