Corpus ID: 229297481

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 computing… Expand

Figures and Tables from this paper

References

SHOWING 1-10 OF 34 REFERENCES
A Robust Numerical Scheme For Pricing American Options Under Regime Switching Based On Penalty Method
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, theExpand
A new efficient numerical method for solving American option under regime switching model
TLDR
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
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 θ-method. With regime-switching,Expand
High-order accurate implicit finite difference method for evaluating American options
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 methodExpand
A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides
TLDR
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
TLDR
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
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 secondExpand
Fourth-order compact schemes for the numerical simulation of coupled Burgers' equation
TLDR
Two new modified fourth-order exponential time differencing Runge–Kutta (ETDRK) schemes in combination with a global fourth- order compact finite difference scheme for direct integration of nonlinear coupled viscous Burgers’ equations in their original form without using any transformations or linearization techniques are introduced. Expand
Far Field Boundary Conditions for Black-Scholes Equations
TLDR
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 Black–Scholes Model
We consider the problem of pricing American options using the generalized Black–Scholes model. The generalized Black–Scholes model is a modified form of the standard Black–Scholes model with theExpand
...
1
2
3
4
...