Tensoring Volatility Calibration

  title={Tensoring Volatility Calibration},
  author={Mariano Zeron Medina Laris and Ignacio Ruiz},
  journal={Derivatives eJournal},
Inspired by a series of remarkable papers in recent years that use Deep Neural Nets to substantially speed up the calibration of pricing models, we investigate the use of Chebyshev Tensors instead of Deep Neural Nets. Given that Chebyshev Tensors can be, under certain circumstances, more efficient than Deep Neural Nets at exploring the input space of the function to be approximated, due to their exponential convergence, the problem of calibration of pricing models seems, a priori, a good case… Expand
1 Citations
Chebyshev Greeks: Smoothing Gamma without Bias
The computation of Greeks is a fundamental task for risk managing of financial instruments. The standard approach to their numerical evaluation is via finite differences. Most exotic derivatives areExpand


Deep calibration of rough stochastic volatility models
This work showcases a direct comparison of different potential approaches to the learning stage and presents algorithms that provide a suffcient accuracy for practical use and provides a first neural network-based calibration method for rough volatility models for which calibration can be done on the y. Expand
Deep Learning Volatility
A neural network based calibration method that performs the calibration task within a few milliseconds for the full implied volatility surface and brings several numerical pricers and model families within the scope of applicability in industry practice. Expand
Low-Rank Tensor Approximation for Chebyshev Interpolation in Parametric Option Pricing
The core of the method is to express the tensorized interpolation in tensor train (TT) format and to develop an efficient way, based on tensor completion, to approximate the interpolation coefficients. Expand
Chebyshev interpolation for parametric option pricing
The Chebyshev method turns out to be more efficient than parametric multilevel Monte Carlo and its combination with Monte Carlo simulation and the effect of (stochastic) approximations of the interpolation is analyzed. Expand
Market smiles and skews are usually managed by using local volatility models a la Dupire. We discover that the dynamics of the market smile predicted by local vol models is opposite of observedExpand
Pricing Under Rough Volatility
From an analysis of the time series of volatility using recent high frequency data, Gatheral, Jaisson and Rosenbaum previously showed that log-volatility behaves essentially as a fractional BrownianExpand
Model Calibration with Neural Networks
In the following a method is presented to calibrate models using artificial neural networks, which can perform the calibration significantly faster regardless of the model, hence removing the calibration speed from consideration for a model's usability. Expand
Riemannian Optimization for High-Dimensional Tensor Completion
A nonlinear conjugate gradient scheme within the framework of Riemannian optimization which exploits this favorable scaling to obtain competitive reconstructions from uniform random sampling of few entries compared to adaptive sampling techniques such as cross-approximation. Expand
The Volatility Surface: A Practitioner's Guide
List of Figures. List of Tables. Foreword. Preface. Acknowledgments. Chapter 1: Stochastic Volatility and Local Volatility. Stochastic Volatility. Derivation of the Valuation Equation, LocalExpand
Functional Central Limit Theorems for Rough Volatility
We extend Donsker's approximation of Brownian motion to fractional Brownian motion with Hurst exponent $H \in (0,1)$ and to Volterra-like processes. Some of the most relevant consequences of ourExpand