Related papers: Time Deep Gradient Flow Method for pricing America…
Despite significant advancements in machine learning for derivative pricing, the efficient and accurate valuation of American options remains a persistent challenge due to complex exercise boundaries, near-expiry behavior, and intricate…
In this paper, we introduce two novel methods to solve the American-style option pricing problem and its dual form at the same time using neural networks. Without applying nested Monte Carlo, the first method uses a series of neural…
In American options, the early exercise feature allows the option to be exercised at any time prior to expiration. However, this flexibility introduces a challenge: the pricing model must value the option while simultaneously determining an…
This paper introduces a new method based on Deep Galerkin Methods (DGMs) for solving high-dimensional stochastic Mean Field Games (MFGs). We achieve this by using two neural networks to approximate the unknown solutions of the MFG system…
We study the binomial, trinomial, and Black-Scholes-Merton models of option pricing. We present fast parallel discrete-time finite-difference algorithms for American call option pricing under the binomial and trinomial models and American…
This paper proposes and analyzes two fully discrete mixed interior penalty discontinuous Galerkin (DG) methods for the fourth order nonlinear Cahn-Hilliard equation. Both methods use the backward Euler method for time discretization and…
The paper focuses on pricing European-style options on several underlying assets under the Black-Scholes model represented by a nonstationary partial differential equation. The proposed method combines the Galerkin method with…
Option pricing models, essential in financial mathematics and risk management, have been extensively studied and recently advanced by AI methodologies. However, American option pricing remains challenging due to the complexity of…
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…
Accurate and rapid prediction of flow-fields is crucial for aerodynamic design. This work proposes a discontinuous Galerkin method (DGM) whose performance enhances with increasing data, for rapid simulation of transonic flow around airfoils…
In this paper, we propose a novel numerical method for Path-Dependent Partial Differential Equations (PPDEs). These equations firstly appeared in the seminal work of Dupire [2009], where the functional It\^o calculus was developed to deal…
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…
Deep neural networks are powerful tools for approximating functions, and they are applied to successfully solve various problems in many fields. In this paper, we propose a neural network-based numerical method to solve partial differential…
A new method for stochastic control based on neural networks and using randomisation of discrete random variables is proposed and applied to optimal stopping time problems. The method models directly the policy and does not need the…
Dynamic hedging is a financial strategy that consists in periodically transacting one or multiple financial assets to offset the risk associated with a correlated liability. Deep Reinforcement Learning (DRL) algorithms have been used to…
In this article we propose a novel approach to reduce the computational complexity of various approximation methods for pricing discrete time American options. Given a sequence of continuation values estimates corresponding to different…
We propose a gradient-based deep learning framework to calibrate the Heston option pricing model (Heston, 1993). Our neural network, henceforth deep differential network (DDN), learns both the Heston pricing formula for plain-vanilla…
High-dimensional PDEs have been a longstanding computational challenge. We propose to solve high-dimensional PDEs by approximating the solution with a deep neural network which is trained to satisfy the differential operator, initial…
We extend the Deep Galerkin Method (DGM) introduced in Sirignano and Spiliopoulos (2018)} to solve a number of partial differential equations (PDEs) that arise in the context of optimal stochastic control and mean field games. First, we…
We investigate methods for pricing American options under the variance gamma model. The variance gamma process is a pure jump process which is constructed by replacing the calendar time by the gamma time in a Brownian motion with drift,…