SPX return distribution

Discussion in 'Technical Analysis' started by garyw, Nov 20, 2017.

  1. Marcas

    Marcas Well-Known Member

    I watched it.
    Firstly I thought you are undertaking unnecessary step because all probabilities you calculating are contained within price. Later I realized that it is not quite so – price is a function of prob. but also depends on DTE and vol. If your plan is to enter by prob rather than price it's all good, you gain more flexibility this way. I didn't watch the whole presentation, but I imagine you give the number and each trader decide, accordingly to risk appetite, what will be theirs cut-off level. Nice job.

    Back to question about distribution. (I remember I should be rather quiet but can't stop thinking - maybe it's that turkey…).

    First question is: does normal distribution properly model markets behavior?
    Answer: most likely – not.
    Two clues.
    First: Jim Riggio's story when he was turned down by big institution manager because of sticking to SD. If I was that manager and I knew that SD does not correctly reflects what's going on on markets, I'd do the same, no matter how brilliant rest of the system was. Why bother with something that has flaw at the base?
    Second clue is seen by deep OTM traders. They, most likely, noticed that in that case greeks are often off, sometimes way off, and can't be trusted. (They can be more or less corrected but it is a patch on obviously wrong output.) That indicates flawed model in this area

    Second question is: should we attempt to improve model?
    Answer is: (standard answer nr 1) – it depends.
    The way it works now is applying SD across whole volSkew. As we get from q1 it is, at least not entirely, correct. But, you may say, everybody is using it. Well… Changes will require using skewed distribution (or other if necessary) in BSM model. I don't think it is that hard (really I don't know), why not then? Because in many (most) cases BSM works well and it won't be wise to throw it right away. [Now I skip part of reasoning to save space and jump to local conclusion.]
    In my opinion good model should predict not only changes in volSkew but also changes in distribution, meaning close to ATM we have SD and moving father and farther OTM distribution becomes more and mode skewed to the left. (I'm NOT saying it is – I'm just giving an example - it needs to be thoroughly researched. And I'm also leaving out thoughts about Call side.) In other words we are dealing not only with dynamic Skew but also with dynamic distribution. Seems that there is enough problems with dynamic skew to add dynamic distribution on top at the moment.

    There, if I was about to modify model anyway, how would I go about it? I'd need access to experience of many trades from many markets or vast amount of data to do data mining or both (best option). At first glance you see amount of work that needs to be done. This leads us to more detailed answer to q2. I'm a retail trader trading small account and living my life – I can play with those ideas but won't be able to perform any serious work. It's just not worth it. On other hand big boy trading billions with various resources may do it, and in this case it seems to be well worth the effort.

    Can we draw any practical conclusions?
    Yes. [Again, I use shortcuts to save space and time.]
    BSM, BS in our case, model works fine if used in relatively calm markets, not too far from ATM (my guess will be 1%, maybe 2%) and close to t+0 line - let's say t+1, t+2, maybe even t+3 lines are ok IF calculated properly. T+20 above ATM can give you rough gestimate, t+20 and 10% OTM is like learning about women curves from Picasso's paintings. That ofc creates huge problem in risk management, especially for big boys and reckless retailers, putting too much trust in models. From here you can draw further conclusions about trades management if you wish.

    Summa summarum: In my opinion it is well worth investigating distribution types in our models (only after confirmation that we are truly dealing with non-SD in life markets). It is worth even for retailers for purpose of better grasp of the problem, thus better grasp of risk, not to develop full model.

    Let's get to work.

    PS. Anybody who wishes to correct my thinking are warmly welcome to do so - in any manner.
  2. Mark17

    Mark17 Well-Known Member

    My thinking goes back to this epic quote: "who is to say that this history is any less proper than the other?" It could have happened in other combinations/permutations. However, that it happened should carry a bit more weight than things that didn't happen (a la creating a set of daily % price moves synthetically from scratch). One approach to this could therefore be to take the existing set of [real] price moves, shake them up, and pick until they're gone ("sampling" is a misnomer... we're going to end up with the same number of data points, or trading days). This would be sampling without replacement. You could generate as many simulations as desired. I think sampling with replacement gives more weight to things that already happened but biases the simulation to the downside because now the worst-case scenarios aren't limited to just the number that actually happened. This is the real reason I like the idea of sampling with replacement: biasing the test toward loss will theoretically offset some artificial inflation of profits that frequently creeps into backtesting.

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