Hi Horace: I'm actually not looking for anything. Someone sent in a question
asking for a way
of simulating a stock price series in a realistic way. So, some people said
take a stock series
and bootstrap it. My suggestion was totally different but depending on the
goal in mind,
could possibly be realistic enough ? I don't have any more details but
that's why I sent it.
On Tue, Apr 12, 2011 at 3:32 PM, Horace Tso wrote:
> Mark, not sure what you're looking for. Simulating a compound Poisson or
> a Cauchy process is not hard. I'm aware of EMJumpDiffusion to fit and
> simulate these sort of things. I'm sure other R packages could do similar
> simulation, too.
>
> H
>
> ------------------------------
> *From:* Mark Leeds [mailto:markleeds2@gmail.com]
> *Sent:* Tuesday, April 12, 2011 12:09 PM
> *To:* Horace Tso
> *Cc:* Mark Breman; r-sig-finance@stat.math.ethz.ch; David St John
>
> *Subject:* Re: [R-SIG-Finance] Artificial price series
>
> 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 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
>> 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
>> >
>> > > 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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>> >
>>
>> [[alternative HTML version deleted]]
>>
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>
>
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