09. Quiz: Estimate Volatility
Estimate Volatility
Create an exponential moving average model of volatility. Use the following formula:
\sigma_n^2 = \frac{r_n^2 + \lambda r_{n-1}^2 + \lambda^2 r_{n-2}^2 + …+ \lambda^n r_{0}^2}{1 + \lambda + \lambda^2 + …+ \lambda^n}
where r_n is the nth daily return, and \sigma_n is the nth estimate of the volatility. \lambda is a constant between 0 and 1 that defines how quickly weights on older data should decrease. A high value of \lambda (close to 1) will cause older data to matter relatively more in the calculation of \sigma_n . A very low value of \lambda will mean that recent data matter more—in this case, the successive daily estimates of \sigma_n themselves will be volatile.
Pandas provides built-in
exponentially weighted moving window
functions with the
.ewm
method. Consider using
.ewm().mean()
, and be sure to properly specify the
alpha
parameter (hint: it is related to, but not equal to
\lambda
).
Note that
.ewm().std()
and
.ewm().var()
implement
ewmvar(x) = ewma(x**2) - ewma(x)**2
, which is slightly different than what you'll want to implement for this problem.
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