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The purpose of this paper is to analyze the problem of option pricing when the short rate follows subdiffusive fractional Merton model. We incorporate the stochastic nature of the short rate in our option valuation model and derive explicit…

Pricing of Securities · Quantitative Finance 2018-05-03 Foad Shokrollahi

It is well known that the Black-Scholes-Merton model suffers from several deficiencies. Jump-diffusion and Levy models have been widely used to partially alleviate some of the biases inherent in this classical model. Unfortunately, the…

Computational Engineering, Finance, and Science · Computer Science 2007-05-23 Kenneth R. Jackson , Sebastian Jaimungal , Vladimir Surkov

We propose a time-adaptive, high-order compact finite difference scheme for option pricing in a family of stochastic volatility models. We employ a semi-discrete high-order compact finite difference method for the spatial discretisation,…

Computational Finance · Quantitative Finance 2024-03-26 Bertram Düring , Christof Heuer

This paper investigates analytic properties of American option prices under the finite moment log-stable (FMLS) model. Under this model the price of American options is characterised by the free boundary problem of a fractional partial…

Computational Finance · Quantitative Finance 2017-10-25 Wenting Chen , Kai Du , Xinzi Qiu

We provide an European option pricing formula written in the form of an infinite series of Black Scholes type terms under double Levy jumps model, where both the interest rate and underlying price are driven by Levy process. The series…

Pricing of Securities · Quantitative Finance 2023-05-19 Qian Li , Li Wang

his paper presents finite element methods for solving numerically the Risk-Adjusted Pricing Methodology (RAPM) Black-Scholes model for option pricing with transaction costs. Spatial finite element models based on P1 and/or P2 elements are…

Computational Finance · Quantitative Finance 2021-03-16 Dongming Wei , Yogi Ahmad Erlangga , Andrey Pak , Laila Zhexembay

In this paper, we discuss a simple yet robust PDE method for evaluating path-dependent Asian-style options using the non-oscillatory forward-in-time second-order MPDATA finite-difference scheme. The valuation methodology involves casting…

Computational Finance · Quantitative Finance 2025-06-02 Paweł Magnuszewski , Sylwester Arabas

The Black-Scholes theory of option pricing has been considered for many years as an important but very approximate zeroth-order description of actual market behavior. We generalize the functional form of the diffusion of these systems and…

Computational Physics · Physics 2009-11-06 Lester Ingber

We discuss in this note applications of the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA) to numerical solutions of partial differential equations arising from stochastic models in quantitative finance. In…

Computational Finance · Quantitative Finance 2019-06-24 Sylwester Arabas , Ahmad Farhat

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…

Statistical Mechanics · Physics 2009-11-07 G. Montagna , O. Nicrosini , N. Moreni

We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility jump models, e.g. in Bates model. In such models the option price is determined as the solution of a partial integro-differential…

Computational Finance · Quantitative Finance 2019-02-25 Bertram Düring , Alexander Pitkin

We present a new high-order compact scheme for the multi-dimensional Black-Scholes model with application to European Put options on a basket of two underlying assets. The scheme is second-order accurate in time and fourth-order accurate in…

Computational Finance · Quantitative Finance 2015-05-29 Bertram Düring , Christof Heuer

We study here the approximation by a finite-volume scheme of a heat equation forced by a Lipschitz continuous multiplicative noise in the sense of It\^o. More precisely, we consider a discretization which is semi-implicit in time and a…

Analysis of PDEs · Mathematics 2023-07-13 Caroline Bauzet , Flore Nabet , Kerstin Schmitz , Aleksandra Zimmermann

In this paper we develop numerical pricing methodologies for European style Exchange Options written on a pair of correlated assets, in a market with finite liquidity. In contrast to the standard multi-asset Black-Scholes framework, trading…

Pricing of Securities · Quantitative Finance 2020-06-16 Kevin S. Zhang , Traian A. Pirvu

Multigrid methods are popular for solving linear systems derived from discretizing PDEs. Local Fourier Analysis (LFA) is a technique for investigating and tuning multigrid methods. P-multigrid is popular for high-order or spectral finite…

Numerical Analysis · Mathematics 2023-01-20 Jeremy L. Thompson , Jed Brown , Yunhui He

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…

Computational Engineering, Finance, and Science · Computer Science 2014-04-30 Snehanshu Saha , Swati Routh , Bidisha Goswami

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…

Computational Engineering, Finance, and Science · Computer Science 2016-12-04 Maciej Balajewicz , Jari Toivanen

We introduce a new cell-centered finite volume discretization for elasticity with weakly enforced symmetry of the stress tensor. The method is motivated by the need for robust discretization methods for deformation and flow in porous media,…

Numerical Analysis · Mathematics 2015-12-04 Eirik Keilegavlen , Jan Martin Nordbotten

Following the foundational work of the Black--Scholes model, extensive research has been developed to price the option by addressing its underlying assumptions and associated pricing biases. This study introduces a novel framework for…

Mathematical Finance · Quantitative Finance 2025-08-21 Tapan Kar , Suprio Bhar , Barun Sarkar , Sesha Meka

In this paper, we present a novel approach to solving the American put options pricing model by hugely relying on a front-fixing Crank-Nicolson finite difference method. Since the American put option pricing model is a widely used financial…

Analysis of PDEs · Mathematics 2025-12-09 Z. I. Ali , M. A. Abebe