arXiv subjects

Arturo Kohatsu-Higa

Publications and source records attributed to Arturo Kohatsu-Higa.

21 records · Page 2Linked to original sources

arXiv2006

A duality approach for the weak approximation of stochastic differential equations

In this article we develop a new methodology to prove weak approximation results for general stochastic differential equations. Instead of using a partial differential equation approach as is usually done for diffusions, the approach considered here uses the properties of the linear equation satisfied by the error process. This methodology seems to apply to a large class of processes and we present as an example the weak approximation of stochastic delay equations.

math.PR↗

arXiv2004

Hints for an extension of the early exercise premium formula for American options

Characterization of the American put option price is still an open issue. From the beginning of the nineties there exists a non-closed formula for this price but nontrivial numerical computations are required to solve it. Strong efforts have been done to propose methods more and more computationally efficient but most of them have few mathematical ground as to ascertain why these methods work well and how important is to consider a good approximation to the boundary or to the smooth pasting condition. We perform an extension of the American put price aiming to catch weaknesses of the numerical methods given in the literature.

cond-mat.other↗

arXiv2001

An application of Malliavin Calculus to Finance

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. The Greeks are computed through Monte Carlo simulation.

cond-mat.stat-mech↗