Timeline for Simple question about Ornstein-Uhlenbeck process
Current License: CC BY-SA 3.0
11 events
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| May 3, 2016 at 20:29 | comment | added | Quantuple | Personally, this is what I understand. Day 1, (1) run OLS to get $\hat{\beta_0}$ and $\hat{\beta}$, (2) build auxiliary process from regression residuals and estimate OU parameters (3) generate signal and trade accordingly. Day 2 to Day 5, instead of step (1) just use the value found at day 1 and continue with steps (2) and (3) as usual. Day 6, do as Day 1 that is find the new $\hat{\beta}$ etc. Maybe you would get more insight if you asked this question on Quantitative Finance Stack Exchange, please be specific on what you tried and what you already know if you do so people there can help | |
| May 3, 2016 at 18:42 | comment | added | Arti | Do I understand correctly that after running OLS: 1) I get beta and alpha, 2) I estimate OU parameters, 3) then I hold all parameters constant for next 5 days, 4) get 5 residuals from the regression, add them up to X(k) one by one, 5) estimate Z score for rach of these 5 days via (X(k)-mu)/sigma, where mu and sigma are OU parameters obtained in step 2). | |
| May 3, 2016 at 17:46 | comment | added | Quantuple | @Arti No I never ran this strategy myself. My bad: I only mentioned this daily re-calibration to illustrate why $s$-scores were not constant as you initially claimed. If you look in your reference (bottom right paragraph at page 1 and figure 2.2), you see that they suggest to keep $\hat{\beta}$ (OLS weights obtained when regressing $R^1$ on $R^2$) piecewise constant over intervals of 5 days to preclude rebalancing costs from eating up the profit from trading mean reversion. Also I suggest you first benchmark your impl using the same data set as the reference paper to see how it compares. | |
| May 3, 2016 at 17:11 | comment | added | Arti | Quantuple, do you have any experience of implementing this algo? I ran several simulations estimating s-scores for each day based on the historical 60 days period. I estimated around 100 s-scores and then applied trading tresholds from Avellaneda paper, the results are just random trading there is no visible edge at all. Is it correct to run the regression everyday? shouldn't some parameters be kept constant for some time? | |
| May 3, 2016 at 0:21 | vote | accept | Arti | ||
| May 2, 2016 at 15:05 | comment | added | Quantuple | @Arti, I have edited my answer for you to get a better grasp of what really happens in practice. Please re-read everything since I've added details everywhere :) If the answer suits you, don't hesitate to accept it: if it helped you it might help others. | |
| May 2, 2016 at 15:04 | history | edited | Quantuple | CC BY-SA 3.0 |
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| May 2, 2016 at 14:53 | history | edited | Quantuple | CC BY-SA 3.0 |
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| May 2, 2016 at 14:47 | history | edited | Quantuple | CC BY-SA 3.0 |
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| May 2, 2016 at 14:09 | comment | added | Arti | Thanks Quantuple, great answer. So now, if I understand you correctly I should use X from the auxiliary values series (2.5) to fit in the Z-score equation. Regarding the Avellaneda papers, the notation that s=(-m)/sigma is a bit confusing to me, since both m and sigma are constants the s-score will also be constant, but Figure 7 from the paper, shows its evolution as a mean reverting process, is that example calculated using auxiliary values? In the 3rd section it is defined as per equation (2.1) above. | |
| May 2, 2016 at 13:29 | history | answered | Quantuple | CC BY-SA 3.0 |