Reducing the number of factors in a model by reducing the rank of a correlation matrix is a problem that often arises in finance, for instance in pricing interest rate derivatives with Libor market models. A simple iterative algorithm for correlation rank reduction is introduced, the eigenvalue...

Levy processes can be used to model asset return's distributions. Monte Carlo methods must frequently be used to value path dependent options in these models, but Monte Carlo methods can be prone to considerable simulation bias when valuing options with continuous reset conditions. This paper...

Lattice methods are often used to value derivative instruments. Multinomial lattice methods can in principle converge to the true value of the derivative to very high order. In this paper we describe how very high order multinomial lattices can be constructed and implemented when the SDE...

In this paper, we describe a numerical method to price barrier options on a zero-coupon bond. The method can be applied to one-factor short rate models where the transtion distribution function of the short rate is known and no explicit solutions for barrier bond options are available. We give...

Evidence from the financial markets suggests that empirical returns distributions, both historical and implied, do not arise from diffusion processes. A growing literature models the returns process as a Levy process, finding a number of explicit formulae for the values of some derivatives in...

We present an economically motivated two-factor term structure model that generalizes existing stochastic mean term structure models. By allowing a certain parameter to acquire dynamical behavior we extend the two-factor model to obtain a nonlinear three-factor model that is shown, in a...