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In the context of compliance and market abuse monitoring, what relative change threshold would you choose to decide if transactions should be looked into?

For example, if a bond price had a relative price change of +/- X% and the bond was sold or bought around the time the price move occurred, there could be a market abuse (for example, insider knowledge).

I am trying to get a decent level in order to avoid false positives (the desk is mainly trading EM bonds).

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How about using either option-implied or historically derived daily $\sigma$ and then setting a threshold of $\pm 2\sigma$ or what may seem reasonable to you?

I think you would also have to scan for a pattern. If the price jumped up by say $+2\sigma$ and then remained at that level, that would likely indicate some new information becoming generally available.

However, if there was a single trade up by $+2\sigma$ and the subsequent trades were again at the price level prevailing before the potentially suspicious trade, then that is clearly something you would want to look into further.

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I would back out the price impact of factors that are probably beyond the control of the traders. For example, in corporate bonds, I would remove the price impact of the local interest rate moves and the impact of any currency effects. The credit spread impact is a little difficult in that the insider information would probably also impact the credit spread. For this factor, one could take the approach above where a 2 sigma move on the credit spread could alert one to a suspicious trade. This is an example for a credit risky bond. Of course if one is to look at information leakage from central banks etc, one would need to look at factors that impact those bonds for large moves, and local interest rates would of course need to be included in that analysis. Also, one could look at similar instruments to see if an expected impact on those instruments were in sync with the move in those bonds. For example, did the equity also get impacted similarly (taking into account the subordination)? What about the options, asset swaps, credit default swaps, etc.?

I would also look at volume spikes.

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