# Volatility Part II

Part II  (Part I is here)

Historical Volatility

HV is a characteristic of the underlying stock or index and is a statistical measurement of how much it has moved (in either direction) over a specified period of time.

Stocks with a high historical volatility are (usually) expected to continue to trade with a high volatility in the future.  For that reason, the prices of their options are relatively expensive.

Stocks with a low historical volatility tend to be larger, more stable companies, and often pay decent dividends.  Because there is no reason to expect such stocks to trade very differently than they have in the past, their options carry a low premium and are far less costly than the options of stocks with a high historical volatility.

Implied Volatility

IV is a characteristic of the option.  One way to look at IV is to say that's it's the volatility that traders in the marketplace are estimating for the underlying stock, during the period of time from the present, until the option expires.

Because IV cannot be known in advance, it is sometimes referred to as the estimated volatility or forecast volatility. Being able to estimate the future volatility with accuracy allows a trader to get a fair price when buying or selling options.  When prices are too high, a trader can sell the 'overvalued' option, or when prices are too low, buy the 'undervalued' option.  If an appropriate hedge can be found for the option just traded, then the trader has an expectation of earning a profit – if and when that mis-priced option becomes fairly valued.

This is no simple matter, as people often disagree on what that implied volatility should be.  The option's price is very dependent on the volatility estimate.

As a simple example of how much option prices can vary depending on the implied volatility of an options, consider a 6-month call option,
with a strike price of 50, when the stock price is 50:

When IV = 90, the fair value of the option is \$1250

When IV = 50, the fair value of the option is   \$725

When IV = 30, the fair value of the option is  \$450

It's easy to see that if you make a poor estimate of future volatility, you may not be trading the option at anywhere near its theoretical (fair) value.

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