Finite difference methods for pricing American put option with rationality parameter: Numerical analysis and computing

A Simple Numerical Method for Pricing an American Put Option

We present a simple numerical method to find the optimal exercise boundary in an American put option. We formulate an intermediate function with the fixed free boundary that has Lipschitz character near optimal exercise boundary. Employing it, we can easily determine the optimal exercise boundary by solving a quadratic equation in time-recursive way. We also present several numerical results wh...

Accurate Finite Difference Methods for Option Pricing

Numerical Solution of Pricing of European Put Option with Stochastic Volatility

In this paper, European option pricing with stochastic volatility forecasted by well known GARCH model is discussed in context of Indian financial market. The data of Reliance Ltd. stockprice from 3/01/2000 to 30/03/2009 is used and resulting partial differential equation is solved byCrank-Nicolson finite difference method for various interest rates and maturity in time. Thesensitivity measures...

Error estimates for finite difference approximations of American put option price

Finite difference approximations to multi-asset American put option price are considered. The assets are modelled as a multi-dimensional diffusion process with variable drift and volatility. Approximation error of order one quarter with respect to the time discretisation parameter and one half with respect to the space discretisation parameter is proved by reformulating the corresponding optima...

Finite Element Methods for Option Pricing

The finite element method is well suited to the numerical solution of the partial differential equations arising in finance because they allow for a posteriori error estimates and mesh adaptivity. The method will be described on three simple examples and its advantages will be emphasized.