We investigate the pricing performance of eight trinomial trees and one binomial tree, which was found to be most effective in an earlier paper, under twenty different implementation methodologies for pricing American put options. We conclude that the binomial tree, the Tian third order moment...

We study 20 different implementation methodologies for each of 11 different choices of parameters of binomial trees and investigate the speed of convergence for pricing American put options numerically. We conclude that the most effective methods involve using truncation, Richardson...

The pricing of snowball notes in the full-factor LIBOR market model is considered. The primary aspect of the problem considered is the early exercise feature, and it is shown how to characterize a class of sub-optimal points of exercise. By combining this characterization with least-squares...

A new binomial approximation to the Black-Scholes model is introduced. It is shown that for digital options and vanilla European call and put options that a complete asymptotic expansion of the error in powers of 1/n exists. This is the first binomial tree for which such an asymptotic expansion...

We consider a generic framework which allows to calculate robust Monte-Carlo sensitivities seamlessly through simple finite difference approximation. The method proposed is a generalization and improvement of the proxy simulation scheme method (Fries and Kampen, 2005). As a benchmark we apply...

The problem of pricing a continuous barrier option in a jump-diffusion model is studied. It is shown that via an effective combination of importance sampling and analytic formulas thatsubstantial speed ups can be achieved. These techniques are shown to be particularly effective for computing deltas

An algorithm for computing the drift in the LIBOR market model with additional idiosyncratic terms is introduced. This algorithm achieves a computational complexity of order equal to the number of common factors times the number of rates. It is demonstrated that this allows better matching of...

It is well-known that the Dirichlet problem for the Laplacian on a reasonably smooth compact domain in Rn can be solved using Brownian motion. Indeed the result was found by Kakutani in 1944. In this note, I want to discuss how this result can be reinterpreted financially. Our objective is to...

The pricing of callable derivative products with complicated pay-offs is studied. A new method for finding upper bounds by Monte Carlo simulation is introduced, this relies on modelling the callable product directly. The method has a wide range of applicability and is shown to be effective for...

A number of standard market models are studied. For each one, algorithms of computational complexity equal to the number of rates times the number of factors to carry out the computations for each step is introduced. Two new classes of market models are developed and it is shown for them that...