Functional quantization of rough volatility and applications to the VIX

Abstract

We develop a product functional quantization of rough volatility. Since the quantizers can be computed offline, this new technique, built on the insightful works by Luschgy and Pagès, becomes a strong competitor in the new arena of numerical tools for rough volatility. We concentrate our numerical analysis to pricing VIX Futures in the rough Bergomi model and compare our results to other recently suggested benchmarks.

Rough multifactor volatility for SPX and VIX options

“…The Clark-Ocone formula yields BS(M 0 ) = E BS(M 0 ) + N i=1 T 0 E s D i s BS(M 0 ) dW i s and, by the Gamma-Vega-Delta relation (13) we have…”

“…By incorporating a Zumbach effect, the quadratic rough Heston model [24] achieves good results for the joint calibration at one given date. Further numerical methods were developed in [13,14,41]. However, the lack of analytical tractability of rough volatility models is holding back the progress of theoretical results on the VIX, with the notable exception of large devations results from [19,35] and the small-time asymptotics of [2].…”