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On a numerical approximation scheme for construction of the early exercise boundary for a class of nonlinear Black-Scholes equations
numerical approximation construction nonlinear Black-Scholes equations
2010/10/21
The purpose of this paper is to construct the early exercise boundary for a class of nonlinear Black--Scholes equations with a nonlinear volatility depending on the option price. We review a method h...
Analytical and Numerical Approaches to Pricing the Path-Dependent Options with Stochastic Volatility
Analytical Numerical Pricing Path-Dependent Options Stochastic Volatility
2010/10/21
In this paper new analytical and numerical approaches to valuating path-dependent options of European type have been developed. The model of stochastic volatility as a basic model has been chosen. Fo...
A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance
HJB Equation Numerical Solution Penalty Method
2010/10/21
We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a vi...
The aim of this work is to provide fast and accurate approximation schemes for the Monte-Carlo pricing of derivatives in the L\'evy LIBOR model of Eberlein and \"Ozkan (2005). Standard methods can be...