4 citations · 5 across the 6 of their papers we have counts for
15 papers
Magic strikes for variance and gamma contracts, and other attainable claims
Florian Bourgey, Jim Gatheral
Building on the forest expansion of Alòs, Gatheral and Radoičić and on the explicit Bergomi-Guyon smile expansion derived by Bourgey and Gatheral (2026), we derive fixed-point appr…
Demystifying the Bergomi-Guyon expansion
Florian Bourgey, Jim Gatheral
Alòs, Gatheral and Radoičić derived the Bergomi-Guyon expansion of the implied variance smile from the forest expansion of the cumulant generating function. Its coefficients are su…
Computing the SSR
Peter K. Friz, Jim Gatheral
The skew-stickiness-ratio (SSR), examined in detail by Bergomi in his book, is critically important to options traders, especially market makers. We present a model-free expression…
A generalization of the rational rough Heston approximation
Jim Gatheral, Radoš Radoičić
Previously, in [GR19], we derived a rational approximation of the solution of the rough Heston fractional ODE in the special case λ= 0, which corresponds to a pure power-law kernel…
Diamonds and forward variance models
Peter Friz, Jim Gatheral
In this non-technical introduction to diamond trees and forests, we focus on their application to computation in stochastic volatility models written in forward variance form, roug…
A rough SABR formula
Masaaki Fukasawa, Jim Gatheral
Following an approach originally suggested by Balland in the context of the SABR model, we derive an ODE that is satisfied by normalized volatility smiles for short maturities unde…
Forests, cumulants, martingales
Peter K. Friz, Jim Gatheral, Radoš Radoičić
This work is concerned with forest and cumulant type expansions of general random variables on a filtered probability spaces. We establish a "broken exponential martingale" expansi…
The quadratic rough Heston model and the joint S&P 500/VIX smile calibration problem
Jim Gatheral, Paul Jusselin, Mathieu Rosenbaum
Fitting simultaneously SPX and VIX smiles is known to be one of the most challenging problems in volatility modeling. A long-standing conjecture due to Julien Guyon is that it may…
The Zumbach effect under rough Heston
Omar El Euch, Jim Gatheral, Radoš Radoičić +1
Previous literature has identified an effect, dubbed the Zumbach effect, that is nonzero empirically but conjectured to be zero in any conventional stochastic volatility model. Ess…
Short-term at-the-money asymptotics under stochastic volatility models
Omar El Euch, Masaaki Fukasawa, Jim Gatheral +1
A small-time Edgeworth expansion of the density of an asset price is given under a general stochastic volatility model, from which asymptotic expansions of put option prices and at…
Affine forward variance models
Jim Gatheral, Martin Keller-Ressel
We introduce the class of affine forward variance (AFV) models of which both the conventional Heston model and the rough Heston model are special cases. We show that AFV models can…
Optimal execution with nonlinear transient market impact
Gianbiagio Curato, Jim Gatheral, Fabrizio Lillo
We study the problem of the optimal execution of a large trade in the presence of nonlinear transient impact. We propose an approach based on homotopy analysis, whereby a well beha…
Volatility is rough
Jim Gatheral, Thibault Jaisson, Mathieu Rosenbaum
Estimating volatility from recent high frequency data, we revisit the question of the smoothness of the volatility process. Our main result is that log-volatility behaves essential…
Arbitrage-free SVI volatility surfaces
Jim Gatheral, Antoine Jacquier
In this article, we show how to calibrate the widely-used SVI parameterization of the implied volatility surface in such a way as to guarantee the absence of static arbitrage. In p…
Convergence of Heston to SVI
Jim Gatheral, Antoine Jacquier
In this short note, we prove by an appropriate change of variables that the SVI implied volatility parameterization presented in Gatheral's book and the large-time asymptotic of th…