Related papers: Explicit local volatility formula for Cheyette-typ…

This study investigates the short-term asymptotic behavior of the implied volatility surface (IVS), with a particular focus on the at-the-money (ATM) skew and curvature, which are key determinants of the IVS shape and whose are widely…

It has been recently shown that spot volatilities can be very well modeled by rough stochastic volatility type dynamics. In such models, the log-volatility follows a fractional Brownian motion with Hurst parameter smaller than 1/2. This…

In this work the implicit function theorem is used for searching local symbolic resolution of differential equations. General results of existence for first order equations are proven and some examples, one relative to cavitation in a…

In [Precise Asymptotics for Robust Stochastic Volatility Models; Ann. Appl. Probab. 2021] we introduce a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and…

Rough volatility models have gained considerable interest in the quantitative finance community in recent years. In this paradigm, the volatility of the asset price is driven by a fractional Brownian motion with a small value for the Hurst…

We illustrate how to compute local risk minimization (LRM) of call options for exponential L\'evy models. We have previously obtained a representation of LRM for call options; here we transform it into a form that allows use of the fast…

We present an extension of local sensitivity analysis, also referred to as the perturbation approach for uncertainty quantification, to Bayesian inverse problems. More precisely, we show how moments of random variables with respect to the…

We introduce a method for quantifying the inherent unpredictability of a continuous-valued time series via an extension of the differential Shannon entropy rate. Our extension, the specific entropy rate, quantifies the amount of predictive…

Quantile regression is a technique to estimate conditional quantile curves. It provides a comprehensive picture of a response contingent on explanatory variables. In a flexible modeling framework, a specific form of the conditional quantile…

In a recent paper "Deep Learning Volatility" a fast 2-step deep calibration algorithm for rough volatility models was proposed: in the first step the time consuming mapping from the model parameter to the implied volatilities is learned by…

Black-Scholes implied volatility is a quantile. The insight follows from the normalized option price being a probability on the variance scale, with the inverse Gaussian distribution providing the link. It enables analytically exact and…

This article presents a generic hybrid numerical method to price a wide range of options on one or several assets, as well as assets with stochastic drift or volatility. In particular for equity and interest rate hybrid with local…

We develop a stochastic volatility framework for modeling multiple currencies based on CBI-time-changed L\'evy processes. The proposed framework captures the typical risk characteristics of FX markets and is coherent with the symmetries of…

Implied volatilities form a well-known structure of smile or surface which accommodates the Bachelier model and observed market prices of interest rate options. For the swaptions that we study, three parameters are taken into account for…

We propose a novel and generic calibration technique for four-factor foreign-exchange hybrid local-stochastic volatility models with stochastic short rates. We build upon the particle method introduced by Guyon and Labord\`ere [Nonlinear…

In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\Delta t$, and a…

This paper proposes a local representation for Empirical Likelihood (EL). EL admits the classical local linear quadratic representation by its likelihood ratio property. A local estimator is derived by using the new representation.…

Using Malliavin Calculus techniques, we derive closed-form expressions for the at-the-money behaviour of the forward implied volatility, its skew and its curvature, in general Markovian stochastic volatility models with continuous paths.

For any strictly positive martingale $S = \exp(X)$ for which $X$ has a characteristic function, we provide an expansion for the implied volatility. This expansion is explicit in the sense that it involves no integrals, but only polynomials…

We find approximate solutions of partial integro-differential equations, which arise in financial models when defaultable assets are described by general scalar L\'evy-type stochastic processes. We derive rigorous error bounds for the…