46 research outputs found
Conditional sampling for barrier option pricing under the LT method
We develop a conditional sampling scheme for pricing knock-out barrier
options under the Linear Transformations (LT) algorithm from Imai and Tan
(2006). We compare our new method to an existing conditional Monte Carlo scheme
from Glasserman and Staum (2001), and show that a substantial variance
reduction is achieved. We extend the method to allow pricing knock-in barrier
options and introduce a root-finding method to obtain a further variance
reduction. The effectiveness of the new method is supported by numerical
results
ANIMAL BIODIVERSITY CONSERVATION, A KEY OF SUSTAINABLE AGRICULTURE. CASE STUDY: THE ROMANIAN PINZGAU BREED IN TRANSILVANIA REGION
Abstract Pinzgau breed or Pinzgauer is called after its region of origin . These things are the main reasons why race should be kept in a form of active conservation. Moreover, in order to preserve the tradition and traditional products in Romania, is required to maintain this breed and even the formation of its national park
A finite difference method for pricing European and American options under a geometric Lévy process
In this paper we develop a numerical approach to a fractional-order differential Linear Complementarity Problem (LCP) arising in pricing European and American options under a geometric Lévy process. The LCP is first approximated by a nonlinear penalty fractional Black-Scholes (fBS) equation. We then propose a finite difference scheme for the penalty fBS equation. We show that both the continuous and the discretized fBS equations are uniquely solvable and establish the convergence of the numerical solution to the viscosity solution of the penalty fBS equation by proving the consistency, stability and monotonicity of the numerical scheme. We also show that the discretization has the 2nd-order truncation error in both the spatial and time mesh sizes. Numerical results are presented to demonstrate the accuracy and usefulness of the numerical method for pricing both European and American options under the geometric Lévy process