# Explicit RKF-Compact Scheme for Pricing Regime Switching American Options with Varying Time Step

@article{Nwankwo2020ExplicitRS, title={Explicit RKF-Compact Scheme for Pricing Regime Switching American Options with Varying Time Step}, author={Chinonso Nwankwo and Weizhong Dai}, journal={ArXiv}, year={2020}, volume={abs/2012.09820} }

In this research work, an explicit Runge-Kutta-Fehlberg time integration with a fourth-order compact finite difference scheme in space is employed for solving the regime-switching pricing model. First, we recast the free boundary problem into a system of nonlinear partial differential equations with a multi-fixed domain. We further introduce a transformation based on the square root function with a fixed free boundary from which a high order analytical approximation is obtained for computingβ¦Β Expand

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SHOWING 1-10 OF 34 REFERENCES

A Robust Numerical Scheme For Pricing American Options Under Regime Switching Based On Penalty Method

- Mathematics
- 2014

This paper is devoted to develop a robust numerical method to solve a system of complementarity problems arising from pricing American options under regime switching. Based on a penalty method, theβ¦ Expand

A new efficient numerical method for solving American option under regime switching model

- Computer Science, Mathematics
- Comput. Math. Appl.
- 2016

A system of coupled free boundary problems describing American put option pricing under regime switching and explicit finite difference method is considered, which allows the computation not only of the option price but also of the optimal stopping boundary. Expand

New Numerical Scheme for Pricing American Option with Regime-Switching

- Mathematics
- 2009

This paper is concerned with regime-switching American option pricing. We develop new numerical schemes by extending the penalty method approach and by employing the ΞΈ-method. With regime-switching,β¦ Expand

High-order accurate implicit finite difference method for evaluating American options

- Economics
- 2004

A numerical method is presented for valuing vanilla American options on a single asset that is up to fourth-order accurate in the log of the asset price, and second-order accurate in time. The methodβ¦ Expand

A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides

- Mathematics, Computer Science
- TOMS
- 1990

A family of explicit Runge-Kutta formulas that contains imbedded formulas of all orders 1 through 4 is derived, which is very efficient for problems with smooth solution as well as problems having rapidly varying solutions. Expand

A Local Radial Basis Function Method for Pricing Options Under the Regime Switching Model

- Computer Science, Mathematics
- J. Sci. Comput.
- 2019

An efficient meshfree method based on radial basis functions (RBFs) to solve a system of partial differential equations arising from pricing options under the regime switching model and the uniqueness of solution is proved for the discretized system of equations. Expand

An iterative algorithm for evaluating approximations to the optimal exercise boundary for a nonlinear Black-Scholes equation

- Economics, Mathematics
- 2007

The purpose of this paper is to analyze and compute the early exercise boundary for a class of nonlinear Black--Scholes equations with a nonlinear volatility which can be a function of the secondβ¦ Expand

Fourth-order compact schemes for the numerical simulation of coupled Burgers' equation

- Mathematics, Computer Science
- Comput. Phys. Commun.
- 2016

Two new modified fourth-order exponential time differencing RungeβKutta (ETDRK) schemes in combination with a global fourth- order compact finite difference scheme for direct integration of nonlinear coupled viscous Burgersβ equations in their original form without using any transformations or linearization techniques are introduced. Expand

Far Field Boundary Conditions for Black-Scholes Equations

- Mathematics, Computer Science
- SIAM J. Numer. Anal.
- 2000

The partial differential equations approach for valuing European-style options is considered and pointwise bounds for the error caused by various boundary conditions imposed on the artificial boundary are derived. Expand

On a Free Boundary Problem for American Options Under the Generalized BlackβScholes Model

- Mathematics
- 2020

We consider the problem of pricing American options using the generalized BlackβScholes model. The generalized BlackβScholes model is a modified form of the standard BlackβScholes model with theβ¦ Expand