152 Frequently Asked Questions In Quantitative Finance
assume that the volatility of the next sixty days is the
same as over the previous sixty days. This will give us
an idea of what a sixty-day option might be worth.
Implied volatility is the number you have to put into
the Black–Scholes option-pricing equation to get the
theoretical price to match the market price. Often said
to be the market’s estimate of volatility.
Let’s recap. We haveactual volatilitywhich is the
instantaneous amount of noise in a stock price return.
It is sometimes modelled as a simple constant, some-
times as time dependent, sometimes as stock and time
dependent, sometimes as stochastic and sometimes
as a jump process, and sometimes as uncertain, that
is, lying within a range. It is impossible to measure
exactly, the best you can do is to get a statistical esti-
mate based on past data. But this is the parameter we
would dearly love to know because of its importance in
pricing derivatives. Some hedge funds believe that their
edge is in forecasting this parameter better than other
people, and so profit from options that are mispriced in
the market.
Since you can’t see actual volatility people often rely
on measuringhistoricalorrealized volatility.Thisis
a backward looking statistical measure of what volatil-
ity has been. And then one assumes that there is some
information in this data that will tell us what volatility
will be in the future. There are several models for mea-
suring and forecasting volatility and we will come back
to them shortly.
Implied volatilityis the number you have to put into
the Black–Scholes option-pricingformulato get the
theoretical price to match the market price. This is
often said to be the market’s estimate of volatility.
More correctly, option prices are governed by supply
