At one time, the Jainas in India and Greeks abroad held that unity was not a number. This paper provides an insight for first time into thoughts offered by as to why number them.

In this work, we propose to price Parisian options using Laplace transforms. Not only, do we compute the Laplace transforms of all the different Parisian options, but we also explain how to invert them numerically. We discuss the accuracy of the numerical inversion and present the evolution of the Greeks through a few graphs.

In this paper we introduce efficient Monte Carlo estimators for the valuation of high-dimensional derivatives and their sensitivities (”Greeks”). These estimators are based on an analytical, usually approximative representation of the underlying density. We study approximative densities obtained by the WKB method. The results are applied in the context of a Libor market model.