In financial modelling, filtering and other areas the underlying dynamics are often specified via stochastic differential equations (SDEs) of jump-diffusion type. The class of jump-diffusion SDEs that admits explicit solutions is rather limited. Consequently, there is a need for the systematic...

Alternative approaches to hedging swaptions are explored and tested by simulation. Hedging methods implied by the Balck swaption formula are compared with a lognormal forward LIBOR model approach encompassing all the relevant forward rates. The simulation is undertaken within the LIBOR model...

This paper constructs strong discrete time approximations for pure jump processes that can be described by stochastic differential equations. Strong approximations based on jump-adapted time discretizations, which produce no discretization bias, are analyzed. The computational complexity of...

In finance and economics the key dynamics are often specified via stochastic differential equations (SDEs) of jump-diffusion type. The class of jump-diffusion SDEs that admits explicit solutions is rather limited. Consequently, discrete time approximations are required. In this paper we give a...

The paper considers the derivation of weak discrete time approximations for solutions of stochastic differential equations with time delay. These are suitable for Monte Carlo simulation and allow the computation of expectations for functionals of stochastic delay equations. The suggested...

An important assumption underlying traditional theories of financial time-series behaviour is that consecutive changes in the price of an asset (ie. asset returns) are independent of each other. For analysts seeking to predict the future value of an asset, this implies that the best step-ahead...

The paper introduces an approach for the derivation of discrete time approximations for solutions of stochastic differential equations with time delay. The suggested approximations converge in a strong sense. Furthermore, explicit solutions for linear stochastic delay equations are given.