[R-SIG-Finance] Artificial price series

[Ron Michael]

Thanks Horace and Mark for replying on my query. However I believe that my question was not properly understood or may be I could not understand your statement. Whatever it happened, I believe there is some miscommunication.

I want to understand that: between these 2 candidates GBM & RW (form of them I already mentioned in my previous mail), which could be better. I understand that both are very simplistic in modelling any price, however if I have to chose anyone from them then what should I chose? GBM or RW.

Many previous mails seems to me that, they are in support of GBM, where I believe that there are no fundamental difference between them. Or perhaps I am missing something?

Thanks,

--- On Tue, 19/4/11, Horace Tso <Horace.Tso at pgn.com> wrote:

> From: Horace Tso <Horace.Tso at pgn.com>
> Subject: RE: [R-SIG-Finance] Artificial price series
> To: "Ron Michael" <ron_michael70 at yahoo.com>, "r-sig-finance at r-project.org" <r-sig-finance at r-project.org>
> Date: Tuesday, 19 April, 2011, 1:44 AM
> Ron & others,
> 
> I venture to give my 2 cent worth of opinion here. Many
> (the Professors on the list please weigh in) have more
> insight than I do. 
> 
> Here is what I find curious. As Worik pointed out in his
> original post, if you use any of the R simulation functions
> to generate a random walk or a fancier brownian motion
> series, plot it with some real price data, let's say daily
> closing level of the Dow Jones Industrial Average, you could
> tell they are different. But it's hard to say exactly what
> makes them look different to the human eyes. 
> 
> Not too long ago I played this trick on a friend of mine,
> who claimed he had no prior knowledge of finance nor
> familiar with securities price patterns. I sampled a number
> of time series from Bloomberg. I think I picked daily
> S&P, minute ticks of gold, nymex natural gas, the
> Shanghai Composite stock index, and other unrelated real
> prices. Then I simulated equal number of artificial data
> series using different stochastic models. A few were just
> straightforward random walk with varying sigma, others were
> jump diffusion (EMJumpDiffusion) with different jump prob
> and size. I plotted them along side and I was careful to
> remove the axis labels so he couldn't see the scale of
> things. 
> 
> I asked my friend to tell me which were real and which were
> artificial data. Amazingly he got many of them right. (OK,
> full disclosure here: this occurred in a bar after he had a
> couple of beers.)
> 
> I could see how even the most sophisticated simulation
> models couldn't quite imitate reality. First, many stock
> data have trend. The buy-and-hold crowd is right. Secondly,
> the unobserved volatility parameter is in itself a
> stochastic process (huge literature on this). Third, the
> jump processes in simulation models are probably too
> simplistic. Just plot Dow Jones from July to Dec, 1987. 
> 
> Horace
> 
> 
> 
> 
> 
> 
> 
> 
>  
> 
> -----Original Message-----
> From: r-sig-finance-bounces at r-project.org
> [mailto:r-sig-finance-bounces at r-project.org]
> On Behalf Of Ron Michael
> Sent: Monday, April 18, 2011 8:05 AM
> To: r-sig-finance at r-project.org
> Subject: [R-SIG-Finance] Artificial price series
> 
> Hi Worik, I have been following this thread in "http://r.789695.n4.nabble.com/Artificial-price-series-td3443230.html",
> for quite a time now, however could not convince myself in
> one aspect. You said that simple RW model is not quite
> satisfactory (Horace Tso:: evidence is clear that financial
> prices are anything but brownian motion) hence, many people
> suggested GBM for that. But I could not understand why they
> are essentially different. I have:
> 
> for vanilla RW:   log(S[t+1]) = log(S[t]) +
> epsilon~N(.,.)
> for vanilla GBM:  log(S[t+1]) = log(S[t]) + (mu -
> 0.5sigma^2) + epsilon~N(.,.)
> 
> Of course hare I am comparing both **vanilla** type and if
> I want to incorporate other features like jump, heavy tail
> etc., then I can incorporate those features in either case.
> Therefore driven by some common sense, why those 2 models
> would be fundamentally different? Only difference I see
> that, I generally do not include Intercept in RW, because
> including an Intercept signifies some deterministic trend in
> the underlying price, which also makes sense.
> 
> Additionally Mark says, "returns follow brownian motion",
> did he mean to say that **price** follows brownian motion?
> 
> Any clarification would be highly appreciated.
> 
> Thanks,
> 
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