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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…
The multilevel Monte Carlo (MLMC) method is highly efficient for estimating expectations of a functional of a solution to a stochastic differential equation (SDE). However, MLMC estimators may be unstable and have a poor (noncanonical)…
In this paper we provide a quantum Monte Carlo algorithm to solve multidimensional Black-Scholes PDEs with correlation for option pricing. The payoff function of the option is of general form and is only required to be continuous and…
Contrary to the common view that exact pricing is prohibitive owing to the curse of dimensionality, this study proposes an efficient and unified method for pricing options under multivariate Black-Scholes-Merton (BSM) models, such as the…
We develop a numerical method for pricing multidimensional vanilla options in the Black-Scholes framework. In low dimensions, we improve an adaptive integration algorithm proposed by two of the authors by introducing a new splitting…
This paper covers a massive acceleration of Monte-Carlo based pricing method for financial products and financial derivatives. The method is applicable in risk management settings, where a financial product has to be priced under a number…
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…
In this work we detail the application of a fast convolution algorithm computing high dimensional integrals to the context of multiplicative noise stochastic processes. The algorithm provides a numerical solution to the problem of…
This paper studies equity basket options -- i.e., multi-dimensional derivatives whose payoffs depend on the value of a weighted sum of the underlying stocks -- and develops a new and innovative approach to ensure consistency between options…
In this paper we propose an efficient method to compute the price of multi-asset American options, based on Machine Learning, Monte Carlo simulations and variance reduction technique. Specifically, the options we consider are written on a…
Quasi-Monte Carlo (QMC) method is a useful numerical tool for pricing and hedging of complex financial derivatives. These problems are usually of high dimensionality and discontinuities. The two factors may significantly deteriorate the…
Option contracts can be valued by using the Black-Scholes equation, a partial differential equation with initial conditions. An exact solution for European style options is known. The computation time and the error need to be minimized…
Pricing of high-dimensional options is one of the most important problems in Mathematical Finance. The objective of this manuscript is to present an original self-contained treatment of the multidimensional pricing. During the past decades…
Pricing financial derivatives, in particular European-style options at different time-maturities and strikes, means a relevant problem in finance. The dynamics describing the price of vanilla options when constant volatilities and interest…
This research addresses accurate option pricing by employing models beyond the traditional Black-Scholes framework. While Black-Scholes provides a closed-form solution, it is limited by assumptions of constant volatility, no dividends, and…
We present a new numerical method to price vanilla options quickly in time-changed Brownian motion models. The method is based on rational function approximations of the Black-Scholes formula. Detailed numerical results are given for a…
In this paper, we consider the numerical pricing of financial derivatives using Radial Basis Function generated Finite Differences in space. Such discretization methods have the advantage of not requiring Cartesian grids. Instead, the nodes…
An efficient computational algorithm to price financial derivatives is presented. It is based on a path integral formulation of the pricing problem. It is shown how the path integral approach can be worked out in order to obtain fast and…
This paper explores advancements in quantum algorithms for derivative pricing of exotics, a computational pipeline of fundamental importance in quantitative finance. For such cases, the classical Monte Carlo integration procedure provides…
Taking advantage of the recent litterature on exact simulation algorithms (Beskos, Papaspiliopoulos and Roberts) and unbiased estimation of the expectation of certain fonctional integrals (Wagner, Beskos et al. and Fearnhead et al.), we…