TY - JOUR
T1 - A computational scheme for uncertain volatility model in option pricing
AU - Zhang, K.
AU - Wang, Song
PY - 2009
Y1 - 2009
N2 - In this paper we develop a novel numerical scheme for a nonlinear partial differential equation arising from the uncertain volatility model in option pricing. The fitted finite volume method is developed for the space discretization with implicit scheme in time discretization, which results in a nonlinear discrete system. We prove that this method is consistent, stable and monotone, hence it ensures the convergence to the viscosity solution. We also propose an iteration scheme for the nonlinear discrete scheme and show its convergence property. Numerical experiments are implemented to verify the efficiency and usefulness of this method.
AB - In this paper we develop a novel numerical scheme for a nonlinear partial differential equation arising from the uncertain volatility model in option pricing. The fitted finite volume method is developed for the space discretization with implicit scheme in time discretization, which results in a nonlinear discrete system. We prove that this method is consistent, stable and monotone, hence it ensures the convergence to the viscosity solution. We also propose an iteration scheme for the nonlinear discrete scheme and show its convergence property. Numerical experiments are implemented to verify the efficiency and usefulness of this method.
U2 - 10.1016/j.apnum.2009.01.004
DO - 10.1016/j.apnum.2009.01.004
M3 - Article
VL - 59
SP - 1754
EP - 1767
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
SN - 0168-9274
IS - 8
ER -