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>When you run the Black Scholes model to solve for price (to determine
>whether the market
>price is over- or under-valued) the input is (for stocks) the 20 day
>statistical volatility.
When YOU run the model, YOU may use the 20-day statistical volatility, but
that doesn't mean it's the only way to do it. Everyone uses a different
historical volatility -- that's the problem.
But when I'm talking about solving the model, I don't mean solving for
price. I mean solving for volatility.
An example will help.
First of all, I'm going to use 200-day historical volatility of about 17%
for November Beans because that will provide answers closer to actual
prices (believe me, it will). I run the model and the theoretical prices
are...
Nov 550 call 23.70
Nov 600 call 5.35
Nov 650 call 0.68
But I look in the paper and the actual closes were:
Nov 550 call 24.50
Nov 600 call 7.75
Nov 650 call 3.00
So what gives? Is our model screwed up? Of course it is. Models don't trade
options. People do.
So let's adjust our model for a moment. It's inputs are strike price,
underlying price, time to expiration, interest rate and volatility.
Except for volatility, all of the rest of the inputs cannot be changed. The
ONLY variable is volatility. (Interest rate may be subject to debate but it
has only a tiny impact on options that have short expiration periods)
So, you ask yourself a question. What would volatility HAVE TO BE to make
the equations provide the answers in the newspaper. So you try different
volatilities until you get the right answer...the "right" answer being the
one in the paper. You want to find out what the market is IMPLYING that the
volatility should be...hence the term implied volatility.
Well, it turns out that using the prices in the paper, the volatility you
would need to put in the equation for soybeans to equal those prices are:
Nov 550 call 17.81%
Nov 600 call 19.96%
Nov 650 call 23.51%
(BTW I ran 20 day historical volatility and found it at 28% -- nowhere near
any of these levels)
These figures have absolutely nothing to do with historical volatility.
They are computed from the prices of the options themselves. After all,
what is 19.96%? Who knows? It might be the 54-day statitisical volatility
or the 94-day statistical volatility or none of them at all.
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