what is monte carlo simulation?

Answer 1

Now that Chrisi has copied a long definition from an encylopedia, and Axl gives this same blog site no matter what the question, you are no closer to the Answer than when you began with a Question.

Monte Carlo Simulation is a problem solving technique used to approximate the probability of certain outcomes by running multiple trial runs, called simulations, using random variables.

Monte Carlo simulation is named after the city in Monaco, where the primary attractions are casinos that have games of chance. Gambling games, like roulette, dice, and slot machines, exhibit random behavior.

That said, it is used to make assumptions in theoretical risk models to compare actual market performance. It also provides a measure and model for volatility, which can be used as a proxy for risk.

It gives a better approximation of risk and volatility than say, standard deviation, or the almost goofy Random Walk Theory, because the distributions are not linear. But even the Monte Carlo fails in some cases, because the final price outcomes are lognormal (meaning the distribution would look more normal if the x-axis were converted to the natural log of x).

The Monte Carlo actually assumes a random walk: that returns from one period to the the next are totally independent, which is not proven, nor trivial.

If you believe returns follow trends, you are technically saying they show positive serial correlation. If you think they 'revert to the mean", then technically you are saying they show negative serial correlation. Neither stance is consistent with independence.

Answer 2

Monte Carlo methods are a widely used class of computational algorithms for simulating the behavior of various physical and mathematical systems. They are distinguished from other simulation methods (such as molecular dynamics) by being stochastic, that is nondeterministic in some manner - usually by using random numbers (or more often pseudo-random numbers) - as opposed to deterministic algorithms. Because of the repetition of algorithms and the large number of calculations involved, Monte Carlo is a method suited to calculation using a computer, utilizing many techniques of computer simulation.

A Monte Carlo algorithm is a numerical Monte Carlo method used to find solutions to mathematical problems (which may have many variables) that cannot easily be solved, for example, by integral calculus, or other numerical methods. Its efficiency relative to other numerical methods increases when the dimension of the problem increases.

Monte Carlo methods are especially useful in studying systems with a large number of coupled degrees of freedom, such as liquids, disordered materials, and strongly coupled solids. More broadly, Monte Carlo methods are useful for modeling phenomena with significant uncertainty in inputs, such as the calculation of risk in business. A classic use is for the evaluation of definite integrals, particularly multidimensional integrals with complicated boundary conditions.

Monte Carlo methods are very important in computational physics and related applied fields, and have diverse applications from esoteric quantum chromodynamics calculations to designing heat shields and aerodynamic forms.

Monte Carlo methods have also proven efficient in solving coupled integral differential equations of radiation fields and energy transport, and thus these methods have been used in global illumination computations which produce photorealistic images of virtual 3D models, with applications in video games, architecture, design, computer generated films, special effects in cinema, business, economics and other fields.

Application areas
Areas of application include:

Graphics, particularly for ray tracing; a version of the Metropolis-Hastings algorithm is also used for ray tracing where it is known as Metropolis light transport
Modelling light transport in multi-layered tissues (MCML)
Monte Carlo methods in finance
Reliability Engineering
In simulated annealing for protein structure prediction
In semiconductor device research, to model the transport of current carriers
Environmental science, dealing with contaminant behaviour
Monte Carlo molecular modeling as an alternative for computational molecular dynamics.
Search And Rescue and Counter-Pollution. Models used to predict the drift of a liferaft or movement of an oil slick at sea.
In computer science
Las Vegas algorithm
LURCH
Modelling the movement of impurity atoms (or ions) in plasmas in existing and tokamaks (e.g.: DIVIMP).
In experimental particle physics, for designing detectors, understanding their behaviour and comparing experimental data to theory
Nuclear and particle physics codes using the Monte Carlo method:
GEANT - CERN's Monte Carlo for high-energy particles physics
MCNP(X) - LANL's radiation transport codes
EGS - Stanford's simulation code for coupled transport of electrons and photons
PEREGRINE - LLNL's Monte Carlo tool for radiation therapy dose calculations
BEAMnrc - Monte Carlo code system for modelling radiotherapy sources (Linac's)
MONK - Serco Assurance's code for the calculation of k-effective of nuclear systems
Other methods employing Monte Carlo
Assorted random models, e.g. self-organised criticality
Direct simulation Monte Carlo
Dynamic Monte Carlo method
Kinetic Monte Carlo
Quantum Monte Carlo
Quasi-Monte Carlo method using low-discrepancy sequences and self avoiding walks
Semiconductor charge transport and the like
Electron microscopy beam-sample interactions
Stochastic Optimization

need more?

Answer 3

lengthy explanation as above.