B/S Volatility and StdDevs

Discussion in 'Options' started by trd, May 19, 2009.

  1. trd


    can someone please confirm whether the following assumptions are correct:

    If the volatility parameter for the B/S formula is 40%
    then the statistical daily change is vola / sqrt(tradedaysinyear).

    Ie. using annual 256 tradedays this gives 40/sqrt(256)=2.5 %,
    meaning the price of the underlying can vary +/- 2.5% daily.
    But this represents just 1 StdDev.
    How many StdDevs should one take in a simulation?
    I read somewhere that +/- 1 SD represents about 68.3% of the cases,
    +/- 2 SD=95.4% and +/- 3 SD represents about 99.7 % of the cases.

    So my question is this: if the above said is correct, then how many SDs
    should I take for generating artifical stock prices in a random walk simulation?
  2. heech


    *The* fundamental assumption underlying the BS model is that (log) stock returns are normally distributed.

    They make this assumption because it's convenient from a mathematical point of view, not because it's correct. So, if you're going to generate random stock prices based on that model... keep in mind you're missing out a *lot* (when compared to empirical observations of how prices move).

    If you *are* going to use this model... then in whatever program/platform you're using, I'm sure it has a built-in function to give you random samples from a normal distribution, with the standard deviation you set. You really don't need to do that calculation yourself.
  3. RobtF


    Why don't you narrow your universe (rather than all stocks) and use historical volatilties?