arXiv subjects

Guido Gazzani

Publications and source records attributed to Guido Gazzani.

5 recordsLinked to original sources

arXiv2026

Ultra-short-term volatility surfaces

Options with maturities below one week, hereafter "ultra-short-term" options, have seen a sharp increase in trading activity in recent years. Yet, these instruments are difficult to price jointly using classical pricing models due to the pronounced oscillations observed in the at-the-money implied-volatility term structure across ultra-short-term tenors. We propose Edgeworth++, a parsimonious jump-diffusion model featuring a nonparametric stochastic volatility component, which provides flexibility in capturing implied-volatility smiles for each tenor, combined with a deterministic shift extension, which allows the model to fit rich at-the-money implied-volatility shapes across tenors. We derive a local (in tenor) expansion of the process characteristic function suited to value ultra-short-term options. The expansion leads to fast and accurate option pricing in closed form via standard Fourier inversion. We discuss the benefits of the proposed approach relative to benchmarks.

q-fin.MF↗

arXiv2025

Pricing and calibration in the 4-factor path-dependent volatility model

We consider the path-dependent volatility (PDV) model of Guyon and Lekeufack (2023), where the instantaneous volatility is a linear combination of a weighted sum of past returns and the square root of a weighted sum of past squared returns. We discuss the influence of an additional parameter that unlocks enough volatility on the upside to reproduce the implied volatility smiles of S\&P 500 and VIX options. This PDV model, motivated by empirical studies, comes with computational challenges, especially in relation to VIX options pricing and calibration. We propose an accurate \emph{pathwise} neural network approximation of the VIX which leverages on the Markovianity of the 4-factor version of the model. The VIX is learned pathwise as a function of the Markovian factors and the model parameters. We use this approximation to tackle the joint calibration of S\&P 500 and VIX options, quickly sample VIX paths, and price derivatives that jointly depend on S\&P 500 and VIX. As an interesting aside, we also show that this \emph{time-homogeneous}, low-parametric, Markovian PDV model is able to fit the whole surface of S\&P 500 implied volatilities remarkably well.

q-fin.CP↗

arXiv2024

Joint calibration to SPX and VIX options with signature-based models

We consider a stochastic volatility model where the dynamics of the volatility are described by a linear function of the (time extended) signature of a primary process which is supposed to be a polynomial diffusion. We obtain closed form expressions for the VIX squared, exploiting the fact that the truncated signature of a polynomial diffusion is again a polynomial diffusion. Adding to such a primary process the Brownian motion driving the stock price, allows then to express both the log-price and the VIX squared as linear functions of the signature of the corresponding augmented process. This feature can then be efficiently used for pricing and calibration purposes. Indeed, as the signature samples can be easily precomputed, the calibration task can be split into an offline sampling and a standard optimization. We also propose a Fourier pricing approach for both VIX and SPX options exploiting that the signature of the augmented primary process is an infinite dimensional affine process. For both the SPX and VIX options we obtain highly accurate calibration results, showing that this model class allows to solve the joint calibration problem without adding jumps or rough volatility.

q-fin.MF↗

arXiv2022

Signature-based models: theory and calibration

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-inferred) Brownian motion to a general multidimensional continuous semimartingale. The framework is universal in the sense that classical models can be approximated arbitrarily well and that the model's parameters can be learned from all sources of available data by simple methods. We provide conditions guaranteeing absence of arbitrage as well as tractable option pricing formulas for so-called sig-payoffs, exploiting the polynomial nature of generic primary processes. One of our main focus lies on calibration, where we consider both time-series and implied volatility surface data, generated from classical stochastic volatility models and also from S&P500 index market data. For both tasks the linearity of the model turns out to be the crucial tractability feature which allows to get fast and accurate calibrations results.

q-fin.MF↗

arXiv2022

Risk measures under model uncertainty: a Bayesian viewpoint

We introduce two kinds of risk measures with respect to some reference probability measure, which both allow for a certain order structure and domination property. Analyzing their relation to each other leads to the question when a certain minimax inequality is actually an equality. We then provide conditions under which the corresponding robust risk measures, being defined as the supremum over all risk measures induced by a set of probability measures, can be represented classically in terms of one single probability measure. We focus in particular on the mixture probability measure obtained via mixing over a set of probability measures using some prior, which represents for instance the regulator's beliefs. The classical representation in terms of the mixture probability measure can then be interpreted as a Bayesian approach to robust risk measures.

q-fin.RM↗