Chapter 2: FAQs 151
What is Volatility?
Short Answer
Volatility is annualized standard deviation of returns. Or
is it? Because that is a statistical measure, necessarily
backward looking, and because volatility seems to vary,
and we want to know what it will be in the future, and
because people have different views on what volatility
will be in the future, things are not that simple.
Example
Actual volatility is theσthat goes into the Black–Scholes
partial differential equation. Implied volatility is the
number in the Black–Scholes formula that makes a
theoretical price match a market price.
Long Answer
Actual volatility is a measure of the amount of random-
ness in a financial quantity at any point in time. It’s
what Desmond Fitzgerald calls the ‘bouncy, bouncy.’ It’s
difficult to measure, and even harder to forecast but it’s
one of the main inputs into option pricing models.
It’s difficult to measure since it is defined mathemati-
cally via standard deviations which requires historical
data to calculate. Yet actual volatility is not a historical
quantity but an instantaneous one.
Realized/historical volatilities are associated with a
period of time, actually two periods of time. We might
say that the daily volatility over the last sixty days has
been 27%. This means that we take the last sixty days’
worth of daily asset prices and calculate the volatility.
Let me stress that this has two associated timescales,
whereas actual volatility has none. This tends to be the
default estimate of future volatility in the absence of
any more sophisticated model. For example, we might
