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Say I have access to logs of all trades executed on an ECN with the price maker and taker named.

These traders are only executing some of their flow on this ECN (anywhere from 5%-80% of their volume). I do not have any information about their trades done elsewhere, so I can not say for sure what their positions are and therefore what their P&L is.

But I can still get an idea of who is buying low and selling high. Is there any standard approach or literature on how to analyze the profitability of an incomplete set of trades like this?

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What feed names all of the makers and takers? Even the MPID doesn't tell us much of anything because of sponsored access. –  chrisaycock Aug 4 '12 at 18:14
    
It's actually an OTC market, so I know everything about the individual entities and can link them to their trades. –  user2303 Aug 4 '12 at 20:07
    
Ah, that makes more sense. The only thing we exchange-traded guys can see is the occasional 13F, which doesn't list the dates of a trade or the short positions. –  chrisaycock Aug 4 '12 at 20:13

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There is no standard way in quant finance to do this. Nevertheless you can use:

  • standard ways in statistics to deal with incomplete data sets;
  • specific points to take into account that you are dealing with transactions.

The standard statistical way to manage incomplete data is to use a Bayesian method: you model the usual cross-dependences between the variables and replace missing points by the max likely one (like in Inference and missing data by Donald B. Rubin).

You can add some specific considerations like the fact that short selling is probably not allowed (except if you are working on a market where it is possible). more generally, it means that you have to compute some characteristics of what you see from the strategies, like the PnL, the risk, the time to unwind positions, etc. You should do it a sliding way (i.e. over a sliding window of few days / weeks), so that you would be able to detect some full sequences you have.

Practically, it means that you need:

  1. to isolate some full sequences you have
  2. infer the joint distribution of all your variables
  3. use it to fill gaps that you will have identified in your dataset
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That's an interesting approach. I hadn't considered a statistical solution to fill in the missing trades. But I don't see how I could estimate any probability distributions when I don't even know how much of the flow I'm missing; I could be seeing 100% of their trades or 5%. And the market is FX, so short selling is quite natural and common. –  user2303 Aug 5 '12 at 17:49
    
I tried to modify my answer to be more accurate: you need to use your knowledge of this market and the real constraints to find full sequences (or sequence that are most probably full). Then identify the gaps in terms of joint variables (price/quantity/duration/etc). Perform statistics on these joint variables to be able to compute likelihoods for each of them (Bayesian models are good that for). And then you can fill the gaps with the most probable values. –  lehalle Aug 6 '12 at 6:40

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