Abstract: Current Monte Carlo pricing engines may face computational challenge for the Greeks, because of not only their time consumption but also their poor convergence when using a finite difference estimate with a brute force perturbation. The same story may apply to conditional expectation. In this short paper, following Fourni Discuss this paper
Description:
EMMANUEL GOBET ARTURO KOHATSU-HIGA1 Abstract In this article, we consider the numerical computations associated to the Greeks of barrier and lookback options, using Malliavin calculus. For this, we derive some integration by parts formulae involving the maximum and minimum of a one dimensional di Discuss this paper
Abstract We use the Malliavin integration by parts formula in order to provide a family of representations of the joint density (which does not involve Dirac measures) of (X,X+), where X is a d-dimensional Markov diffusion (d 1), > 0 and > 0. Following [5], the different representations are determined by a pair of localizing functions. We discuss the problem of variance reduction within the family of separable localizing functions: We characterize a pair of exponential functions as the unique integrated-variance minimizer among this class of separable localizing functions. We test our method on the d-dimensional Brownian motion and provide an application to the problem of American options valuation by the quantization tree method introduced
Description:
107 pages of notes by Han Zhang School of Mathematics, The University of New South Wales. December 2004 Submitted in partial fulfillment of the requirements of the degree of Bachelor of Science with Honours
Contents Chapter 1 Tools From Analysis 1 1.1 Functions of Bounded Variation . . . . . . . . . . . . . . . . . . . . 1 1.2 Random Variables and Stochastic Processes . . . . . . . . . . . . . 5 Chapter 2 It Discuss this paper
Description:
Miquel Montero and Arturo Kohatsu-Higa
Abstract In this article, we give a brief informal introduction to Malliavin Calculus for newcomers. We apply these ideas to the simulation of Greeks in Finance. First to European-type options where formulas can be computed explicitly and therefore can serve as testing ground. Later we study the case of Asian options where close formulas are not available, and we also open the view for including more exotic derivatives. The Greeks are computed through Monte Carlo simulation.
Description:
New York University Peter K. Friz These lecture-notes are based on a couple of seminar-talks I gave at Courant in Spring 2001. I am extremely grateful to Prof. S.R.S. Varadhan for supporting and stimulating my interest in Malliavin Calculus. I am also indepted to Nicolas Victoir, Enrique Loubet for their careful reading of this text. Peter F.
)
Date (
Visit Link 
(0 Votes) 
(1 Vote) 