Journal ArticleDOI
A Fast Numerical Method for the Black--Scholes Equation of American Options
Houde Han,Xiaonan Wu +1 more
TLDR
This paper introduces a fast numerical method for computing American option pricing problems governed by the Black--Scholes equation that is very efficient and gives better accuracy than the normal finite difference method.Abstract:
This paper introduces a fast numerical method for computing American option pricing problems governed by the Black--Scholes equation. The treatment of the free boundary is based on some properties of the solution of the Black--Scholes equation. An artificial boundary condition is also used at the other end of the domain. The finite difference method is used to solve the resulting problem. Computational results are given for some American call option problems. The results show that the new treatment is very efficient and gives better accuracy than the normal finite difference method.read more
Citations
More filters
Posted Content
Solving stochastic differential equations and Kolmogorov equations by means of deep learning
TL;DR: In this article, a numerical approximation of the Kolmogorov PDE on an entire region $[a,b]^d$ without suffering from the curse of dimensionality is presented.
Journal ArticleDOI
Numerical pricing of options using high-order compact finite difference schemes
TL;DR: In this paper, the authors considered high-order compact schemes for quasilinear parabolic partial differential equations to discretise the Black-Scholes PDE for the numerical pricing of European and American options.
Journal Article
Solving stochastic differential equations and Kolmogorov equations by means of deep learning.
TL;DR: A numerical approximation method is derived and proposed which aims to overcome both of the above mentioned drawbacks and intends to deliver a numerical approximation of the Kolmogorov PDE on an entire region without suffering from the curse of dimensionality.
Journal ArticleDOI
A fast high-order finite difference algorithm for pricing American options
TL;DR: An improvement of Han and Wu's algorithm for the Black-Scholes equation of American options converges rapidly and numerical solutions with good accuracy are obtained.
Journal ArticleDOI
Convergence of a fitted finite volume method for the penalized Black–Scholes equation governing European and American Option pricing
Lutz Angermann,Song Wang +1 more
TL;DR: An analysis of a numerical method for a degenerate partial differential equation, called the Black–Scholes equation, governing American and European option pricing, based on a fitted finite volume spatial discretization and an implicit time stepping technique is presented.
References
More filters
Journal ArticleDOI
The Pricing of Options and Corporate Liabilities
Fischer Black,Myron S. Scholes +1 more
TL;DR: In this paper, a theoretical valuation formula for options is derived, based on the assumption that options are correctly priced in the market and it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks.
Book
Conduction of Heat in Solids
H. S. Carslaw,John Conrad Jaeger +1 more
TL;DR: In this paper, a classic account describes the known exact solutions of problems of heat flow, with detailed discussion of all the most important boundary value problems, including boundary value maximization.
Journal ArticleDOI
Option pricing: A simplified approach☆
TL;DR: In this paper, a simple discrete-time model for valuing options is presented, which is based on the Black-Scholes model, which has previously been derived only by much more difficult methods.
Journal ArticleDOI
Absorbing boundary conditions for the numerical simulation of waves
Björn Engquist,Andrew J. Majda +1 more
TL;DR: This work develops a systematic method for obtaining a hierarchy of local boundary conditions at these artifical boundaries that not only guarantee stable difference approximations, but also minimize the (unphysical) artificial reflections that occur at the boundaries.