Transformation Methods for Evaluating Approximations to the Optimal Exercise Boundary for Linear and Nonlinear Black-Scholes Equations

Transformation methods for evaluating approximations to the optimal exercise boundary for linear and nonlinear Black-Scholes equations

Abstract. The purpose of this survey chapter is to present a transformation technique that can be used in analysis and numerical computation of the early exercise boundary for an American style of vanilla options that can be modelled by class of generalized Black-Scholes equations. We analyze qualitatively and quantitatively the early exercise boundary for a linear as well as a class of nonline...

An iterative algorithm for evaluating approximations to the optimal exercise boundary for a nonlinear Black–Scholes equation

The purpose of this paper is to analyze and compute the early exercise boundary for a class of nonlinear Black–Scholes equations with a nonlinear volatility which can be a function of the second derivative of the option price itself. A motivation for studying the nonlinear Black–Scholes equation with a nonlinear volatility arises from option pricing models taking into account e.g. nontrivial tr...

Evaluating Approximations to the Optimal Exercise Boundary for American Options

We consider series solutions for the location of the optimal exercise boundary of an American option close to expiry. By using Monte Carlo methods, we compute the expected value of an option if the holder uses the approximate location given by such a series as his exercise strategy, and compare this value to the actual value of the option. This gives an alternative method to evaluate approximat...

On Nonlinear Black-Scholes Equations

This paper revisits some solution methods for Black-Scholes equation and some of its nonlinear versions arising in option pricing theory.

The use of iterative methods for solving Black-Scholes equation