On the Joint Calibration of SPX and VIX Options

Since VIX options started trading in 2006, many researchers have attempted to build a model for the SPX that jointly calibrates to SPX and VIX options. Many have argued that jumps in the SPX were needed. Does there exist a... [ view full abstract ]

Since VIX options started trading in 2006, many researchers have attempted to build a model for the SPX that jointly calibrates to SPX and VIX options. Many have argued that jumps in the SPX were needed. Does there exist a continuous model on the SPX that jointly calibrates to SPX and VIX options? In the case of instantaneous VIX, the answer is clear and involves convex ordering and a novel application of martingale transport to finance. The real case of 30-day VIX is more involved, and we show that rough volatility models have the potential for jointly calibrating.