Published by De Gruyter

Volume 13 Issue 2

Issue of Monte Carlo Methods and Applications

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Contents
Journal Overview

June 28, 2007

On a real-time scheme for the estimation of volatility

Shigeyoshi Ogawa, Koji Wakayama

Page range: 99-116

Abstract

We are interested in the numerical scheme for the estimation of the volatility of a given price process S t , which in the Black-Sholes paradigm is supposed to follow the Itô type stochastic differential equation.

June 28, 2007

Weak approximations of solutions of a first order hyperbolic stochastic partial differential equation

Christian Roth

Page range: 117-133

Abstract

The present article focuses on the use of difference methods in order to approximate the solutions of stochastic partial differential equations of Itô type, in particular hyperbolic equations. We develop the main notions of deterministic difference methods, i.e. convergence, consistency and stability for the stochastic case. We prove a stochastic version of Lax-Richtmyer theorem giving the existence of a weak convergent subsequence of the approximating scheme if the scheme is both consistent and stable.

June 28, 2007

Exact retrospective Monte Carlo computation of arithmetic average Asian options

Benjamin Jourdain, Mohamed Sbai

Page range: 135-171

Abstract

Taking advantage of the recent literature on exact simulation algorithms (Beskos, Papaspiliopoulos and Roberts [A. Beskos, O. Papaspiliopoulos, and Gareth O. Roberts, Retrospective exact simulation of diffusion sample paths. Bernoulli 12 (December 2006).]) and unbiased estimation of the expectation of certain functional integrals (Wagner [W. Wagner, Unbiased Monte Carlo evaluation of certain functional integrals. J. Comput. Phys . 71 (1987), 21–33.], Beskos et al. [A. Beskos, O. Papaspiliopoulos,Gareth O. Roberts, and P. Fearnhead, Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes. To appear in the Journal of the Royal Statistical Society, Series B .] and Fearnhead et al. [P. Fearnhead, O. Papaspiliopoulos, and G. O. Roberts, Particle Filters for Partially observed diffusions. Working paper: Lancaster University . (2006).]), we apply an exact simulation based technique for pricing continuous arithmetic average Asian options in the Black & Scholes framework. Unlike existing Monte Carlo methods, we are no longer prone to the discretization bias resulting from the approximation of continuous time processes through discrete sampling. Numerical results of simulation studies are presented and variance reduction problems are considered.

About this journal

Objective
Monte Carlo Methods and Applications is a quarterly published journal that presents original articles on the theory and applications of Monte Carlo and Quasi-Monte Carlo methods. Launched in 1995 the journal covers all stochastic numerics topics with emphasis on the theory of Monte Carlo methods and new applications in all branches of science and technology. Stochastic models in all fields of applied sciences, in particular turbulence, rarefied gas dynamics and nanotechnology, bioscience, medicine, chemical kinetics and combustion, stochastic models in mathematical finance

Topics

Theory of Monte Carlo methods
Quasi-Monte Carlo methods
Integration
Boundary value problems for PDE's
Numerics of stochastic differential equations
Simulation of random variables, stochastic processes and fields

Article formats
Research articles

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