UNDERSTANDING VOLATILITY

The value of an option depends mainly on two things:

The likelihood that the option will finish in the money.
The difference between the underlying price and the option’s exercise pric
if the option does finish in the money.
Effectively, the value of an option depends on the distribution of possible
underlying prices, which depends on:
How much the underlying price is likely to change on any given tradin
day during the option’s life (daily volatility).
How many days the underlying price will have an opportunity to chang
before the option expires (the option’s time to expiration in trading days).

TWO TYPES OF VOLATILITY

1. HISTORICAL VOLATILITY:**

A statistical measure of the past volatility o
the underlying price.
If a trader intends to use a theoretical pricing model he must try to make an
intelligent guess about the future volatility. In option evaluation, a goo-
starting point is historical data.
Converting Underlying Price Volatility:

Rules of Thumb:
Annualized price volatility is about 16 times greater than daily price vola
Weekly price volatility is about 7.2 times greater than daily price volatility

2. IMPLIED VOLATILITY:

The volatility being implied to the underlying
contract through the pricing of the option in the marketplace. Effectively, it
is the volatility estimate which matches the observable market price of the
option with its theoretical value.
It is the volatility we must input into our theoretical pricing model to yield a
theoretical value identical to the price of the option in the marketplace.
Remember, the more volatile the underlying market is expected to be over
the life of the option, the higher the option price.
Why Are Implied & Historical Volatilities Different?
Gap or Jump Risk
Expectations
Supply and Demand
Risk/Liquidity Premium
Standard Deviations:
** The most widely quoted volatility measure is a standard deviation of
percent changes in the underlying price.

1. One standard deviation of returns captures about 68% of all possible
   outcomes.
2. Two standard deviations of returns captures about 95% of all possible
   outcomes.
3. Three standard deviations of returns captures about 99% of all possible
   outcomes
   mplications for Trading:
   A one-standard deviation change in the underlying price (using the option’s
   implied volatility scaled to suit the time horizon) represents a break-even
   level of underlying volatility vs. implied volatility.
   The distributions of returns on a long (purchased) option position is
   large gains.
   characterized by a high frequency of small losses interrupted by occasional large gains