Implied Volatility
Volatility is one of the six inputs of an option-pricing model. Some of the
other inputs—strike price, stock price, the number of days until expiration,
and the current interest rate—are easily observable. Past dividend policy
allows an educated guess as to what the dividend input should be. But
where can volatility be found?
As discussed in Chapter 2, the output of the pricing model—the option’s
theoretical value—in practice is not necessarily an output at all. When
option traders use the pricing model, they commonly substitute the actual
price at which the option is trading for the theoretical value. A value in the
middle of the bid-ask spread is often used. The pricing model can be
considered to be a complex algebra equation in which any variable can be
solved for. If the theoretical value is known—which it is—it along with the
five known inputs can be combined to solve for the unknown volatility.
Implied volatility (IV) is the volatility input in a pricing model that, in
conjunction with the other inputs, returns the theoretical value of an option
matching the market price.
For a specific stock price, a given implied volatility will yield a unique
option value. Take a stock trading at $44.22 that has the 60-day 45-strike
call at a theoretical value of $1.10 with an 18 percent implied volatility
level. If the stock price remains constant, but IV rises to 19 percent, the
value of the call will rise by its vega, which in this case is about 0.07. The
new value of the call will be $1.17. Raising IV another point, to 20 percent,
raises the theoretical value by another $0.07, to $1.24. The question is:
What would cause implied volatility to change?