Re: [Quantlib-dev] Black-Scholes Process required in MCHimalayanEngine

[Marcin P. <paw...@gm...>]

On 27 November 2010 19:18, Andreas Spengler <an...@sp...> wrote:
> Hi Marcin,
>
> Am 27.11.2010 15:35, schrieb Marcin Pawlik:
>
>> Perhaps you could feed GenBSProc with the following:
>>  - flat interest rates curve with a rate that suits you (mu + 0.5*sigma^2)
>>  - flat dividend yield curve with a rate equal to 0
>>  - BlackConstantVol initiated with your sigma
>
> How would that make a GenBSProc represent a _Geometric_BrownianMotian?

I used GenBSProc as short for GeneralizedBlackScholesProcess.

I understood that you want to use in your simulation something as
simple as GeometricBrownianMotion where the simulated trajectories are
determined by constant parameters (mu, sigma). Unfortunately the MC
himalaya option engine uses StochasticProcessArray consisting of n
GeneralizedBlackScholesProcesses and those are not as simple as the
thing you wanted to use (i.e. GeneralizedBlackScholesProcess).

What I'm trying to propose is to emulate GeometricBrownianMotion (GBM
for short) with an instance of GeneralizedBlackScholesProcess (GBSP
for short). Since you cannot instantiate GBSP with constants as you're
doing it with GBM, you may try to instantiate GBSP using flat yield
curve (FlatForwardCurve class) and const vol (BlackConstantVol). Such
approach would result in GBSP with constant drift coefficient (just
like in GBM) and constant volatility (again just like in GBM).

Is it what you're looking for?

M.