Volatility estimation – models

As discussed above, energy commodity prices show both high and variable volatility.
This characteristic poses particular difficulty for the standard volatility models. The
starting point for estimation of volatility is the standard constant volatility models as
applied within the Black and Scholes model (1973). This allows us to incorporate the
standard Brownian motion assumptions14 in and expand them over a continuous
time period using the square-root (uncorrelated) assumption.15
Many simplistic models have taken this assumption to estimate volatility in the
energy markets. Given the lack of implied volatility estimates, the most common
have taken simple average volatility (for instance, the average of the last six months’
spot data) and projected it forward to create an annualized number which can be
later converted for option pricing models or holding period for Value-at-Risk estimation
(Figure 18.5).
A slight improvement to is to use a weighted average approach that weights the
more recent events more heavily. This approach will undoubtedly improve the events
but will not take account of the ‘events’ problem in energy (such as seasonality) or
mean reversion. In other words the constant forward volatility assumption does not
hold.
As can be seen from Figure 18.6 and as confirmed by the statistical tests, significant
clustering occurs around the seasons and particular events. So while the basic
stochastic ‘random’ toolkit with constant volatility provides a useful starting point it
is not helpful in estimating the volatility parameters in energy. In fact, a number of
issues need to be overcome before the quantitative models can be used effectively in
the energy markets. These are addressed below.