stratified sampling
- Thread starter ajsa
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Hi asja,
Jorion has a summary description on p. 320-321 of VaR 3rd Ed. Here is my attempt at "accelerating" the explain
say we want to Monte Carlo simulate 1-period, relative normal (parametric) VaR for asset with vol = 10%
we can run 1,000 computations of =10%*NORMSINV(RAND())
i.e., the NORMSINV performs the "inverse transform method" on the uniform distribution produced by RAND()
to get the 95% VaR we sort this list of 1,000 scaled volatilities and "look down" the list toward the bottom at the ~ 950th entry
but this implies most of the RAND()s are not used.
in stratified sampling, instead we analyze the bottom 10% (e.g.), so we use:
=10%*NORMSINV(RAND()/10); i.e., RAND()/10 gives a random number from 0 to 0.1
i.e., we are simulating the bottom 10% of outcomes directly
the median here is the 5% of the overall distribution (50% * 10% = 5%)
the "acceleration" refers to requiring fewer computations, or greater accuracy for the same number of computations
David
Jorion has a summary description on p. 320-321 of VaR 3rd Ed. Here is my attempt at "accelerating" the explain
say we want to Monte Carlo simulate 1-period, relative normal (parametric) VaR for asset with vol = 10%
we can run 1,000 computations of =10%*NORMSINV(RAND())
i.e., the NORMSINV performs the "inverse transform method" on the uniform distribution produced by RAND()
to get the 95% VaR we sort this list of 1,000 scaled volatilities and "look down" the list toward the bottom at the ~ 950th entry
but this implies most of the RAND()s are not used.
in stratified sampling, instead we analyze the bottom 10% (e.g.), so we use:
=10%*NORMSINV(RAND()/10); i.e., RAND()/10 gives a random number from 0 to 0.1
i.e., we are simulating the bottom 10% of outcomes directly
the median here is the 5% of the overall distribution (50% * 10% = 5%)
the "acceleration" refers to requiring fewer computations, or greater accuracy for the same number of computations
David
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