SERVING THE QUANTITATIVE FINANCE COMMUNITY

 
User avatar
Richyiee
Topic Author
Posts: 57
Joined: September 2nd, 2008, 5:20 pm

The problem with random walk theory

October 6th, 2009, 12:48 pm

All 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?Then what is the difference in essence between quantatative finance and charting (taking into account its possible for charting to be as 'precise' as quant finance with computer aided signal processing and pattern recognition)?
 
User avatar
quantmeh
Posts: 5974
Joined: April 6th, 2007, 1:39 pm

The problem with random walk theory

October 6th, 2009, 1:15 pm

QuoteOriginally posted by: RichyieeYet 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?no
 
User avatar
Richyiee
Topic Author
Posts: 57
Joined: September 2nd, 2008, 5:20 pm

The problem with random walk theory

October 6th, 2009, 2:01 pm

why not ?, by calibrating with historical data your saying history has an effect on the future, but the model asserts history has no effect on the future.
 
User avatar
quantmeh
Posts: 5974
Joined: April 6th, 2007, 1:39 pm

The problem with random walk theory

October 6th, 2009, 2:11 pm

QuoteOriginally posted by: Richyieewhy not ?, by calibrating with historical data your saying history has an effect on the future, but the model asserts history has no effect on the future.look at the simplest BM model of your choice. there'll be one parameter there - constant volatility.where will you get it from? unless God gives it to you in revelation, you'll have to calibrate it to something. calibrating to historical data is one way of doing it.
 
User avatar
Beachcomber
Posts: 140
Joined: May 25th, 2004, 5:56 pm

The problem with random walk theory

October 6th, 2009, 3:16 pm

As jawabean says, you need to get your assumptions about the underlying distribution from somewhere. Getting them from historical data doesn't violate any tenets of a random walk.Suppose I repeatedly run an experiment of flipping a coin ten times and recording the number of heads. Knowing that 6 heads came up last time doesn't help me figure out how many heads will come up next time, but I certainly can get an idea of the underlying probability distribution from past results that will be helpful going forward.
 
User avatar
AlanB
Posts: 662
Joined: July 14th, 2002, 3:00 am

The problem with random walk theory

October 6th, 2009, 6:55 pm

By calibrating to historical data, are you not making the assumption that the process you're using to model future behavior is the process that was followed by historical data....? If your model for future evolution is lognormal, yet you're using historical data (which is known to follow Gaussian statistics, for example), is there not an inconsistency? Is this not, in part, why there is a volatility smile/skew (trying to fit the actual distrubtion of returns, exhibiting fat tails, into a lognormal "calculator")? If I'm in err, please let me know (why).QuoteOriginally posted by: jawabeanQuoteOriginally posted by: Richyieewhy not ?, by calibrating with historical data your saying history has an effect on the future, but the model asserts history has no effect on the future.look at the simplest BM model of your choice. there'll be one parameter there - constant volatility.where will you get it from? unless God gives it to you in revelation, you'll have to calibrate it to something. calibrating to historical data is one way of doing it.
Last edited by AlanB on October 5th, 2009, 10:00 pm, edited 1 time in total.
 
User avatar
quantmeh
Posts: 5974
Joined: April 6th, 2007, 1:39 pm

The problem with random walk theory

October 6th, 2009, 7:09 pm

QuoteOriginally posted by: AlanBBy calibrating to historical data, are you not making the assumption that the process you're using to model future behavior is the process that was followed by historical data....? If your model for future evolution is lognormal, yet you're using historical data (which is known to follow Gaussian statistics, for example), is there not an inconsistency? yes, that's the assumption. no, it's not in violation with markov stuff.
 
User avatar
Beachcomber
Posts: 140
Joined: May 25th, 2004, 5:56 pm

The problem with random walk theory

October 6th, 2009, 8:14 pm

If the historical distribution is stable or evolving is an issue separate from the Markov assumption. The primary result of a markov process is that I gain no new information from the historical results. It is an argument about independence; it says that the unconditional expected value of the future is the same as the conditional expected value given the historical results.
 
User avatar
Gmike2000
Posts: 801
Joined: September 25th, 2003, 9:49 pm

The problem with random walk theory

October 6th, 2009, 8:43 pm

QuoteOriginally posted by: jawabeanQuoteOriginally posted by: Richyieewhy not ?, by calibrating with historical data your saying history has an effect on the future, but the model asserts history has no effect on the future.look at the simplest BM model of your choice. there'll be one parameter there - constant volatility.where will you get it from? unless God gives it to you in revelation, you'll have to calibrate it to something. calibrating to historical data is one way of doing it.God would have to specify whether the volatility he gives you is the true volatility of the process (which is yet to evolve), or the sample vol that you will realize over the life of the option. The latter case is more preferable. Still, it would not be enough, because as a hedger you would also need to know the realization of the sample path as your delta hedging depends on where on the path the big moves happen in relation to your gamma. But, if you knew the realized sample path in advance, there would be no need for delta hedging to begin with (and no need to know the vol)...all you would care about is the final price....just my 2 philosophical cents at 11:45 p.m....
 
User avatar
Fermion
Posts: 4486
Joined: November 14th, 2002, 8:50 pm

The problem with random walk theory

October 6th, 2009, 10:29 pm

QuoteOriginally posted by: RichyieeYet any model calibration which uses empirical data violates the essence of efficient market hypothesis, the 'markovness' of stock price processes,No. "Markovness" says nothing about the market price being the true value.Quoteisn't it contradictory to model stocks as stochastic processes and then calibrate these models with historical data?No. A stochastic process (even an apparently Markovian one) can have parameters that correlate with past data.QuoteThen what is the difference in essence between quantatative finance and charting (taking into account its possible for charting to be as 'precise' as quant finance with computer aided signal processing and pattern recognition)?That's a qualitative remark, not a quantitative one. If your charting ever becomes as quantitatively useful as "quantitative finance", then yes you are doing quantitative finance and it would be silly to call it "charting". But if all you are saying is that markets are not perfectly efficient, then I don't think you'll find many people here, who'll disagree. Of course that's no guarantee they won't still be using models that assume it!
Last edited by Fermion on October 6th, 2009, 10:00 pm, edited 1 time in total.
 
User avatar
Richyiee
Topic Author
Posts: 57
Joined: September 2nd, 2008, 5:20 pm

The problem with random walk theory

October 7th, 2009, 7:27 pm

since random walk theory is based on the view that future prices are independent of historical prices(am i right in saying this ?),then to calibrate the models using historical prices... seems slightly self-contradictory?, isnt that what the chartists do .. except the chartists(who use computers) analyse technical data in much more detail. Is it correct to summarise:-the random walk theorists view - "prices are too random so its impossible to predict movements in too much detail, best we can do is to hypothesise a range(distribution) in which they may move"... "but when we test theory to data, there are inaccuracies highlighted for example by the smile... so lets tweak our models to fit data... but hang on, didnt we start off with the princple that the future is independent of past data.... then why are we using past data to calibrate our models?", thats what i kind of meant with the markov bit. the chartist: "We make no prior assumptions and deduce relationships from data alone" the anti-chartist: "your indicators are elementry, theres no empirical evidence, no one makes money using MA + RSI .. or that fibonacci voodoo"the chartist: "They are so 1970's"the anti-chartist: "what dyou use then, lets see the evidence"the chartist: "I cant explain it/I'm not telling you"the anti-chartist: "lies"Btw im not a chartist im just trying to affirm some views to complete my masters thesis , all enlightening comments apprieciated "Quote--------------------------------------------------------------------------------Then what is the difference in essence between quantatative finance and charting (taking into account its possible for charting to be as 'precise' as quant finance with computer aided signal processing and pattern recognition)?--------------------------------------------------------------------------------That's a qualitative remark, not a quantitative one. If your charting ever becomes as quantitatively useful as "quantitative finance", then yes you are doing quantitative finance and it would be silly to call it "charting". "I guess from my perspective right now the fundamental distinguising feature between 'charting' and 'quantative finance' is that chartists approach markets with the belief that historical data affects future data, and 'quantatative finance people' dont
Last edited by Richyiee on October 6th, 2009, 10:00 pm, edited 1 time in total.
 
User avatar
quantmeh
Posts: 5974
Joined: April 6th, 2007, 1:39 pm

The problem with random walk theory

October 7th, 2009, 7:38 pm

QuoteOriginally posted by: Richyieesince random walk theory is based on the view that future prices are independent of historical prices(am i right in saying this ?),then to calibrate the models using historical prices... seems slightly self-contradictory?you're repeating your first post here. it doesn't help.there were several posts which explain why you statement is incorrect. read them carefully.
 
User avatar
Richyiee
Topic Author
Posts: 57
Joined: September 2nd, 2008, 5:20 pm

The problem with random walk theory

October 7th, 2009, 7:59 pm

"look at the simplest BM model of your choice. there'll be one parameter there - constant volatility.where will you get it from? unless God gives it to you in revelation, you'll have to calibrate it to something. calibrating to historical data is one way of doing it. " - jawabeanMao (roughly): "We are communists! , in this society !everyone is equal!! now hand over your trust to the state (along with the house)"
 
User avatar
quantmeh
Posts: 5974
Joined: April 6th, 2007, 1:39 pm

The problem with random walk theory

October 7th, 2009, 8:19 pm

QuoteOriginally posted by: Richyiee"look at the simplest BM model of your choice. there'll be one parameter there - constant volatility.where will you get it from? unless God gives it to you in revelation, you'll have to calibrate it to something. calibrating to historical data is one way of doing it. " - jawabeanMao (roughly): "We are communists! , in this society !everyone is equal!! now hand over your trust to the state (along with the house)"stop b/s. you wont have intelligent conversation unless you start making sense on basic level.
 
User avatar
beaker
Posts: 25
Joined: June 25th, 2009, 5:59 pm

The problem with random walk theory

October 7th, 2009, 9:41 pm

Quotesince random walk theory is based on the view that future prices are independent of historical prices(am i right in saying this ?),I don't think that's correct.
Last edited by beaker on October 6th, 2009, 10:00 pm, edited 1 time in total.
ABOUT WILMOTT

PW by JB

Wilmott.com has been "Serving the Quantitative Finance Community" since 2001. Continued...


Twitter LinkedIn Instagram

JOBS BOARD

JOBS BOARD

Looking for a quant job, risk, algo trading,...? Browse jobs here...


GZIP: On