Second NUS—Stanford Workshop in Quantitative Finance: Statistical Issues

Title: 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.

Keywords:    Volatility models, risk management, risk measures, risk components, VIX index, and VIX futures.

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