Implied Volatility is a very important tole in Option Pricing

1. IMPLIED VOLATILITY EXPLANATION
How to use implied volatility to estimate how much a stock or index will move?
When the implied volatility of an option is 35%, what does that mean?
Volatility is a measure of how much a stock can move over a specific
amount of time, and is defined as the standard deviation of daily
percentage changes of the stock price.
Implied volatility is simply the volatility that makes the theoretical value of
an option equal to the market price of an option.
Volatility is usually expressed in annual terms, and represents a one
standard deviation move in the stock.
Dip into any statistics book, and it’ll explain that one standard deviation, up
and down, encompasses about two-thirds of all occurrences. So, two-thirds
of the time, the stock with an implied volatility will theoretically be
between up 35% and down 35% in one year. But how do you convert
that to a more useful timeframe, when most of the options you trade expire
in the next couple of months?
If you assume that a stock has an annualized volatility of 35%, how much
might it move in 1 day, 1 week, or 1 month? Well, open that statistics book
again and see that the standard deviation increases proportionately
to the square root of time. So, if there are 252 days in a year, you want
to multiply 35% by the square root of 1/252 to get the 1 standard deviation
for 1 day. That comes out to about 2.2%. So, in one day, two-thirds of the
time the stock will be between up and down 2.2%.
To get that number for any number of trading days from today,
multiply 35% by the square root of the number of days/252. That is,
for the range 5 days from now, multiply 35% by the square root of
5/252. For 20 days from now, multiply 35% by the square root of
20/252. So, in 5 days, theoretically two-thirds of the time the stock
will between up and down 4.93%, and in 20 days, between up and
down 9.86%.
You can use this data to gauge the risk of certain positions. Let’s look at
short call verticals. The stock is $80, and April options have an average
implied volatility of 40% and 15 days to expiration. Two-thirds of the time,
the stock will theoretically be between up and down 9.76% in 15 days, or
between 72.89 and 87.81. So, if you’re thinking about selling the 85/90 call
vertical, there’s a pretty good chance that the short 85 calls will be in the

2. money at expiration. If you don’t like that scenario, but still want to be short
a call vertical, you may want to consider selling a 90/95 or a 95/100 call
vertical instead. You won’t receive as much premium as if you sold the
85/90, but there’s less risk of the short options being in the money at
expiration.
This calculation is no guarantee of what a stock will do, and is susceptible to
changes in volatility. But it is one more tool you can use to become a more
informed trader.