Mini course by Julien Guyon (Ecole des Ponts): “Recent advances in VIX modeling

The minicourse will cover (as time permits):

  1. Optimal bounds for VIX futures given S&P 500 smiles
  2. Robust bounds for derivatives on S&P 500 and/or VIX: VIX-constrained martingale optimal transport
  3. Joint S&P 500/VIX arbitrages
  4. Exact joint calibration of S&P 500 and VIX smiles: VIX-constrained martingale Schrodinger problems/bridges
  5. The VIX Future in Bergomi Models: Closed-Form Approximation Formulas and Joint Calibration with S&P 500 Skew
  6. Inversion of convex ordering: a remarkable empirical feature of the VIX market
  7. Inversion of convex ordering: Local volatility does not maximize the price of VIX futures