November 8, 2023 (NO COMMENTS)

Julien Guyon and Scander Mustapha simultaneously calibrate neural stochastic differential equations to Standard & Poor’s 500 smiles, the Chicago Board Options Exchange’s Volatility Index futures and VIX smiles. The drifts and volatilities are modelled as neural networks. Minimising a suitable loss allows us to fit the market data for multiple S&P 500 and VIX maturities. A one-factor Markovian stochastic local volatility model is shown to fit both smiles and VIX