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# B/S Volatility and StdDevs

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

1. ### trd

Hi,
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?

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