Joint calibration to the Standard & Poor’s 500 (SPX) and Chicago Board Options Exchange (CBOE) Volatility Index (VIX) market data can be computationally burdensome, especially when the standard course of action for pricing volatility derivatives is nested Monte Carlo simulation, as is the case for the four-factor Markov path-dependent volatility model of Guyon and Lekeufack. A crucial boost to solving the joint problem was developed by Gazzani and Guyon, who trained a neural network to learn to model VIX as a random variable: the network replaces the inner simulation, and the pricing of VIX derivatives is reduced to a standard Monte Carlo computation. This is a step in the right direction but it is not sufficient. In this paper, Fabio Baschetti, Giacomo Bormetti and Pietro Rossi aim to further accelerate calibration by training neural networks to learn SPX implied volatilities, VIX futures and call option prices as a function of model parameters and contract specifications. As a result, pricing boils down to a matrix-vector product that can be calculated in real time, while calibration only takes a few seconds.
Neural networks unleashed: joint SPX/VIX calibration has never been faster
Giacomo Bormetti;
2026-01-01
Abstract
Joint calibration to the Standard & Poor’s 500 (SPX) and Chicago Board Options Exchange (CBOE) Volatility Index (VIX) market data can be computationally burdensome, especially when the standard course of action for pricing volatility derivatives is nested Monte Carlo simulation, as is the case for the four-factor Markov path-dependent volatility model of Guyon and Lekeufack. A crucial boost to solving the joint problem was developed by Gazzani and Guyon, who trained a neural network to learn to model VIX as a random variable: the network replaces the inner simulation, and the pricing of VIX derivatives is reduced to a standard Monte Carlo computation. This is a step in the right direction but it is not sufficient. In this paper, Fabio Baschetti, Giacomo Bormetti and Pietro Rossi aim to further accelerate calibration by training neural networks to learn SPX implied volatilities, VIX futures and call option prices as a function of model parameters and contract specifications. As a result, pricing boils down to a matrix-vector product that can be calculated in real time, while calibration only takes a few seconds.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
