Related papers: Parallel Pricing Algorithms for Multi--Dimensional…
The Multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty Quantification (UQ) in Partial Differential Equation (PDE) models, combining model computations at different levels…
In this paper we develop a deep learning method for optimal stopping problems which directly learns the optimal stopping rule from Monte Carlo samples. As such, it is broadly applicable in situations where the underlying randomness can…
Sequential Monte Carlo (SMC) methods have successfully been used in many applications in engineering, statistics and physics. However, these are seldom used in financial option pricing literature and practice. This paper presents SMC method…
Pricing of exotic financial derivatives, such as Asian and multi-asset American basket options, poses significant challenges for standard numerical methods such as binomial trees or Monte Carlo methods. While the former often scales…
This note proposes a method for pricing high-dimensional American options based on modern methods of multidimensional interpolation. The method allows using sparse grids and thus mitigates the curse of dimensionality. A framework of the…
With the goal to provide absolute lower bounds for the best possible running times that can be achieved by $(1+\lambda)$-type search heuristics on common benchmark problems, we recently suggested a dynamic programming approach that computes…
We present an adaptive multi-GPU Exchange Monte Carlo method designed for the simulation of the 3D Random Field Model. The algorithm design is based on a two-level parallelization scheme that allows the method to scale its performance in…
We discuss two numerical methods, based on a path integral approach described in a previous paper (I), for solving the stochastic equations underlying the financial markets: the Monte Carlo approach, and the Green function deterministic…
In this article we consider the problem of pricing and hedging high-dimensional Asian basket options by Quasi-Monte Carlo simulation. We assume a Black-Scholes market with time-dependent volatilities and show how to compute the deltas by…
The Variational Monte Carlo method has recently seen important advances through the use of neural network quantum states. While more and more sophisticated ans\"atze have been designed to tackle a wide variety of quantum many-body problems,…
This paper deals with the numerical approximation of American-style option values governed by partial differential complementarity problems. For a variety of one- and two-asset American options we investigate by ample numerical experiments…
In parallelized Monte-Carlo simulations, the order of summation is not always the same. When the mean is calculated in running fashion, this may create an artificial randomness in results which ought to be reproducible. This note takes a…
The aim of this study was to develop methods for evaluating the American-style option prices when the volatility of the underlying asset is described by a stochastic process. As part of this problem were developed techniques for modeling…
We propose a methodology for computing single and multi-asset European option prices, and more generally expectations of scalar functions of (multivariate) random variables. This new approach combines the ability of Monte Carlo simulation…
In this paper we introduce and study the concept of optimal and surely optimal dual martingales in the context of dual valuation of Bermudan options, and outline the development of new algorithms in this context. We provide a…
In this work, we develop a novel efficient quadrature and sparse grid based polynomial interpolation method to price American options with multiple underlying assets. The approach is based on first formulating the pricing of American…
Bayesian global optimization (BGO) is an efficient surrogate-assisted technique for problems involving expensive evaluations. A parallel technique can be used to parallelly evaluate the true-expensive objective functions in one iteration to…
We propose a novel algorithm which allows to sample paths from an underlying price process in a local volatility model and to achieve a substantial variance reduction when pricing exotic options. The new algorithm relies on the construction…
European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. American option prices can be obtained by solving…
We study perpetual American option pricing problems in an extension of the Black-Merton-Scholes model in which the dividend and volatility rates of the underlying risky asset depend on the running values of its maximum and maximum drawdown.…