Hedging with a correlated asset: Solution of a nonlinear pricing PDE
Journal of Computational and Applied Mathematics
Augmented Lagrangian method applied to American option pricing
Automatica (Journal of IFAC)
50th ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications
Management Science
Numerical solution of two asset jump diffusion models for option valuation
Applied Numerical Mathematics
Adaptive θ-methods for pricing American options
Journal of Computational and Applied Mathematics
Penalty methods for the numerical solution of American multi-asset option problems
Journal of Computational and Applied Mathematics
Infinite reload options: Pricing and analysis
Journal of Computational and Applied Mathematics
An efficient implementation of a least squares Monte Carlo method for valuing American-style options
International Journal of Computer Mathematics - SPECIAL ISSUE ON FINANCIAL DERIVATIVES
Exponential Rosenbrock integrators for option pricing
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Parallel Two-Grid Semismooth Newton-Krylov-Schwarz Method for Nonlinear Complementarity Problems
Journal of Scientific Computing
A robust and accurate finite difference method for a generalized Black-Scholes equation
Journal of Computational and Applied Mathematics
A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance
SIAM Journal on Numerical Analysis
Trend Following Trading under a Regime Switching Model
SIAM Journal on Financial Mathematics
Methods for Pricing American Options under Regime Switching
SIAM Journal on Scientific Computing
Concurrency and Computation: Practice & Experience
Penalty Methods for the Solution of Discrete HJB Equations—Continuous Control and Obstacle Problems
SIAM Journal on Numerical Analysis
Convergence analysis of power penalty method for American bond option pricing
Journal of Global Optimization
Stabilized explicit Runge-Kutta methods for multi-asset American options
Computers & Mathematics with Applications
Hi-index | 0.01 |
The convergence of a penalty method for solving the discrete regularized American option valuation problem is studied. Sufficient conditions are derived which both guarantee convergence of the nonlinear penalty iteration and ensure that the iterates converge monotonically to the solution. These conditions also ensure that the solution of the penalty problem is an approximate solution to the discrete linear complementarity problem. The efficiency and quality of solutions obtained using the implicit penalty method are compared with those produced with the commonly used technique of handling the American constraint explicitly. Convergence rates are studied as the timestep and mesh size tend to zero. It is observed that an implicit treatment of the American constraint does not converge quadratically (as the timestep is reduced) if constant timesteps are used. A timestep selector is suggested which restores quadratic convergence.