Thanks Horace. That type of thing might be in the book too ? I don't know.
I just glanced and saw that one method. but your'e right. and , if anyone
knew exactly, they probably wouldn't say anyway !!!!!!


Mark


On Tue, Apr 12, 2011 at 3:02 PM, Horace Tso <Horace.Tso@pgn.com> wrote:

> Mark, except in some rare instances, evidence is clear that financial
> prices are anything but brownian motion. And i think that's the reason Worik
> notices in some qualitative way random walk simulation appears unreal. One
> of the key differences is real price series have jumps. All these recent
> papers by Ait-Sahalia (2010, 2009, 2008, 2004) and others have shown one is
> better off with a semimartingale model with some compound Poisson process.
>
> In fact, the guy is arguing whether brownian motion is even necessary to
> model high frequency data (Annals of Statistics 2010, Vol. 38, No. 5,
> 3093-3128).
>
> H
>
>
> -----Original Message-----
> From: r-sig-finance-bounces@r-project.org [mailto:
> r-sig-finance-bounces@r-project.org] On Behalf Of Mark Leeds
> Sent: Tuesday, April 12, 2011 11:05 AM
> To: Mark Breman
> Cc: r-sig-finance@stat.math.ethz.ch; David St John
> Subject: Re: [R-SIG-Finance] Artificial price series
>
> Hi: if you can assume that returns follow brownian motion, then, in his
> book
> Simulation and Infernce for Stochastic Differential equations  on pg 26,
> Stefano Iacus shows how to generate the  trajectory of the stock price of
> S_N starting at S_0 and using increments of deltaT.  The code below is from
> the book directory of his sde package and is labelled ex1.10.R. If you
> don't
> have his book, the explanation for below is also in Hull and any other
> decent derivatives text.
>
>
> #==============================================================================
>
> set.seed(123)
> r <- 1
> sigma <- 0.5
> x <- 10
> N <- 100   # number of end points of the grid including T
> T <- 1 # length of the interval [0,T] in time units
> Delta <- T/N # time increment
> W <- numeric(N+1) # initialization of the vector W
> t <- seq(0,T, length=N+1)
> for(i in 2:(N+1))
>        W[i] <- W[i-1] + rnorm(1) * sqrt(Delta)
> S <- x * exp((r-sigma^2/2)*t + sigma*W)
> plot(t,S,type="l",main="geometric Brownian motion")
>
>
>
>
>
>
>
>
>
>
> On Tue, Apr 12, 2011 at 1:28 PM, Mark Breman <breman.mark@gmail.com>
> wrote:
>
> > Hi David,
> >
> > That's what i like so much about following this list: you regularly read
> > about things you never knew existed!
> > This package looks great David.
> >
> > -Mark-
> >
> > 2011/4/12 David St John <dstjohn@math.uic.edu>
> >
> > > Make sure to use bootstrap() for returns data and generateSample() for
> > > price
> > > data.  bootstrap() only makes sense for a stationary series.  The
> > > stationarity assumptions make it desirable to sample from the returns.
> > > generateSample() creates returns from prices, bootstraps them, then
> > > calculates the random prices from the bootstrapped returns.
> > > -David
> > >
> > >        [[alternative HTML version deleted]]
> > >
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> > > should go.
> > >
> >
> >        [[alternative HTML version deleted]]
> >
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> >
>
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