Article2009

High-order compact scheme for solving nonlinear Black–Scholes equation with transaction cost

48 citations0/0 files storedInternational Journal of Computer Mathematics

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Stochastic processes and financial applications Advanced Numerical Methods in Computational Mathematics Differential Equations and Numerical Methods

Abstract

In this paper, an unconditionally stable high-order compact finite difference scheme is proposed. The compact scheme is fourth-order accurate in both the temporal and spatial dimensions. The new method computes both the option price and the hedging delta ∂ V/∂ S simultaneously. Two numerical examples are presented to demonstrate the accuracy and efficiency of the proposed scheme.

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References

1973The Pricing of Options and Corporate Liabilities 1985Option Pricing and Replication with Transactions Costs 1993European Option Pricing with Transaction Costs 1992Option Replication in Discrete Time with Transaction Costs 1998Option pricing with transaction costs and a nonlinear Black-Scholes equation 1997Numerical Methods in Finance 1997Convergence of Numerical Schemes for Degenerate Parabolic Equations Arising in Finance Theory 1994Dynamic hedging portfolios for derivative securities in the presence of large transaction costs

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2012The numerical approximation of nonlinear Black–Scholes model for exotic path-dependent American options with transaction cost 2016Analysis of the Nonlinear Option Pricing Model Under Variable Transaction Costs 2013High-Order Compact Finite Difference Schemes for Option Pricing in Stochastic Volatility Models on Non-Uniform Grids 2016Fourth-order compact schemes for a parabolic-ordinary system of European option pricing liquidity shocks model 2011A high-order compact method for nonlinear Black–Scholes option pricing equations of American options

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