Monte - Carlo Methods for Single - and Multi - Factor Models
نویسنده
چکیده
It is not surprising that Monte-Carlo methods may be related to the finite-difference schemes for solving PDE’s through the Feynmac-Kac characterization. However, while finite difference methods tend to be quicker than Monte-Carlo methods for low dimensional problems they suffer from the curse of dimensionality and quickly become impractical as the number of dimensions grow. Monte-Carlo simulation does not suffer from this drawback and is not limited to Markovian frameworks as PDE methods are. In the context of term structure models, Monte-Carlo simulation appears to be the computational tool of choice for HJM and LIBOR market models. It is also ubiquitous in the related fields of credit risk, mortgage-backed securities and risk-management generally.
منابع مشابه
Monte Carlo characterization of photoneutrons in the radiation therapy with high energy photons: a Comparison between simplified and full Monte Carlo models
Background: The characteristics of secondary neutrons in a high energy radiation therapy room were studied using the MCNPX Monte Carlo (MC) code. Materials and Methods: Two MC models including a model with full description of head components and a simplified model used in previous studies were implemented for MC simulations. Results: Results showed 4-53% difference between full and wit...
متن کاملMC/QMC Methods for Option Pricing under Stochastic Volatility Models
In the context of multi-factor stochastic volatility models, which contain the widely used Heston model, we present variance reduction techniques to price European options by Monte Carlo (MC) and QuasiMonte Carlo (QMC) methods. We formulate a stochastic integral as a martingale control for the payoffs to be evaluated. That control corresponds to the cost of an approximate delta hedging strategy...
متن کاملA Comparison of Single Factor Markov-functional and Multi Factor Market
We compare single factor Markov-functional and multi factor market models for hedging performance of Bermudan swaptions. We show that hedging performance of both models is comparable, thereby supporting the claim that Bermudan swaptions can be adequately risk-managed with single factor models. Moreover, we show that the impact of smile can be much larger than the impact of correlation. We use t...
متن کاملThe Impact of Nano-Sized Gold Particles on the Target Dose Enhancement Based on Photon Beams Using by Monte Carlo Method
Objective(s): In this study we evaluate the impact of the different aspects of Gold Nano-Particles (GNPs) on the target absorptive Dose Enhancement Factor (DEF) during external targeted radiotherapy with photon beams ranging from kilovolt to megavolt energies using Monte Carlo simulation. Methods: We have simulated the interaction of photon beams wi...
متن کاملDesign 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...
متن کامل