Apr

4

Question, from Sushil Kedia

April 4, 2009 |

What may be a good way for generating synthetic series of stock prices that shows OHLC for each day? What assumptions are reasonable to make in this endeavor?

Adam G Replies:

How about bootstrapping an existing series to remove any serial correlation (which also would remove any persistence of vol shocks)? Could carry further and mix and match daily “bars” from various instruments into one synthetic in random order.


Comments

Name

Email

Website

Speak your mind

3 Comments so far

  1. Adam G on April 6, 2009 12:52 pm

    How about bootstrapping an existing series to remove any serial correlation (which also would remove any persistence of vol shocks)? Could carry further and mix and match daily “bars” from various instruments into one synthetic in random order.

  2. Anton Johnson on April 6, 2009 3:21 pm

    During chart model development, I determined that creating an open from the prior close is an accurate way to start a new period calculation. Next build the high and low, then lastly the close.

    Obtain historic data as far back as possible for the security to be modeled. Compute key statistics such as max moves, magnitude and number of up and down days, magnitude and number of consecutive up and down days, standard deviation for different lengths of time, etc, etc. Create the same statistics for your model and adjust formula input values to fit. I use a starter series of actual historic data.

    I use these for modeling stock indices:

    Inverse Normal Distribution with a slightly positive mean for daily open with a several prior periods price look-back component

    Random range bands for daily high and low, with a last period high or low component dependant on current open direction, (per historic statistics)

    Inverse Beta Distribution for daily close, use separate Inverse Beta Distribution calculation for an up or down day, (per historic statistics)

    Standard deviation for distribution equations are a ratio of model created and randomly derived, with increased downside relative to upside volatility after consecutive down days, (per historic statistics)

    Inverse Beta Distribution for random standard deviation

    Hopefully the above information will be of assistance.

    Good Luck
    Anton

    [Edited 2009/0406 6:18pm]

  3. Russell Sears on April 7, 2009 2:57 pm

    Adam,
    It appears to me.
    If the Highs and Lows are important, than the vols are important.
    Hence, removing the persistence of vol shock would in most cases give a much different outcome. This would especially be true for the down markets, generally would not be as severe.

    If the having accurate “ranges” for certain periods I would suggest.

    Use GARCH to find the Vol for the day.

    Use use this to find the nightly vol.

    Use this with random number and appropriate to find the open.

    Use a random draw and aa adjusted uniform distribution to place the open with respect to the range. You need to adjust the distribution because the open is diproportionaly equal to either the high of the day or the low.

    Once the open is placed, this gives you the High and Low for the day.

    Finally, likewise,use a random draw and aa adjusted uniform distribution to place the close with respect to the range. You need to adjust the distribution because the close is diproportionaly equal to either the high of the day or the low.

Archives

Resources & Links

Search