Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff

Application of Monte Carlo Simulation in the Assessment of European Call Options

In this paper, the pricing of a European call option on the underlying asset is performed by using a Monte Carlo method, one of the powerful simulation methods, where the price development of the asset is simulated and value of the claim is computed in terms of an expected value. The proposed approach, applied in Monte Carlo simulation, is based on the Black-Scholes equation which generally def...

Comparison dose distributions from gamma knife unit 4C with CT data and non-CT data options of beamnrc code

Todays gamma knife radiosurgery is used widely for treatment of very small brain tumors. In order to investigate accuracy of dosimetry and treatment planning calculations, using Monte Carlo simulation with dedicated code named as beamnrc including non-CT data and CT data options is necessary. The aim of this study is choosing the best options in order to have an accurate tools based on their ad...

An effective optimization algorithm for locally nonconvex Lipschitz functions based on mollifier subgradients

Design of Light Multi-layered Shields for Use in Diagnostic Radiology and Nuclear Medicine via MCNP5 Monte Carlo Code

Introduction Lead-based shields are the most widely used attenuators in X-ray and gamma ray fields. The heavy weight, toxicity and corrosion of lead have led researchers towards the development of non-lead shields. Materials and Methods The purpose of this study was to design multi-layered shields for protection against X-rays and gamma rays in diagnostic radiology and nuclear medicine. In this...

Variance Reduction Techniques of Importance Sampling Monte Carlo Methods for Pricing Options

In this paper we discuss the importance sampling Monte Carlo methods for pricing options. The classical importance sampling method is used to eliminate the variance caused by the linear part of the logarithmic function of payoff. The variance caused by the quadratic part is reduced by stratified sampling. We eliminate both kinds of variances just by importance sampling. The corresponding space ...