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The Monte Carlo method solves a problem by simulating directly the physical process, and is not necessary to write down the differential equations that describe the behavior of the system. This is very general and is valid not only for our real options problem as in other areas of knowledge like physics, chemistry, etc.
The name “Monte Carlo” appeared in the World War II times, and sometimes is attributed to the researcher Nicholas Metropolis, inspired in the interest of Stanislaw Ulam, his colleague of Manhattan Project at Los Alamos, in the poker game. Monte Carlo, the capital of Monaco, was a known reference for gambling.
According Eckhardt, Ulam invented the Monte Carlo method in 1946 while pondering the probabilities of winning a card game of solitaire. However, Metropolis “attributes the germ of this statistical method to Enrico Fermi, who had used such ideas some 15 years earlier”.
According Liu (2001, p.vii-viii): “The basic idea underlying the method was first brought up by Ulam and deliberated between him and von Neumann in a car when they drove together from Los Alamos to Lamy. Allegedly, Nick Metropolis coined the name ‘Monte Carlo’, which played an essential role in popularizing the method”. Liu comments that the Los Alamos scientists aiming to take advante of the first “super” computer MANIAC, invented a statistical sampling-based technique to solve problems related to stochastic neutron diffusion in atomic bomb project and for estimating eigenvalues of the Schrödinger equation.
Winston (1996, p.22) wrote that the term was coined by mathematicians S. Ulam and J. von Neumann in the feasibility project of atomic bomb by simulations of nuclear fission, and they given the code name Monte Carlo for these simulations.
The first Monte Carlo paper, “The Monte Carlo Method” by Metropolis & Ulam, was published in 1949 in the Journal of the American Statistical Association. Since then, several different areas has been using the Monte Carlo simulations. With the advent of personal computers and the popularization of faster computational machines, the Monte Carlo simulations has been increasing popular as an important alternative for the solution of complex problems.
Monte Carlo simulation is one of the recognized numerical tools for pricing derivative securities, particularly flexible and useful for complex models of real markets. In this model, the maker of this template constructed a Monte Carlo simulation to price an option contract where it can be used to value a stock or a currency option.
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Monte Carlo Option Pricing Simulation in Microsoft Excel
Author : Metin Kilic
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