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quantmeh
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The problem with random walk theory

October 9th, 2009, 1:31 pm

QuoteOriginally posted by: TitanPartnersThe original response by Jawabean of simply "no" to these questions, is quite simply, pathetic. But then I guess you are getting paid to be so shallow, so each to their own.original response was to original question. the correct answer was and still is "no".i'm not the one to say that markets are always efficient. there are anomalies. but this is all irrelevant to the original post. simply re-read it. QuoteAll these models which are based on random walk theory justify themselves with the efficient market hypothesis. Yet any model calibration which uses empirical data violates the essence of efficient market hypothesis, the 'markovness' of stock price processes, isn't it contradictory to model stocks as stochastic processes and then calibrate these models with historical data?
Last edited by quantmeh on October 8th, 2009, 10:00 pm, edited 1 time in total.
 
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TitanPartners
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The problem with random walk theory

October 9th, 2009, 2:03 pm

Fermion: 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. 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.The discussion on the distribution is wrong, we do not imply the distribution from the market on a small timescale, it is an assumption of the model (or perhaps to put it another way, an observation of some statistical best fit for some periods of time, ignoring "black swan events" in the historical data), and may be derived from the assumptions of the concept of infinitessimal time (our risk neutral portfolios construction) and the markov assumption; BOTH of which I believe to be sophistry. It 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)? Its the exotics in the OTC market which blew up, and it is these which require some justified true believe in the markov assumption (and therefore aomongst other things, the EMH assumption). This resulted in an ongoing financial disaster where a small amount of people (bankers) resulted in great pain (unemployment) for the rest of the people (the proletariat?).Jawabean, you were sharp with the question, and there was no need to be. These are deep concepts, we all know that in our hearts.
 
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Beachcomber
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Joined: May 25th, 2004, 5:56 pm

The problem with random walk theory

October 9th, 2009, 2:17 pm

QuoteOriginally posted by: Richyiee" some people are making money because they understand how to interpret the "preachings of financial mathematics". "Sure, i like this sentence. Although im not sure we share same views on the "how" in the "how to interpret" bitIf we all agreed on the "how", there would be no market. BTW, I don't think I ever said anything about my impressions of the market, I was only talking about coin flips and Markov processes.
 
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hungryquant
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The problem with random walk theory

October 9th, 2009, 2:47 pm

Last edited by hungryquant on October 8th, 2009, 10:00 pm, edited 1 time in total.
 
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hungryquant
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The problem with random walk theory

October 9th, 2009, 3:24 pm

I'm not sure if I like this term memorylessnes. I understand the markow process is effectively states that all data is contained within the current observation, but this doesn't mean that the history is irrelevent. Indeeed it is the historical process which has bought us to this point.If the historical volatility had been very low or very high in the preceding period this would affet the volatility one would need to use.
Last edited by hungryquant on October 8th, 2009, 10:00 pm, edited 1 time in total.
 
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Fermion
Posts: 4486
Joined: November 14th, 2002, 8:50 pm

The problem with random walk theory

October 9th, 2009, 9:05 pm

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?
 
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Richyiee
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Joined: September 2nd, 2008, 5:20 pm

The problem with random walk theory

October 10th, 2009, 4:18 pm

"original response was to original question. the correct answer was and still is "no"." - Jawabeanno or oh no! ? "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)? " - TitanPartnersI guess because we are optimistic fundamentals of technical analysis is sound, Black, Scholes and Merton shared this view as they built an elabourate technical indicator in their B-S-M model. At the end of the day it is a technical indicator as it takes as input historical data, no matter how mathematically involved the intermediate transformations are. In a sense we can say mathematical finance is technical analysis with mathematical rigour, charting is technical analysis with no mathematical rigour. Mathematics is but a metaphor for real life, sometimes may be it is more efficient to work directly with reality than to work with a metaphor of reality. "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" - FermionIt is wise to seperate the two concepts above as you mentioned, however these two 'sources of randomness' are closely related, market participants interactions with the market is directly reflected in prices, a source of information for market participants (unless the particular trader uses no historical data whatsoever to influence their decision making, unlikely).Market prices are reflective of traders decision making process. On the issue of the feasibility of 'charting': Historical prices alone is an extremely coarse summary of the collection of many complex(possibly) individual decisions, whether any useful information can be extracted from price alone to be exploitable relies on a substantial number of market participants to be perceptive to historical data, and for the collective to be unfickle in their strategies. In a sense financial mathematics goes a long way to realise this by preaching a set of specific, convincing rules with large influence in practitioners (assuming a large proportion practitioners take the teachings at face or near face level).
Last edited by Richyiee on October 9th, 2009, 10:00 pm, edited 1 time in total.
 
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Richyiee
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Joined: September 2nd, 2008, 5:20 pm

The problem with random walk theory

January 30th, 2011, 9:26 am

here is the equity line of a mid freq trading system that feeds off simple technical signals of historical data, so my question is: what is the probability of this result given the (true) underlying stock processes are random walks?
 
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MustafaCrap
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Joined: January 29th, 2011, 9:12 pm

The problem with random walk theory

February 3rd, 2011, 9:48 am

QuoteOriginally posted by: Richyiee"Richyiee, if you think you have found something non-Markovian that the rest of the market hasn't found, good luck; it could be very profitable...or not. " Well im sure theres plenty of people making plenty of money out there one way or another , and I gotta feeling its not because they followed the preachings of financial mathematics, maybe im wrong tho. Perhaps they preach financial mathematics then benefit?Under any trading distribution curve you're going to get some individuals at either end of the curve. But don't think that's necessarily anything to do with their intellectual processes. Almost by definition some will be there. How they got there is another matter entirely. Most will fool themselves into thinking that it was their intellectual process that got them there and the operative word is 'fool'.
Last edited by MustafaCrap on February 2nd, 2011, 11:00 pm, edited 1 time in total.
 
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Richyiee
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The problem with random walk theory

February 4th, 2011, 4:50 am

i refer you back to my post on 'Sun Jan 30, 11 10:26 AM'then what is the probability of this outcome given i have been trading randomly ?
 
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spacemonkey
Posts: 443
Joined: August 14th, 2002, 3:17 am

The problem with random walk theory

February 4th, 2011, 9:03 pm

QuoteOriginally posted by: Richyieei refer you back to my post on 'Sun Jan 30, 11 10:26 AM'then what is the probability of this outcome given i have been trading randomly ?Orifices penetrating flying sand magic mist tube
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