Pairs Trading: The Ornstein-Uhlenbeck Process and Pairs Ratio Determination

In this video, we continue going over some of the material in the book Optimal Mean Reversion Trading: Mathematical Analysis And Practical Applications by Tim Siu-tang Leung, Xin Li. Continuing with what we have done previously, we will use maximum likelihood estimation to estimate the Ornstein-Uhlenbeck parameters. This will be in the context of pairs trading, so we will extend what we’ve done to estimate the optimal share ratio that comprises the pair.
Previous videos in this series:
What is a pairs trade: • What is a Pairs Trade?
Maximum Likelihood Estimation with Ornstein-Uhlenbeck (part 1): • Maximum Likelihood Est...
Maximum Likelihood Estimation with Ornstein-Uhlenbeck (part 2)
: • Maximum Likelihood Est...
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[@xelhaku]

Thanks!

[@ranjansingh9972]

This is brilliant content - well done!

[@gouki1001]

You said that this is a "computationally inefficient" way to do this. Do you have a decent/standard way to find the dollar value of the weights?

[@rich5034]

Thanks for sharing.

[@fostergeoff]

Great work

[@jbthabest]

Hi Kevin, I keep getting the error "Series object has no attribute 'to_numpy' " for the line of code ------ GLD ['Adj Close'].to_numpy(). Any clue how to fix this error?

[@kpmooney]

How are you importing the data? What does type(GLD['Adj Close']) return?

[@jbthabest]

@@kpmooney I imported the data using the file location on my computer, which seemed to work fine. I checked the data type and it says class ‘pandas.core.series.Series’

[@brendanlydon5272]

Curious as to where I could find your video on optimal stoping?

[@kpmooney]

It hasn't come out yet. Trying to figure out how to present it as the book is just page after page of math.

[@FreeMarketSwine]

​@@kpmooney Would love to see that!

[@MikeMane]

@@kpmooney Hey Kevin, did you manage to get this done I am looking forward to this lecture :)

[@brendanlydon5272]

Videos are awesome

[@YannickvDijk]

Thank you for going through the process in this depth. The value for dt seems to be completely irrelevant for the resulting ratio. I assume this is only the case when the datapoints are sampled equidistant. If one would have a look at intraday datapoints across multiple days, would you still say that the value of dt can be assumed constant (for example 1-minute timeframe) and thus can be disregarded?

[@kpmooney]

Yes, it assumes constant time steps. You can adjust for non-uniform spacing easily enough, but I don't know the best way to handle large breaks in time, i.e. minute time steps during the day followed by an overnight session with no data.

[@YannickvDijk]

@@kpmooney Thank you for your prompt response! What I read online is that the breaks may cause jumps that can in turn influence the calibration process quite severely. One more question arose during the implementation; how would you decide on which stock to fix (or pick as A). I tried based on either larger/smaller mean and standard deviation, but this does not lead to a stable process (e.g. some "optimal" ratios for pairs are larger than 1, meaning that the A/B should be flipped as I reckon). Is there a metric for this? Or should one simply try and adjust accordingly?

[@lapapanitel.7995]

Hi how can we get the notebook?

[@kpmooney]

There's a link in the description to the notebook on Github.

[@rohinthakur9995]

A GOOD DAY TRADING SYSTEM written by a well known indian research analyst Rohin Thakur, is one of the best books written on day trading. There are some grammatical errors in the book but it contains alot of knowledge.

[@jeremykaaria6023]

The full formula for term when calculating parameters is a little hidden off screen - i saw: term = Xxy - 2*np.exp(-mu0*dt)*Xxy + np.exp(-2*mu0*dt) * Xxx - 2*theta0*(1-np.exp(-mu0*dt)) * (Xy...

[@kpmooney]

The equations and code are available in at Github linked to in the description.