Thibaut Montes, PhD

Thibaut Montes, PhD

Senior Machine Learning Researcher

Talks and presentations

Stationary Heston model: Calibration and Pricing of exotics using Product Recursive Quantization

February 11, 2020

Talk, Séminaire probabilités et statistiques, Le Mans, France

A major drawback of the Standard Heston model is that its implied volatility surface does not produce a steep enough smile when looking short maturities. For that reason, we introduce the Stationary Heston model where we replace the deterministic initial condition of the volatility by its invariant measure and show, based on calibrated parameters, that this model produce a steeper smile for short maturities than the standard Heston model. We also present numerical solution based on Product Recursive Quantization for the evaluation of exotic options (Bermudan and Barrier options).

Stationary Heston model: Calibration and Pricing of exotics using Optimal Quantization

October 10, 2019

Talk, Groupe de Travail: Finance mathématique, probabilités numériques et statistique des processus, Paris, France

A major drawback of the Standard Heston model is that its implied volatility surface does not produce a steep enough smile when looking short maturities. For that reason, we introduce the Stationary Heston model where we replace the deterministic initial condition of the volatility by its invariant measure and show, based on calibrated parameters, that this model produce a steeper smile for short maturities than the standard Heston model. We also present numerical solution based on Product Recursive Quantization for the evaluation of exotic options (Bermudan and Barrier options).

Tackling Stationary and Randomized Heston Models using Quantization

September 03, 2019

Talk, 12th European Summer School in Financial Mathematics, Padova, Italia

I present a work (still in progress) where we introduce a randomized/stationary version of the well known Heston model. This model allows us to produce steeper implied volatilities for short maturities options. We propose numerical solutions based on optimal quantization for the pricing of European, Bermudan and Barrier options.

New weak error bounds and expansions for optimal quantization with Applications

April 10, 2019

Talk, Young Researchers Seminar, CERMICS, École des Ponts ParisTech, Marne la Vallée, France

I present new weak error bounds and expansion in dimension one for optimal quantization-based cubature formula for different classes of functions, such that piecewise affine functions, Lipschitz convex functions or differentiable function with piecewise-defined locally Lipschitz or α-Hölder derivatives. This new results rest on the local behaviors of optimal quantizers, the Lr-Ls distribution mismatch problem and Zador’s Theorem. This new expansion supports the definition of a Richardson-Romberg extrapolation yielding a better rate of convergence for the cubature formula. An extension of this expansion is then proposed in higher dimension for the first time. We then propose a novel variance reduction method for Monte Carlo estimators, based on one dimensional optimal quantizers.

Below is a map of all the places I've given a talk!