37 citations · 160 across the 29 of their papers we have counts for
40 papers
An Adaptive Algorithm for Rough Differential Equations
Christian Bayer, Simon Breneis, Terry Lyons
We present an adaptive algorithm for effectively solving rough differential equations (RDEs) using the log-ODE method. The algorithm is based on an error representation formula tha…
Rough PDEs for local stochastic volatility models
Peter Bank, Christian Bayer, Peter K. Friz +1
In this work, we introduce a novel pricing methodology in general, possibly non-Markovian local stochastic volatility (LSV) models. We observe that by conditioning the LSV dynamics…
On the weak convergence rate in the discretization of rough volatility models
Christian Bayer, Masaaki Fukasawa, Shonosuke Nakahara
We study the weak convergence rate in the discretization of rough volatility models. After showing a lower bound under a general model, where is the Hurst index of the vol…
Optimal Damping with Hierarchical Adaptive Quadrature for Efficient Fourier Pricing of Multi-Asset Options in Lévy Models
Michael Samet, Christian Bayer, Chiheb Ben Hammouda +2
Efficiently pricing multi-asset options is a challenging problem in quantitative finance. When the characteristic function is available, Fourier-based methods are competitive compa…
A Reproducing Kernel Hilbert Space approach to singular local stochastic volatility McKean-Vlasov models
Christian Bayer, Denis Belomestny, Oleg Butkovsky +1
Motivated by the challenges related to the calibration of financial models, we consider the problem of numerically solving a singular McKean-Vlasov equation $$ d X_t= σ(t,X_t) X_t…
Stability of Deep Neural Networks via discrete rough paths
Christian Bayer, Peter K. Friz, Nikolas Tapia
Using rough path techniques, we provide a priori estimates for the output of Deep Residual Neural Networks in terms of both the input data and the (trained) network weights. As tra…