1 code implementation • 5 Mar 2024 • Christian Bayer, Chiheb Ben Hammouda, Antonis Papapantoleon, Michael Samet, Raúl Tempone
Nonetheless, the applicability of RQMC on the unbounded domain, $\mathbb{R}^d$, requires a domain transformation to $[0, 1]^d$, which may result in singularities of the transformed integrand at the corners of the hypercube, and deteriorate the rate of convergence of RQMC.
no code implementations • 6 Dec 2023 • Christian Bayer, Luca Pelizzari, John Schoenmakers
We propose two signature-based methods to solve the optimal stopping problem - that is, to price American options - in non-Markovian frameworks.
no code implementations • 6 Oct 2023 • Christian Bayer, Simon Breneis
We provide an efficient and accurate simulation scheme for the rough Heston model in the standard ($H>0$) as well as the hyper-rough regime ($H > -1/2$).
no code implementations • 13 Sep 2023 • Christian Bayer, Simon Breneis
The rough Heston model is a very popular recent model in mathematical finance; however, the lack of Markov and semimartingale properties poses significant challenges in both theory and practice.
no code implementations • 18 Jul 2023 • Peter Bank, Christian Bayer, Peter K. Friz, Luca Pelizzari
In this work, we introduce a novel pricing methodology in general, possibly non-Markovian local stochastic volatility (LSV) models.
1 code implementation • 15 Mar 2022 • Michael Samet, Christian Bayer, Chiheb Ben Hammouda, Antonis Papapantoleon, Raúl Tempone
First, we smooth the Fourier integrand via an optimized choice of the damping parameters based on a proposed optimization rule.
no code implementations • 6 Mar 2022 • Christian Bayer, Masaaki Fukasawa, Shonosuke Nakahara
We study the weak convergence rate in the discretization of rough volatility models.
no code implementations • 2 Mar 2022 • Christian Bayer, Denis Belomestny, Oleg Butkovsky, John Schoenmakers
Motivated by the challenges related to the calibration of financial models, we consider the problem of numerically solving a singular McKean-Vlasov equation $$ d X_t= \sigma(t, X_t) X_t \frac{\sqrt v_t}{\sqrt {E[v_t|X_t]}}dW_t, $$ where $W$ is a Brownian motion and $v$ is an adapted diffusion process.
1 code implementation • 19 Jan 2022 • 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.
no code implementations • 2 Nov 2021 • Christian Bayer, Chiheb Ben Hammouda, Raúl Tempone
When approximating the expectations of a functional of a solution to a stochastic differential equation, the numerical performance of deterministic quadrature methods, such as sparse grid quadrature and quasi-Monte Carlo (QMC) methods, may critically depend on the regularity of the integrand.
no code implementations • 11 Aug 2021 • Christian Bayer, Simon Breneis
To remedy this, we study approximations of stochastic Volterra equations using an $N$-dimensional diffusion process defined as solution to a system of ordinary stochastic differential equation.
1 code implementation • 2 Mar 2021 • Christian Bayer, Martin Eigel, Leon Sallandt, Philipp Trunschke
An efficient compression technique based on hierarchical tensors for popular option pricing methods is presented.
no code implementations • 24 Nov 2020 • Christian Bayer, Denis Belomestny, Paul Hager, Paolo Pigato, John Schoenmakers, Vladimir Spokoiny
Least squares Monte Carlo methods are a popular numerical approximation method for solving stochastic control problems.
1 code implementation • 2 Sep 2020 • Christian Bayer, Eric Joseph Hall, Raúl Tempone
We prove rate $H + 1/2$ for the weak convergence of the Euler method for the rough Stein-Stein model, which treats the volatility as a linear function of the driving fractional Brownian motion, and, surprisingly, we prove rate one for the case of quadratic payoff functions.
no code implementations • 7 Aug 2020 • Christian Bayer, Fabian Andsem Harang, Paolo Pigato
We propose a new class of rough stochastic volatility models obtained by modulating the power-law kernel defining the fractional Brownian motion (fBm) by a logarithmic term, such that the kernel retains square integrability even in the limit case of vanishing Hurst index $H$.
no code implementations • 12 Mar 2020 • Christian Bayer, Chiheb Ben Hammouda, Raul Tempone
This study is motivated by the computation of probabilities of events, pricing options with a discontinuous payoff, and density estimation problems for dynamics where the discretization of the underlying stochastic processes is necessary.
no code implementations • 8 Oct 2018 • Christian Bayer, Benjamin Stemper
Sparked by Al\`os, Le\'on, and Vives (2007); Fukasawa (2011, 2017); Gatheral, Jaisson, and Rosenbaum (2018), so-called rough stochastic volatility models such as the rough Bergomi model by Bayer, Friz, and Gatheral (2016) constitute the latest evolution in option price modeling.
no code implementations • 19 Sep 2018 • Christian Bayer, Raúl Tempone, Sören Wolfers
Numerical experiments on vanilla put options in the multivariate Black-Scholes model and a preliminary theoretical analysis underline the efficiency of our method, both with respect to the number of time-discretization steps and the required number of degrees of freedom in the parametrization of the exercise rates.