Re: [Quantlib-users] RandomSequenceGenerator first element always equals startingPrice

[U.Mutlu <um...@mu...>]

Jonathan S. <sw...@gm...> on 2023-09-05 12:53:12 wrote:
 >
 > 1. Could you provide a bit more info on why you want a path containing a
 > single step? The typical use case for PathGenerator is for many steps, with
 > the value at the first step (i.e. at t_0) being equal to the starting
 > price. Maybe what you're looking for isn't a path, but something else.

I'm doing a research on GBM implementations out there in the field
by running Monte Carlo simulations to see how good the generated data is
by comparing it to the table below of timeSteps and ExpectedHitRate%:

I was not able to use timeSteps=1 in QuantLib for verifying
the first case below. timeSteps >= 2 is doable, but as said
the results are far from being correct.
Recent postings here suggested to replace the use of Box-Muller
class by some other classes; I'm now trying to test that too.


Expected HitRate% for 1SD around initial stock price for varying GBM timeSteps
This table is an extension of https://en.wikipedia.org/wiki/68–95–99.7_rule as 
there only timeStep=1 is given.
These numbers are exact values, not the result of simulations.
Params used: S=100 rPct=0 qPct=0 IV=30(s=0.3) DIY=365.00 DTE=365(t=1 dt=1 
dd=365) zFm=-1(SxFm=74.081822) zTo=++1(SxTo=134.985881)
    timeSteps   Expected_HitRate
           1       68.2689%   cf. https://en.wikipedia.org/wiki/68–95–99.7_rule
           2       76.2695%
           3       79.2918%
           4       80.7919%
           5       81.6648%
           6       82.2304%
           7       82.6265%
           8       82.9197%
           9       83.1461%
          10       83.3265%
          15       83.8653%
          20       84.1337%
          25       84.2942%
          30       84.4010%
          35       84.4771%
          40       84.5341%
          45       84.5785%
          50       84.6139%
          60       84.6671%
          70       84.7050%
          80       84.7334%
          90       84.7555%
         100       84.7732%
         500       84.9003%
        1000       84.9162%
       10000       84.9305%
      100000       84.9319%
     1000000       84.9320%
    10000000       84.9320%