Fast exact joint S&P 500/VIX smile calibration in discrete and continuous time

An arbitrage-free model for exotic options that captures smiles and futures is presented


Florian Bourgey and Julien Guyon introduce a novel discrete-time-continuous-time exact calibration method. They build an S&P 500/VIX jointly calibrated discrete-time model, which they later extend to continuous time by martingale interpolation. The benefit of this technique is that both steps can be made much faster than the known methods that calibrate a continuous-time model directly

In previous work, Guyon (2020, 2024) showed how to build a nonparametric discrete

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