What Is Option Volatility?
What is Volatility?
In standard option valuation models, such as Black-Scholes, you calculate the price of an option with five known inputs and one input that is an estimate. The five known inputs are:
- stock price
- strike price
- time to expiration
- interest rate
- dividend (if there is one).
Without volatility, an option would only be worth its tangible value (and the time value determined by interest and dividends). The more a stock has jumped around in the past - and the more unsure investors are about its future trends - the greater this volatility input will be and the higher the optionís time premium will be.
In the Black-Scholes model, volatility is the expected standard deviation of price changes. It is usually expressed (and entered) as an annualized number.
How do you arrive at this volatility input?
One way is to observe what volatility the market is currently using to price options. This is known as the Implied Volatility. One can use also past volatility. This is known as the Historical Volatility.
Implied Volatility
It is easy to calculate what the market thinks volatility should be at any point in time. You simply take the current option premium (as quoted) and use the five known variables and a Black-Scholes model to find the volatility number that would give you that particular premium.
We call this metric implied volatility (i.e. the volatility ìimpliedî by the current premium). Implied volatility is, in effect, the marketís forecast of future volatility.
Historical Volatility
Historical volatility is the annualized standard deviation of price changes in the stock over a specified period of time in the past. Typically, when evaluating an option that expires a certain number of days forward, an option trader calculates the historical volatility of the stock over the same number of days in the past.
Thus, the traderís estimate of the worth of an option that expires in 30 days is likely to be strongly influenced by the past 30 daysí historical volatility. Likewise, a traderís estimate for an option that expires in a year is likely to be strongly influenced by historical volatility over the past year.
Thus, historical volatility is often used as a forecaster of future volatility. However, it is not always an effective forecaster because volatility often tends to be moving in one direction or another. Although historical volatility can give you an idea of the range of future volatility, it rarely tells you whether volatility is likely to rise or fall.
Posted by: Value Line
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About Lawrence D. Cavanagh
Lawrence D. Cavanagh is Editor (and Senior Analyst) of The Value Line Daily Options Survey. The Value Line Daily Options Survey offers evaluations and rankings on virtually the entire universe of regularly listed equity and ETF options, using the Value Line common stock ranks and proprietary volatility forecasting methodology. Before joining Value Line in 1991, Mr. Cavanagh was an options strategist for Capital Market Technologies (subsidiary of Elders Finance), helping design long-term synthetic foreign currency and gold option hedges. Before that, he was Director of Foreign Currency Options for the Chicago Board Options Exchange. Other work experience includes Dean Witter Reynolds (VP, Senior Currency Analyst), European American Bank (Director of Currency Forecasting) and the Federal Reserve Bank of New York (Assistant Economist).
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