**Author**: Leonardo D’Auria

**Advisor**: Marco Marchioro

**Language**: English

**Abstract**

In this work 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 pro- cess to model the VIX dynamics. Following non-arbitrage argument, the market expectation of VIX futures price results in a function of three fi- nancial variables: the spot VIX, the long-run mean of the mean-reverting VIX process, and a time scale parameter. For each trading day in the period 2011-2012 we collect the closing VIX futures market quotes across all available maturities and calibrate the three financial variables using an ad-hoc least-squares procedure. In this way we can extract the VIX fu- tures term-structure for each day in the sample period. We then compute historical scenarios for all financial variables and we apply these scenarios to a calendar spread position on VIX futures to simulate its value. Finally, from the distribution of the simulated spread values we derive the P&L (profit and loss) strip which is used to compute risk figures.

**Keywords**: risk, historical simulation, master thesis, futures, vix, vix futures, vix spreads, pricing functions, risk simulations, risk measures, quantlibxl, linear derivatives, hedging, forward curve

**Pdf file**: DAuria-advs-Marchioro.pdf