Numerical Computation of VIX-Futures Risk Components

We describe a method to perform risk simulations of VIX futures,
according to the historical-simulation model. We assume a
stochastic-volatility mean- reverting constant-elasticity-of-variance
process to model the VIX dynamics. Following non-arbitrage arguments
the market expectation of VIX futures price results in a function of
three financial variables: the spot VIX index, the long-term expected
VIX value, and a time-scale parameter. Using the latest historical
data we compute risk measures for VIX futures at different maturities
and compare them with those of the VIX index. Finally, using a
recently developed technique, we compute the component of risk coming
from each risk driver. We show some numerical results that highlight
the dependence on the maturity of the risk components of the
VIX-futures risk drivers.

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