Hi all,
curious about a few things here and wanted to start a discussion :) , I noticed one of the algorithms in the strat library →
which refers to this paper by Avallaneda →
In QC's implementation (attached backtest, the PCA approach), the reversion was based on just the OLS' residuals and its mean/std, but the residuals themselves was never actually modeled using the O-U process to try getting the speed of reversion, ‘K’, nor incorporated the drift estimate to get the modified s-score →
The std that was used in the QC implementation for the s-score was hence the sample's residual std instead of the theoretical equilibrium std, The algorithm performs considerably okay though, so I'm wondering if anyone have any insight on trying to incorporate the full model, and if it would make much difference (while I'm implementing it myself :D :)
Louis Szeto
Hi Anthony
The O-U process is usually used only as a volatility/short rate model, the dynamic is hardly applicable in long-term return, so only been used for mean-reversion. By using residual in linear regression, it is actually assuming the long-term expectation m_i as the expectation in this dynamic, which is unrealistic for a short-term model.
If you want to implement the full model, it would be better to discretize it into discrete time series step function rather than calibrating in continuous time SDE form. Then fit the parameters kappa_i, m_i, sigma_i by historical price data (be careful of each bar's window should be short). Finally, calculate the short-term expectation and variance (formulas available in google) and thus the z-score.
Note that this type of arbitrage shall be categorized into risk arbitrage, so unlike the usual statistical arbitrage, it has speculation exposure without any hedging position.
Best
Louis Szeto
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Anthony Suherli
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