Compact finite difference method for American option pricing

Compact finite difference scheme for option pricing in Heston’s model

We present a compact high-order finite difference scheme for option pricing in the well-known Heston stochastic volatility model. The scheme is fourth order accurate in space and second order accurate in time. This is also confirmed by the numerical experiments that we present.

Finite Element Method for American Option Pricing: a Penalty Approach

The model for pricing of American option gives rise to a parabolic variational inequality. We first use penalty function approach to reformulate it as an equality problem. Since the problem is defined on an unbounded domain, we truncate it to a bounded domain and discuss error due to truncation and penalization. Finite element method is then applied to the penalized problem on the truncated dom...

Accurate Finite Difference Methods for Option Pricing

A Newton Method for American Option Pricing

The variational inequality formulation provides a mechanism to determine both the option value and the early exercise curve implicitly [17]. Standard finite difference approximation typically leads to linear complementarity problems with tridiagonal coefficient matrices. The second order upwind finite difference formulation gives rise to finite dimensional linear complementarity problems with n...

High-order compact finite difference scheme for option pricing in stochastic volatility models

We derive a new compact high-order finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth order accurate in space and second order accurate in time. To prove results on the unconditional stability in the sense of von Neumann we perform a thorough Fourier analysis of the problem and deduce convergence of our scheme. We present results of numerical exper...