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Found 18 papers, 5 papers with code
Quasi-Monte Carlo for Efficient Fourier Pricing of Multi-Asset Options
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.
Primal and dual optimal stopping with signatures
We propose two signature-based methods to solve the optimal stopping problem - that is, to price American options - in non-Markovian frameworks.
Efficient option pricing in the rough Heston model using weak simulation schemes
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 ($H > -1/2$).
Weak Markovian Approximations of Rough Heston
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.
Rough PDEs for local stochastic volatility models
In this work, we introduce a novel pricing methodology in general, possibly non-Markovian local stochastic volatility (LSV) models.
Optimal Damping with Hierarchical Adaptive Quadrature for Efficient Fourier Pricing of Multi-Asset Options in Lévy Models
First, we smooth the Fourier integrand via an optimized choice of the damping parameters based on a proposed optimization rule.
On the weak convergence rate in the discretization of rough volatility models
We study the weak convergence rate in the discretization of rough volatility models.
A Reproducing Kernel Hilbert Space approach to singular local stochastic volatility McKean-Vlasov models
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.
Stability of Deep Neural Networks via discrete rough paths
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.
Numerical Smoothing with Hierarchical Adaptive Sparse Grids and Quasi-Monte Carlo Methods for Efficient Option Pricing
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.
Markovian approximations of stochastic Volterra equations with the fractional kernel
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.
Pricing high-dimensional Bermudan options with hierarchical tensor formats
An efficient compression technique based on hierarchical tensors for popular option pricing methods is presented.
Reinforced optimal control
Least squares Monte Carlo methods are a popular numerical approximation method for solving stochastic control problems.
Weak error rates for option pricing under linear rough volatility
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.
Log-modulated rough stochastic volatility models
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 $H$.
Multilevel Monte Carlo with Numerical Smoothing for Robust and Efficient Computation of Probabilities and Densities
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.
Deep calibration of rough stochastic volatility models
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.
Pricing American Options by Exercise Rate Optimization
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.
