Multigrid for American option pricing with stochastic volatility

The paper describes an implicit finite difference approach to the pricing of American options on assets with a stochastic volatility. A multigrid procedure is described for the fast iterative solution of the discrete linear complementarity problems that result. The accuracy and performance of this approach is improved considerably by a strike-price related analytic transformation of asset prices and adaptive time-stepping.

Numerical experiments of some Krylov subspace methods for black oil model

This paper discusses preconditioned Krylov subspace methods for solving large scale linear systems that originate from oil reservoir numerical simulations. Two types of preconditioners, one being based on an incomplete LU decomposition and the other being based on iterative algorithms, are used together in a combination strategy in order to achieve an adaptive and efficient preconditioner. Numerical tests show that different Krylov subspace methods combining with appropriate preconditioners are able to achieve optimal performance.

A distributed algorithm for European options with nonlinear volatility

A distributed algorithm is developed to solve nonlinear Black-Scholes equations in the hedging of portfolios. The algorithm is based on an approximate inverse Laplace transform and is particularly suitable for problems that do not require detailed knowledge of each intermediate time steps.