I'm afraid that the spread sequence calculation of arbitrage strategy is not as simple as you think

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The price difference is calculated “ Misunderstandings ”

When we test the strategic signals generated by the mutual operation of two or more financial assets , Inevitably need to involve different price time series , Align with the timeline , Arbitrage is one of them . However , Most of them introduce arbitrage strategies 、 Statistical arbitrage articles , For the generating calculation of price difference series , It's very simple to handle , It's basically the subtraction of two time series . For lower frequency signals , This is not a big deal , But in the field of medium and high frequency signals , Direct subtraction , There will be some problems .

This is because , For different asset price series , There is an exchange push time 、 And the difference in arrival time . Even if we see two back testing Tick The timestamp of is exactly the same , When the real offer server receives the push quotation , Also according to the first 、 In the latter order . We found in the actual transaction that , For example, Shanghai futures exchange for a variety of different delivery month contracts , The push of stock exchange in slicing data is not simultaneous , It's pushed in the order of delivery months , For example, according to RB2010、RB2101、RB2015, Push in this order , The same is true for other varieties , And for the same 500ms Within the slicing time of , received RB2010、RB2101、RB2015 Of Tick The timestamp of the data , It's the same .

Another example is the cross exchange arbitrage of digital currency , Even if the two exchanges transmit at the same time Tick Information , Due to the physical location of the exchange server, the transmission time is different , The probability of arriving at our strategy signal computing server will be different .

A typical example of different frequency of price arrival

If the market information arrival time has priority , There will be a certain amount of price difference calculated by direct subtraction “ Lag ” or “ The future function ” The question is , The frequency of price arrival is different , Then we can't directly subtract the price difference . All in all , We need a more realistic spread calculation method .

Let's look at an example of different frequency of price arrival , In other words, the push frequency of the two varieties is different . If we need stock index futures 、 Stocks ETF Carry out the design of arbitrage strategy , With IC And Zhongzheng 500ETF For example , Calculate the spread of cash arbitrage .

IC Stock index futures Tick Information , Our sources are Wind,IC The corresponding CICC , Its market push frequency is every 1 second 2 Pen data ,Level1 Free market push is 1 The mouth of the gear plate , That is to say, only buy 1、 Sell 1 Information about , Data time is the trading time of stock index futures ：9:29-15:00. Let's take a look at IC Of Tick Sample data .

Let's take a look at the Chinese securities certificate 500ETF Information about , It also comes from Wind,500ETF Market information push frequency comparison IC Much lower , Every time 3 There will be 1 Pen data ,Level1 Free market has 5 Plate mouth of gear , Buy it now 1 To buy 5、 Sell 1 To sell 5, Data push time ：9:15-15:00, Include the call auction period of the stock . Let's take a look at 500ETF Of Tick Sample data .

Skillfully use Pandas Of Merge Function

For this push frequency is different 、 There are also different data on the timeline , Calculate the spread , We need to synthesize according to the time axis .Python Pandas Ku's Merge Function , Exactly what we need . Let's briefly introduce Merge Function .

pd.merge(left, right, how='inner', on=None, left_on=None, right_on=None,left_index=False, right_index=False, sort=True,suffixes=('x', 'y'), copy=True, indicator=False,validate=None)

When we do data synthesis , The most commonly used one is before 4 Group arguments ：

left: The left side of the splice DataFrame thing

right: Right side of the splice DataFrame thing

on: The name of the column or index level to be added . It has to be on the left and right DataFrame Found in the object , For financial time series , Generally speaking, it's a timeline

how: One of ‘left’, ‘right’, ‘outer’, ‘inner’, Presupposition inner.inner It's the intersection ,outer Take Union . such as left：[‘A’,‘B’,‘C’];right[’'A,‘C’,‘D’];inner If you take the intersection ,left That's what happened A Will be with right Buy one A Match and splice , If not, it's B, stay right There is no match in , You lose .'outer’ Take Union , What appears is A It will match one by one , If not, the missing value will be added to the missing part .

And this 4 Group arguments , The preprocessing of arbitrage spread calculation ,how Fields are the most important . We use actual data , Look at the difference how The value of the field , Will calculate the final price difference , What kind of impact .

First ,how = “inner”, Take the intersection of the timeline , There are only two tables DATETIME All of us have time , Will appear in the final summary table . Let's show you the calculated summary table , And calculate the price difference sequence and draw .

 

secondly ,how = “outer”, Take the union of time axes , Just two watches DATETIME Make any list. Some time , It's going to show up in the final matrix , If the other table has no data , Press nan Value padding .

Because of outer The way data is processed , There is a lot of nana value , We can't calculate the spread directly , The usual processing method is to forward fill null data , About to nan Values are filled with the nearest non null value , Recalculate the future （ Middle price ） The price difference , And draw .

Again ,how = 'left', Merge according to the left time axis . Click on the left table (IC) The timeline matches the right table one by one , The time axis of the left table is reserved , The right table has the time of , It is incorporated into the general table , There is no such time in the right table , With nan Instead of .

Also need to forward fill null data , Then we can calculate the future （ Middle price ） The price difference .

Finally ,how = 'right', Merge according to the time axis in the right table . Click on the right table (500ETF) The timeline of is matched with the left table one by one , The timeline in the right table is reserved , The left watch has the time of , It is incorporated into the general table , The left watch doesn't change the time , With nan Instead of .

Due to the frequency of futures information compared to stocks ETF Higher ,nan It mainly appears in the earlier stage of stock call auction than futures , This part nan Data may be deleted as appropriate .

We combine the charts drawn by different price spread calculation methods , You can see , Top left how="inner" The picture of , Points are the most sparse , Because both prices need to be available at the same time , To calculate the price difference ; And the top right how="outer" The picture of , Price differentials are the most intensive , Just one set of price changes , It will calculate 1 Second price difference , And the two pictures below how="left"、how="right", The intensity is in between .

The price difference is calculated in different ways , Bring about the difference in the way of strategy driven

The price difference is calculated in different ways , On the face of it Merge Function selection how The arguments to are different , The resulting price difference series results are different . But it's different how The choice of arguments , In fact, there are different strategies behind it 、 Strategic logic .

No matter in the backtesting of strategy , Treat market information , All need to adopt one kind of “ Event driven ” The way to test , This is the most close to the back test of real trading . Let's assume that historical data is also like a firm offer , Every time a new data is generated , Give it to us once , And every time we get a new piece of information , It's a new event , This event drives the subsequent strategy signal calculation , And the judgment of the opening and closing conditions corresponding to the signal .

Let's go back to different ways of calculating the spread , Its corresponding , In fact, it's the different driving strategies .

how=‘outer’： The corresponding is futures 、 The concurrent driving of stock market , As long as there are stocks 、 Any update of futures information , Our program updates the spread , To determine whether a trade signal is triggered , Now the signal is calculated and triggered , Most frequently .

how = 'left'： The corresponding is the futures market single drive , That is, we don't care whether the stock market reaches , As long as the futures information is updated , The stock price spread is calculated by combining the latest information stored , And determine whether to trigger a trading signal .

how = 'right'： A single drive corresponding to the stock market , That is, we don't care whether the futures market reaches or not , As long as the stock information is updated , Futures combine the latest information stored to calculate the spread , And determine whether to trigger a trading signal ,left and right How to trigger , The signal is not as good as outer Frequently .

how=‘inner’： The corresponding is futures 、 The stock market is driven both ways , We are generally back testing 、 We don't use this way in any firm offer , In the first section of this article , I introduced to you , It is basically impossible for the market to arrive at the same time , This drive is too idealistic , It will also reduce a lot of trading opportunities .

The driving mode that the firm offer should choose

To sum up , We're back testing 、 The alternative way to trade , It can be divided into two categories ： Concurrent driver of two-way market 、 One way market driving . So , These two kinds of different driving methods , How to choose ？

The author according to the statistical arbitrage strategy of real trading experience , Here are some suggestions ：

1. Two types of assets that calculate the spread , There is a clear distinction of activity 、 Subordination ： For example, the near and far months of Futures （ The trading activity of contracts in recent months is usually greater than that in distant months ）、 Futures arbitrage of stocks and stock index futures （ Stock index futures have a price discovery effect on stock spot ） etc. , This should be a time of active trading 、 Varieties with leading role , As the main driver , Driven by a single market .

2. Two types of assets that calculate the spread , There is no clear distinction 、 Subordination ： For example, cross exchange arbitrage of digital currency （OKEX、 Arbitrage between fire currency exchanges , It's quite active , The relationship is equal ）, Can adopt the concurrent drive of two-way market , To capture more trading opportunities .

3. Once the drive mode is determined , In data merging 、 Back testing 、 And the development of the real offer trading system , All need to be driven in the same way , In order to ensure the consistency between the back test results and the real offer transaction to the maximum extent .

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