Monte Carlo simulation
- Thread starter Ludwma
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Hi
Yes, you have a point and an argument. Arguably, it's more philosophical than relevant as MCS is whole discipline unto itself, sort of like trying to defend finance as a social science although finance is mostly the application of a hard science, math (actually, I am liking this analogy
).
VaR has two steps:
1. Getting (producing) the forward-looking distribution. The hard and time consuming part
2. Given the distribution, selecting the VaR. The easy part. (and why critics of VaR tend to miss the point: it's just a distributional quantile).
This typology (parametric vs. non), in the FRM at least, was born out of a focus on (2). In which case, parametric methods refer to methods that plucks the VaR from a final distribution that is described by a (clean) function . Contrast to a final distribution, In the case of MCS, which is an empirical distribution (a set of data). So, this distribution, while simulated data is data not a function, it is itself non-parametric, hence the classification.
I think we could safely argue that most MCS are "semi-parametric:" a parametric distribution informs the final dataset. In contrast to a boostrapped historical simulation (which similarly, defies a strict typology) where empirical data informs a final (empirical) dataset.
But, i guess an easy way to distinguish, as i think about it, is simply: data. The parametric methods exploit data only to fit; then discard the data. Then give you function from which to identify VaR. No mess, no fuss. In non-parametric methods (HS, Monte Carlo), you select the VaR from a dataset (although the means to generate the dataset vary widely)
I hope that helps, thanks,
Yes, you have a point and an argument. Arguably, it's more philosophical than relevant as MCS is whole discipline unto itself, sort of like trying to defend finance as a social science although finance is mostly the application of a hard science, math (actually, I am liking this analogy
).VaR has two steps:
1. Getting (producing) the forward-looking distribution. The hard and time consuming part
2. Given the distribution, selecting the VaR. The easy part. (and why critics of VaR tend to miss the point: it's just a distributional quantile).
This typology (parametric vs. non), in the FRM at least, was born out of a focus on (2). In which case, parametric methods refer to methods that plucks the VaR from a final distribution that is described by a (clean) function . Contrast to a final distribution, In the case of MCS, which is an empirical distribution (a set of data). So, this distribution, while simulated data is data not a function, it is itself non-parametric, hence the classification.
I think we could safely argue that most MCS are "semi-parametric:" a parametric distribution informs the final dataset. In contrast to a boostrapped historical simulation (which similarly, defies a strict typology) where empirical data informs a final (empirical) dataset.
But, i guess an easy way to distinguish, as i think about it, is simply: data. The parametric methods exploit data only to fit; then discard the data. Then give you function from which to identify VaR. No mess, no fuss. In non-parametric methods (HS, Monte Carlo), you select the VaR from a dataset (although the means to generate the dataset vary widely)
I hope that helps, thanks,
Aleksander Hansen
Well-Known Member
Monte Carlo methods do not require a parametric distribution, although it is a special case of Monte Carlo methods and a sufficient condition for Monte Carlo simulations.
Monte Carlo simulations can be run on any distribution, parametric or non-parametric.
As an example, the law of large numbers implies the Glivenko-Cantelli theorem (for some topology). This again, implies that any empirical distribution of a set of invariants (that is, i.i.d variables), as represented by the CDF, converge in probability to the true distribution as the number of observations tend to infinity.
Hence, we can definine the estimator of a generic functional of the true, unknown PDF, by replacing it with the empirical PDF/probability mass function.
In practice, these type of estimators are sensitive to the data (less robust). To see this, remember that the empirical pdf is the sum of Dirac deltas (http://en.wikipedia.org/wiki/Dirac_delta_function) try taking derivatives of a Dirac delta and you'll see why: Dirac deltas are not smooth. To solve this, in practice one would replace the empirical pdf with a regularized distribution by means of the convolution (http://en.wikipedia.org/wiki/Convolution).
Monte Carlo simulations can be run on any distribution, parametric or non-parametric.
As an example, the law of large numbers implies the Glivenko-Cantelli theorem (for some topology). This again, implies that any empirical distribution of a set of invariants (that is, i.i.d variables), as represented by the CDF, converge in probability to the true distribution as the number of observations tend to infinity.
Hence, we can definine the estimator of a generic functional of the true, unknown PDF, by replacing it with the empirical PDF/probability mass function.
In practice, these type of estimators are sensitive to the data (less robust). To see this, remember that the empirical pdf is the sum of Dirac deltas (http://en.wikipedia.org/wiki/Dirac_delta_function) try taking derivatives of a Dirac delta and you'll see why: Dirac deltas are not smooth. To solve this, in practice one would replace the empirical pdf with a regularized distribution by means of the convolution (http://en.wikipedia.org/wiki/Convolution).
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