We learn from data that volatility is mostly path-dependent: up to 90% of the variance of the
implied volatility of equity indexes is explained endogenously by past index returns, and up …

We consider the joint SPX & VIX calibration within a general class of Gaussian polynomial
volatility models in which the volatility of the SPX is assumed to be a polynomial function of a …

We consider asset price models whose dynamics are described by linear functions of the
(time extended) signature of a primary underlying process, which can range from a (market …

We conduct an empirical analysis of rough and classical stochastic volatility models to the
SPX and VIX options markets. Our analysis focusses primarily on calibration quality and is …

We consider a stochastic volatility model where the dynamics of the volatility are described
by linear functions of the (time extended) signature of a primary underlying process, which is …

The quintic Ornstein-Uhlenbeck volatility model is a stochastic volatility model where the
volatility process is a polynomial function of degree five of a single Ornstein-Uhlenbeck …

We solve for the first time a longstanding puzzle of quantitative finance that has often been
described as the holy grail of volatility modelling: build a model that jointly and exactly …

We extend the discrete-time construction of [Guyon, J.: The Joint S&P 500/VIX Smile
Calibration Puzzle Solved, Risk, April 2020] and explain how to build a continuous-time …

We calibrate neural stochastic differential equations jointly to S&P 500 smiles, VIX futures,
and VIX smiles. Drifts and volatilities are modeled as neural networks. Minimizing a suitable …

In this paper, we study a semi‐martingale optimal transport problem and its application to
the calibration of local‐stochastic volatility (LSV) models. Rather than considering the …