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If you've got an option on that stock whose strike price and days to
expiration are close to those desired then you can get a quick and dirty
estimate of the probability of reaching or exceeding that strike price from
the delta of the option. For example, an option with a strike price of S
and a delta D has a D X 100 % chance of finishing in the money, where in the
money means reaching or exceeding the strike price S (= price of underlying
stock).
If you're willing to assume a log normal distribution of price changes (=
bell curve and is what most option pricing software assumes), then you can
use one of the various probability calculators available. DeltaSoft
publishes a freeware calculator that inputs current and two target prices
(hi > current, lo < current), the volatility, and days to reach the targets,
then outputs the probabilities as percentage of both reaching either target,
as well as staying in between them. Their web address is
www.option-oracle.com
The formula used in most of these programs (including DeltaSoft's) is at
www.aantix.com/stock_options/equation.htm.
When using the above programs and formula, note that the volatilities are
annularized, that is they refer to a price change over the course of a year.
Also number of days to reach the target should be very close to the days to
expiration.
To use a different time period than a year, say 60 days, multiply the
volatility by the square root of (60 / 365 ). For very short periods, less
than 30 days, you need to compute historical volatility. For n-period
volatility, first compute the n-period sample mean (average), then the
n-period sample deviation. Excell has functions to do this. Note that
sample deviation = estimate of standard deviation = volatility. Multiply by
100 to get a percentage. Also note that historical volatility has the same
lag problems as moving averages and that it isn't statistically valid for
very short number of bars (< 30). To get 3 day estimates, you're probably
going to need 15 minute intraday charts.
-- Jeff.
-----Original Message-----
From: Richard Stokes <stone@xxxxxxxxxxxx>
To: realtraders@xxxxxxxxxxxxxx <realtraders@xxxxxxxxxxxxxx>
Date: Monday, April 19, 1999 8:12 PM
Subject: Probability applications to stock prices
>Hi everyone,
>
> Does anybody know the formula to compute the probability that a stock
will
>hit a given price at a given time? ie: given a volatility of x and current
>stock price of p, what is the probability that the stock will move to price
>q in three days?
>
> rich
>
>
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