A positivity-preserving numerical scheme for nonlinear option pricing models
type: Item
instance of: scholarly article
title: A positivity-preserving numerical scheme for nonlinear option pricing models
zbMATH Open document ID: 1264.91143
DOI: 10.1155/2012/205686
author: Wei Li
author: Yu Wei
author: Cui Wen
author: Sheng-Wu Zhou
published in: Journal of Applied Mathematics
publication date: 2013-06-03T00:00:00Z
review text: Summary: A positivity-preserving numerical method for nonlinear Black-Scholes models is developed in this paper. The numerical method is based on a nonstandard approximation of the second partial derivative. The scheme is not only unconditionally stable and positive, but also allows us to solve the discrete equation explicitly. Monotone properties are studied in order to avoid unwanted oscillations of the numerical solution. The numerical results for European put option and European butterfly spread are compared to the standard finite difference scheme. It turns out that the proposed scheme is efficient and reliable.
Mathematics Subject Classification ID: 91G60
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 35Q91
zbMATH DE Number: 6169861
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/205686
OpenAlex ID: W1963954594
Wikidata QID: Q58906375
cites work: The pricing of options and corporate liabilities
cites work: Q4905685
cites work: A note on the Boyle-Vorst discrete-time option pricing model with transactions costs.
cites work: Option pricing with transaction costs and a nonlinear Black-Scholes equation
cites work: On the risk-adjusted pricing-methodology-based valuation of vanilla options and explanation of the volatility smile
cites work: Q4550916
cites work: General Black-Scholes models accounting for increased market volatility from hedging strategies
cites work: Option pricing with an illiquid underlying asset market
cites work: An explicit finite difference approach to the pricing of barrier options
cites work: Penalty methods for American options with stochastic volatility
cites work: An upwind approach for an American and European option pricing model
cites work: Exponential time integration and Chebychev discretisation schemes for fast pricing of options
cites work: On smoothing of the Crank-Nicolson scheme and higher order schemes for pricing barrier options
cites work: Finite Volume Schemes for Solving Nonlinear Partial Differential Equations in Financial Mathematics
cites work: A numerical method for European option pricing with transaction costs nonlinear equation
cites work: Consistent stable difference schemes for nonlinear Black-Scholes equations modelling option pricing with transaction costs
cites work: Computing option pricing models under transaction costs
cites work: The numerical approximation of nonlinear Black–Scholes model for exotic path-dependent American options with transaction cost
cites work: Exponential time differencing for stiff systems
cites work: High Order Compact Finite Difference Schemes for a Nonlinear Black-Scholes Equation
cites work: A high-order compact method for nonlinear Black–Scholes option pricing equations of American options
cites work: A high-order conservative Patankar-type discretisation for stiff systems of production--destruction equations
cites work: Positive and elementary stable nonstandard numerical methods with applications to predator-prey models
cites work: Adequate numerical solution of air pollution problems by positive difference schemes on unbounded domains
cites work: An unconditionally positivity preserving scheme for advection-diffusion reaction equations
cites work: Q3240966
cites work: Q5689624
description: scientific article; zbMATH DE number 6169861