BS Path Generation using exact formulea instead of Discritization schemes

[thusitha liyanage]

Hi All,

What is the best way to get BS process to generate paths using the exact formulea instead of the Euler schemes. i.e.

Currently BS process uses
  Sn+1 - Sn = (mu - 0.5*sigma^2)* (Sn)deltat + sigma *Sn*sqrt(deltat)*N(0,1)

What I would like to use is the exact equation to generate the same paths
i.e
  Sn+1 = Sn*exp[(mu - 0.5*sigma^2) + sigma*sqrt(dt)*N(0,1)]

Is this something I can do using existing processes in Quantlib, or do I have to do this myself?
The reason I am asking is I need this done for BS, OU process etc where we have exact and near exact solutions.

Thanks and regards,


Thusitha

[Luigi Ballabio]

On Thu, 2009-01-29 at 12:40 -0800, thusi wrote:

> Hi All,
>
> What is the best way to get BS process to generate paths using the exact
> formulea instead of the Euler schemes. i.e.
>
> Currently BS process uses
>   Sn+1 - Sn = (mu - 0.5*sigma^2)* (Sn)deltat + sigma *Sn*sqrt(deltat)*N(0,1)
>
> What I would like to use is the exact equation to generate the same paths
> i.e
>   Sn+1 = Sn*exp[(mu - 0.5*sigma^2) + sigma*sqrt(dt)*N(0,1)]

Thusitha,
        the existing BS process evolves log(S), so it might already do what you
need in this case.  Is that so?

Luigi



--

Westheimer's Discovery:
A couple of months in the laboratory can frequently save a
couple of hours in the library.



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[thusitha liyanage]

Yeah,

It already does that. I figured that out later on. I forgot to make a post regarding that.

Thanks

Luigi Ballabio wrote

On Thu, 2009-01-29 at 12:40 -0800, thusi wrote:
> Hi All,
>
> What is the best way to get BS process to generate paths using the exact
> formulea instead of the Euler schemes. i.e.
>
> Currently BS process uses
>   Sn+1 - Sn = (mu - 0.5*sigma^2)* (Sn)deltat + sigma *Sn*sqrt(deltat)*N(0,1)
>
> What I would like to use is the exact equation to generate the same paths
> i.e
>   Sn+1 = Sn*exp[(mu - 0.5*sigma^2) + sigma*sqrt(dt)*N(0,1)]

Thusitha,
        the existing BS process evolves log(S), so it might already do what you
need in this case.  Is that so?

Luigi



--

Westheimer's Discovery:
A couple of months in the laboratory can frequently save a
couple of hours in the library.



------------------------------------------------------------------------------
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SourcForge Community
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http://p.sf.net/sfu/sf-spreadtheword
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[e-mail]
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