Ornstein-Uhlenbeck Process

AI & Machine learning
1

I was trading pairs, and I used the spread from my hedge ratio using the Engle Granger approach and then fitted an OU process. So I got:

Theta 



Kappa



Sigma 

Then I modeled a spread based on the previous information.

Im using the OU to get a smoother spread, optimized tp sl and the expected hitting time. Should I use my OU spread to get the weights also? or should I use the hedge ratio (i.e., the typical way to derive weights)?



 

2

Hi Emma,



The decision of whether to use the OU process spread, or the hedge ratio to derive weights in a pairs trading strategy depends on the specifics of your modelling approach and the assumptions you want to make.

  • If the OU process is a good representation of the spread dynamics, using it to derive weights could capture the mean-reverting nature more accurately.
  • If you believe that the relationship between the assets is not constant and may change over time, using the OU spread might be more robust, as it accounts for mean-reversion.
  • However, if the spread dynamics are well-captured by a linear relationship, using the hedge ratio might be simpler and more interpretable.
It could be beneficial to compare the performance of your pairs trading strategy using both approaches. You could conduct backtests or use other performance metrics to evaluate which method provides better results in terms of profitability, risk-adjusted returns, and other relevant criteria. Additionally, you might want to consider factors like transaction costs, liquidity, and market conditions, as these can also impact the effectiveness of your trading strategy.

Hope this helps!
3

I'm deeply thankful for the information you shared! Do you have any papers or code samples on how to derive the weights from the OU spread?

4

Hi Emma,



We do not have a direct paper, but the OU process has been used as a reference in this paper. You can check the same. Also, regarding the code, we have the same covered in the Mean Reversion Strategies course. However, the logic for coding the OU spread can be as follows:

  • If you have the parameters of your OU process (Theta, Kappa, Sigma), you can use the mean-reverting level (Theta) to determine the mean of your spread. The spread, in the context of pairs trading, is often the difference between the prices of the two assets.
  • The mean-reverting level could serve as the "target" for your spread. You might consider the difference between the current spread and the mean-reverting level to determine whether to buy or sell each asset.
Hope this helps!