相关论文: PDEs for pricing interest rate derivatives under t…

SABR models have been used to incorporate stochastic volatility to LIBOR market models (LMM) in order to describe interest rate dynamics and price interest rate derivatives. From the numerical point of view, the pricing of derivatives with…

Parabolic partial differential equations (PDEs) appear in many disciplines to model the evolution of various mathematical objects, such as probability flows, value functions in control theory, and derivative prices in finance. It is often…

With the reform of interest rate benchmarks, interbank offered rates (IBORs) like LIBOR have been replaced by risk-free rates (RFRs), such as the Secured Overnight Financing Rate (SOFR) in the U.S. and the Euro Short-Term Rate (\euro STR)…

We propose two localized Radial Basis Function (RBF) methods, the Radial Basis Function Partition of Unity method (RBF-PUM) and the Radial Basis Function generated Finite Differences method (RBF-FD), for solving financial derivative pricing…

In this article, we propose a new numerical approach to high-dimensional partial differential equations (PDEs) arising in the valuation of exotic derivative securities. The proposed method is extended from Reisinger and Wittum (2007) and…

Following the recent great advance of quantum computing technology, there are growing interests in its applications to industries, including finance. In this paper, we focus on derivative pricing based on solving the Black-Scholes partial…

We study the pricing of derivative securities in financial markets modeled by a sub-mixed fractional Brownian motion with jumps (smfBm-J), a non-Markovian process that captures both long-range dependence and jump discontinuities. Under this…

This article aims to develop a direct numerical approach to solve the space-fractional partial differential equations (PDEs) based on a new differential quadrature (DQ) technique. The fractional derivatives are approximated by the weighted…

This paper introduces a no-arbitrage, Monte Carlo-free approach to pricing path-dependent interest rate derivatives. The Heath-Jarrow-Morton model gives arbitrage-free contingent claims prices but is infinite-dimensional, making traditional…

Denoising diffusion probabilistic models (DDPMs) have emerged as powerful generative models for complex distributions, yet their use in arbitrage-free derivative pricing remains largely unexplored. Financial asset prices are naturally…

This paper proposes a numerical method for pricing foreign exchange (FX) options in a model which deals with stochastic interest rates and stochastic volatility of the FX rate. The model considers four stochastic drivers, each represented…

In this paper we study partial differential equations (PDEs) that can be used to model value adjustments. Different value adjustments denoted generally as xVA are nowadays added to the risk-free financial derivative values and the PDE…

In this paper, we establish several local and global gradient estimates for the positive solution of Porous Medium Equations (PMEs) and Fast Diffusion Equations (FDEs). Our proof is probabilistic and uses martingale techniques.

This paper studies pricing derivatives in an age-dependent semi-Markov modulated market. We consider a financial market where the asset price dynamics follow a regime switching geometric Brownian motion model in which the coefficients…

The work in this paper is four-fold. Firstly, we introduce an alternative approach to solve fractional ordinary differential equations as an expected value of a random time process. Using the latter, we present an interesting numerical…

Stochastic differential equation (SDE) models are the foundation for pricing and hedging financial derivatives. The drift and volatility functions in SDE models are typically chosen to be algebraic functions with a small number (less than…

We propose some numerical schemes for forward-backward stochastic differential equations (FBSDEs) based on a new fundamental concept of transposition solutions. These schemes exploit time-splitting methods for the variation of constants…

Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering, and mathematical problems involving functions of several variables, such as the propagation of heat…

One of the oldest and most studied subject in scientific computing is algorithms for solving partial differential equations (PDEs). A long list of numerical methods have been proposed and successfully used for various applications. In…

We introduce a physics-driven deep latent variable model (PDDLVM) to learn simultaneously parameter-to-solution (forward) and solution-to-parameter (inverse) maps of parametric partial differential equations (PDEs). Our formulation…