QuoteOriginally posted by: TitanPartnersFermion: First of all, again, a markov process is by DEFINITION a memoryless system. As I understand it, you are saying that it is ok to still call something Markovian, because only the parameters evolve with time through some other process, and we still use the same process at infinitessimal time just with different parameters (implied from the market - whatever that means, which we could hypothesise means for example implied from historical data, although in practise this is not the case, it is a measure of "fear" and "greed" IMHO). But this is a philosopical contradiction: you are meerly hiding the non-Markov properties in the undefined dynamical evolution of the parameters of the model, and hence you are not using the markov model to model the dynamics at all, you are simply using it as a yardstick for interpolation.In the sense you interpret Markov, there can be no testable distribution unless you assume the parameters, even if their origin is exogenous to the data, can be tested with available data. Who, in finance, interprets Markov in the way you intend -- which explicitly denies the possibility of verification with past data?Quote It is now UNFALSIFIABLE (or in other words, not really a dynamical model at all, just a statistical property of our best fit of the historical data), because one can always simply say, "oh they were just undervaluing the risk" i.e. the implied volatility was too low.Your interpretation of falsifiability is wrong. I have not suggested that parameters can be arbitrarily adjusted just because the latest data doesn't fit. Rather, the whole point of the exercise from my point of view is to find (relatively) stable parameters. If you have none, then obviously the model has been falsified.In large part, I think the problem gets confused here because of the tendency to think of market prices obeying a single simple stochastic process when elementary common sense will tell us that there are at least two independent sources of randomness at work: (1) the arrival of information and (2) the uncertainty of market participants in how to assimilate this information. Any model that doesn't take both these factors into account will be easily falsified IMHO. That is a major reason (not the only one) why finding stable parameters is so difficult.So, to my mind, the solution is not to throw out the notion of a Markov-like (let's call it pseudo-Markov to satisfy your objection) process but to investigate its complexity. QuoteIt is obvious there is no "infinitessimal time" in the OTC markets, and therefore doing any calculus at all is very dubious. Indeed the only reason the model has any practial use is because really, is because in practise the market sets the prices, and not the model, through implied volatility (and other implied parameters). Philosophically, on an exchange traded market of plain vanillas, therefore, why does one need any concrete model at all (we ONLY need to think about no arbitrage ideas which are not pertaining to any kind of price dynamics)?I thought we were talking about underlyings, not options. Implied volatility is irrelevant and what "no arbitrage ideas" don't take into account the underlying?