  The VSTOXX index tracks the expected 30-day volatility of the EURO STOXX 50
equity index. Futures on the VSTOXX index can, therefore, be used to hedge
against economic uncertainty. We investigate the effect of trader inventory on
the price of VSTOXX futures through a combination of stochastic processes and
machine learning methods. We formulate a simple and efficient pricing
methodology for VSTOXX futures, which assumes a Heston-type stochastic process
for the underlying EURO STOXX 50 market. Under these dynamics, approximate
analytical formulas for the implied volatility smile and the VSTOXX index have
recently been derived. We use the EURO STOXX 50 option implied volatilities and
the VSTOXX index value to estimate the parameters of this Heston model.
Following the calibration, we calculate theoretical VSTOXX future prices and
compare them to the actual market prices. While theoretical and market prices
are usually in line, we also observe time periods, during which the market
price does not agree with our Heston model. We collect a variety of market
features that could potentially explain the price deviations and calibrate two
machine learning models to the price difference: a regularized linear model and
a random forest. We find that both models indicate a strong influence of
accumulated trader positions on the VSTOXX futures price.
