High Order Smoothing Schemes for Inhomogeneous Parabolic Problems with Applications in Option Pricing
نویسندگان
چکیده
A new family of numerical schemes for inhomogeneous parabolic partial differential equations is developed utilizing diagonal Padé schemes combined with positivity–preserving Padé schemes as damping devices. We also develop a split version of the algorithm using partial fraction decomposition to address difficulties with accuracy and computational efficiency in solving and to implement the algorithms in parallel. Numerical experiments are presented for several inhomogeneous parabolic problems, including pricing of financial options with nonsmooth payoffs. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 00: 000–000, 2007
منابع مشابه
High-Order Compact Schemes for Parabolic Problems with Mixed Derivatives in Multiple Space Dimensions
We present a high-order compact finite difference approach for a class of parabolic partial differential equations with timeand space-dependent coefficients as well as with mixed second-order derivative terms in n spatial dimensions. Problems of this type arise frequently in computational fluid dynamics and computational finance. We derive general conditions on the coefficients which allow us t...
متن کاملNonstandard explicit third-order Runge-Kutta method with positivity property
When one solves differential equations, modeling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. Based on general theory for positivity, with an explicit third-order Runge-Kutta method (we will refer to it as RK3 method) pos...
متن کاملEssentially high-order compact schemes with application to stochastic volatility models on non-uniform grids
We present high-order compact schemes for a linear second-order parabolic partial differential equation (PDE) with mixed second-order derivative terms in two spatial dimensions. The schemes are applied to option pricing PDE for a family of stochastic volatility models. We use a nonuniform grid with more grid-points around the strike price. The schemes are fourth-order accurate in space and seco...
متن کاملA Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models
We present a finite difference method for solving parabolic partial integro-differential equations with possibly singular kernels which arise in option pricing theory when the random evolution of the underlying asset is driven by a Lévy process or, more generally, a time-inhomogeneous jumpdiffusion process. We discuss localization to a finite domain and provide an estimate for the localization ...
متن کاملNumerical algorithm for discrete barrier option pricing in a Black-Scholes model with stationary process
In this article, we propose a numerical algorithm for computing price of discrete single and double barrier option under the emph{Black-Scholes} model. In virtue of some general transformations, the partial differential equations of option pricing in different monitoring dates are converted into simple diffusion equations. The present method is fast compared to alterna...
متن کامل