[R-SIG-Finance] Artificial price series

[Horace Tso]

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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