Algorithms of finite difference for pricing American options under fractional diffusion models
type: Item
instance of: scholarly article
title: Algorithms of finite difference for pricing American options under fractional diffusion models
zbMATH Open document ID: 1407.91277
DOI: 10.1155/2014/364868
author: Jun Xi
author: Yanqing Chen
author: Jian-Wen Cao
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: It is well known that linear complementarity problem (LCP) involving partial integro differential equation (PIDE) arises from pricing American options under Lévy Models. In the case of infinite activity process, the integral part of the PIDE has a singularity, which is generally approximated by a small Brownian component plus a compound Poisson process, in the neighborhood of origin. The PIDE can be reformulated as a fractional partial differential equation (FPDE) under fractional diffusion models, including FMLS (finite moment log stable), CGMY (Carr-Madan-Geman-Yor), and KoBol (Koponen-Boyarchenko-Levendorskii). In this paper, we first present a stable iterative algorithm, which is based on the fractional difference approach and penalty method, to avoid the singularity problem and obtain numerical approximations of first-order accuracy. Then, on the basis of the first-order accurate algorithm, spatial extrapolation is employed to obtain second-order accurate numerical estimates. Numerical tests are performed to demonstrate the effectiveness of the algorithm and the extrapolation method. We believe that this can be used as necessary tools by the engineers in research.
Mathematics Subject Classification ID: 91G60
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 91G20
zbMATH DE Number: 7016260
Wikidata QID: Q59064633
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/364868
OpenAlex ID: W2028720793
cites work: The pricing of options and corporate liabilities
cites work: Q4905685
cites work: A Jump-Diffusion Model for Option Pricing
cites work: Option pricing when underlying stock returns are discontinuous
cites work: Q4331490
cites work: Financial Modelling with Jump Processes
cites work: Operator splitting methods for American option pricing.
cites work: A penalty method for American options with jump diffusion processes
cites work: Parabolic variational inequalities: the Lagrange multiplier approach
cites work: A high-order front-tracking finite difference method for pricing American options under jump-diffusion models
cites work: Numerical pricing of options using high-order compact finite difference schemes
cites work: A Fast Numerical Method for the Black--Scholes Equation of American Options
cites work: Front-tracking finite difference methods for the valuation of American options
cites work: A fast high-order finite difference algorithm for pricing American options
cites work: A Front-Fixing Finite Element Method for the Valuation of American Options
cites work: Penalty methods for the numerical solution of American multi-asset option problems
cites work: Q4250595
cites work: Finite difference approximations for fractional advection-dispersion flow equations
cites work: A comparison of numerical solutions of fractional diffusion models in finance
cites work: A second-order accurate numerical approximation for the fractional diffusion equation
Recommended article: Q5257012
Recommended article: Numerical methods for pricing American options with time-fractional PDE models
Recommended article: A fast high-order finite difference algorithm for pricing American options
Recommended article: FINITE-DIFFERENCE BISECTION ALGORITHMS FOR FREE BOUNDARIES OF AMERICAN OPTIONS
Recommended article: Q3501632
Recommended article: Q4984332
Recommended article: Finite difference methods for pricing American put option with rationality parameter: numerical analysis and computing
Recommended article: Compact finite difference method for American option pricing
Recommended article: A HODIE finite difference scheme for pricing American options
Recommended article: Comparison and survey of finite difference methods for pricing American options under finite activity jump-diffusion models
description: scientific article; zbMATH DE number 7016260