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Why are Hidden Markov Models (HMM) a good fit to describe the behaviour of the prices of financial assets, when these models require that the underlying stochastic process satisfies the first-order Markov property?

According to such property, the probability of future events it's only determined by the current state of things. However it's commonly known among technical traders that trend lines, support/resistance levels, previous candels formations, etc. play a big role in determining prices. What am I missing? Are these factors implicitly taken into account when the HMM is trained through the Baum-Welch algorithm?

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    $\begingroup$ ``However it's commonly known among technical traders that trend lines, support/resistance levels, candle formations, etc. play a big role in determining prices.'' I think it's commonly accepted that under (informationally) efficient markets such technical trading systems do not work. The idea that historical information is incorporated in today's prices and you cannot generate an alpha based on that information is standard in finance (EMH) and in financial modelling (almost all stock price models are Markovian). $\endgroup$ – Kevin May 10 at 12:08
  • $\begingroup$ It is not clear what your intended modelling purpose is: pricing or investment? The Markov property boils down to the EMH hypothesis in financial theory. Academics define 3 types of EMH: weak, semi-strong and strong. There is ample evidence that weak EMH holds, whereas there is some evidence that strong EMH does not hold (evidence for semi-strong is mixed). Thus, for the purpose of pricing derivatives, assuming Markovianity is equivalent to assuming EMH which, given the empirical evidence supporting the weak form, is a reasonable hypothesis which eases the theory of derivative pricing. $\endgroup$ – Daneel Olivaw May 10 at 12:50
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    $\begingroup$ For the purpose of investing, models which leverage past information, such as past stock prices or public accounting data, it is of course inconsistent to assume Markovianity, as it would imply your model does not leverage any past information to try to predict future prices. $\endgroup$ – Daneel Olivaw May 10 at 12:52
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    $\begingroup$ quant.stackexchange.com/questions/35335/… $\endgroup$ – Daneel Olivaw May 10 at 19:09
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    $\begingroup$ Finance research has dealt with that question for decades. The overwhelming evidence points towards efficient markets and unskilled fund managers. Warren Buffett's example is on the same level as pointing to your 90 year-old smoking granddad. Nice for him but it does not quite disprove medicine... and "often looking at charting systems" is nice, but if you code such a system and run a proper backtest, there remains no statistically significant alpha. People from behavioural finance (e.g. Shiller & Thaler) don't think money lies on the street either. Buffett himself recommends buying an ETF... $\endgroup$ – Kevin May 10 at 19:16
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The markov property imposes a form of unpredictability on price dynamics within financial models. As you noted, if this was exactly true, technical traders would effectively be wasting their time.

Now, there is a bit of a problem in what you wrote about technical traders. They believe that some price patterns can predict future stock prices, but this is very different from having established this predictability on sound statistical ground. My experience talking with people who engage in analyzing price patterns using concepts such as resistence and support levels, candle stick patterns, trend lines, etc. is that they are using a very fuzzy rule. If you ask them to make those rules explicit, they would all fail to do it which means by definition that they are unable to run backtests. With enough randomness and enough such traders, even in a Markovian world, a handful would be bound to be regarded as geniuses just as running a gazillion backtests on a limited amount of data is bound to turn up arbitrarily high Sharp ratios on a trading strategy, again, even in a Markovian world.

So, who's right? Well, I strongly doubt that financial markets would organize themselves to magically produce exactly Markovian dynamics. On the other hand, people trying to take advantage of non-Markovian dynamics would presumably push prices most of the time towards being more Markovian. That point is precisely why I think your prior should always be that price dynamics obey the Markov property -- in fact, I think that should be a pretty strong prior.

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  • $\begingroup$ "people trying to take advantage of non-Markovian dynamics would presumably push prices most of the time towards being more Markovian." Wouldn't that be the exact opposite? The fact that many people use the same non-Markovian stragies, is bound to make the price behave more non-Markovianly... For example, if you have millions of traders thinking that the price would bounce at a given level of support, and thus all buying there at the same time, would actually make the price to start encrease at that point, thus respecting the support. $\endgroup$ – John May 10 at 17:55
  • $\begingroup$ @John Put it this way: if you found a real arbitrage opportunity and take position to benefit from it, you systemically push the price in a direction that reduces and eventually would eliminate the opportunity. If a lot of traders think the price will bounce back up, they will take a long position in the instrument and the price will bounce NOW. The past information, in other words, will become part of the CURRENT price... That's the point. If this happens all the time, there would be a few early random Joes with profits and a load of suckers who read movements in what is pure noise. $\endgroup$ – Stéphane May 10 at 18:27
  • $\begingroup$ @John With that being said, it's not clear that my informal heuristic is all that robust. It's hard to think about what happens when a lot of people are engaged in different strategies. Not all agent based models will produce essentially unpredictable price patterns -- i.e., in some of them, something like your idea would work. $\endgroup$ – Stéphane May 10 at 18:29
  • $\begingroup$ Stephane: I think what John refers to is exactly why opportunities do exist. It's figuring out what they are that is the difficult part. So, if not everyone knows what they are, that would keep them from being arbitraged away as you describe. $\endgroup$ – mark leeds Jun 3 at 3:41

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