Re: [Quantlib-dev] [Quantlib-users] MakeMCEuropeanEngine<PseudoRandom>

[<fho...@gm...>]

Hi Luigi!
I've thought a bit about changing the discretization scheme for a
StochasticProcess1D at least. I think one should define a new abstract =
class
Discretization outside of StochasticProcess(1D) which should carry the
framework of a general discretization scheme and could inherit to =
derived
classes such as a new EulerDiscretization. Also
StochasticProcess(1D)::evolve has a very specific form which could be a
property of the (Euler)Discretization and not the process itself. As one =
can
easily see from the code, ::expectation, ::stdDeviation, ::variance only
carry over objects from the discretization method which suggests this to =
be
taken out to a new class which could show a more general behavior =
(Milstein,
integrating var, predictor corrector, Runge-Kutta, ...).

Could that make sense?

Regards
Frank

> -----Urspr=FCngliche Nachricht-----
> Von: Luigi Ballabio [mailto:lui...@gm...]=20
> Gesendet: Freitag, 2. November 2007 17:17
> An: fho...@gm...
> Cc: qua...@li...;=20
> qua...@li...
> Betreff: Re: [Quantlib-users] MakeMCEuropeanEngine<PseudoRandom>
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> Hi Frank,
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> On Thu, 2007-11-01 at 22:12 +0100, Frank H=F6vermann wrote:
> > When I change the value which is passed to .withTimeSteps starting=20
> > from 1 to, say, 5 in the case of non-flat vol term=20
> structure (but flat
> > skew) which is defined by 5 points on the time scale, the value 1=20
> > results in a plain vanilla call option's value which corresponds to=20
> > the start vol (all else being equal). Increasing the number of time=20
> > steps the option's value seems to approach the value of the closed=20
> > form solution where the speed of convergence depends on the=20
> particular=20
> > shape of the term structure in the neighborhood of maturity.
> > =20
> > I would expect, especially in the case of one time step for=20
> this plain=20
> > vanilla call, the vol to be taken as the terminal vol not=20
> the initial=20
> > one. Am I wrong?
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> No, you're right. The problem is in the way that the=20
> Black-Scholes stochastic process is discretized. By default,=20
> it uses Euler discretization, which at each step simply takes=20
> the initial value (see
> <ql/processes/eulerdiscretization.cpp>.)  You can obtain the=20
> behavior you want by defining another discretization (you can=20
> do it by cloning the Euler code and modify it) that takes the=20
> terminal value. Once you have implemented it, you can pass it=20
> to the BlackScholesProcess constructor so that it overrides=20
> the default behavior.  If you want, you can implement more=20
> refined behaviors, too (such as integrating the variance, or=20
> using some predictor-corrector algorithm.)
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> Luigi
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> P.S. If you implement the new class and want to contribute=20
> it, I'll be glad to add it to the library.
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> --=20
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> The nice thing about standards is that there are so many of them to=20
> choose from.=20
> -- Andrew S. Tanenbaum=20
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