Penalty methods for American options with stochastic volatility
Journal of Computational and Applied Mathematics
Numerical methods for the solution of partial differential equations of fractional order
Journal of Computational Physics
A Jump-Diffusion Model for Option Pricing
Management Science
A second-order accurate numerical method for the two-dimensional fractional diffusion equation
Journal of Computational Physics
Numerical Approximation of a Time Dependent, Nonlinear, Space-Fractional Diffusion Equation
SIAM Journal on Numerical Analysis
Finite difference approximations for two-sided space-fractional partial differential equations
Applied Numerical Mathematics
SIAM Journal on Numerical Analysis
Pricing American bond options using a penalty method
Automatica (Journal of IFAC)
Pricing American bond options using a penalty method
Automatica (Journal of IFAC)
A power penalty method for linear complementarity problems
Operations Research Letters
A power penalty approach to a Nonlinear Complementarity Problem
Operations Research Letters
| Hi-index | 0.09 |
A power penalty method is proposed for a parabolic variational inequality or linear complementarity problem (LCP) involving a fractional order partial derivative arising in the valuation of American options whose underlying stock prices follow a geometric Levy process. We first approximate the LCP with a nonlinear fractional partial differential equation (fPDE) with a penalty term. We then prove that the solution to the nonlinear fPDE converges to that of the LCP in a Sobolev norm at an exponential rate depending on the parameters used in the penalty term. Numerical results are presented to demonstrate the convergence rates and usefulness of the penalty method for pricing American put options of this type.