Neural joint S&P 500/VIX smile calibration
A one-factor stochastic local volatility model can solve the joint calibration problem
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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
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