Monte Carlo Method

MONTE CARLO M E T H O D 3763 14 86 A Monte Carlo method is a technique that involves using random numbers and probability to solve problems. 777 Buffon's Needle Experiment Consider a floor with equally spaced lines, a distance 8 apart. What is the probability that a needle of length 1 < 8 dropped on the floor will intersect one of the lines? Buffon answered the question himself in 1777. 12 MARIO LAZZARINI Needle Toss (1812) 3408 needle tosses later, he got the value of Pi. 3.14159265358979... 930 FERMIAC Enrico Fermi 1930s, Enrico Fermi perviously considered using Monte Carlo techniques in the calculation of neutron diffusion, however, he proposed to use a mechanical device, the so- called “Fermiac," for generating the randomness. COMPUTER Historically, the main drawback of Monte Carlo methods was that they used to be expensive to carry out. Physical random experiments were difficult to perform and so was the numerical processing of their results. This however changed fundamentally with the advent of the digital computer. To generate random numbers without computer, the following methods were used. 18 36 LOTTERY RAND Corp. Machines used in lottery or roulette The RAND corporation published a book with 1 million random numbers NICHOLAS JOHN VON STANISLAW METROPOLIS NEUMAN ULAM They were working for the Manhattan project in Lost Alamos. They proposed in 1947 to use a computer simulation for solving the problem of neutron diffusion in fissionable material. Stanislaw Ulam had the idea of using random experiments from a Canfield solitaire. Monte Carlo techniques are widely used in physics and chemistry to simulate complex reactions and interactions. Also in... %24 80 finance business engineering games FÍNCAD Founded in 1990, FINCAD provides advanced modelling solutions built on award-winning, patent pending technology. With more than 4,000 clients in over 80 countires around the world, FINCAD is the leading providor of financial analytics technology, enabling global market participants to make informed hedging and investment decisions. fincad provides software and services supporting the valuation, reporitng and risk management of derivatives and fixed income portfolios to banks, corporate treasuries, hedge funds, asset management firms, audit firms and gov- ernments. FINCAD analytics can be accessed through excel, matlab, as a software-as-a-service or embedded into an existing system through software development kits. Now, over 70 fincad alliance partners embed fincad analytics within their solutions. FINCAD provides sales and client services from Dublin, Ireland, and Vancouver, Canada. INFORMATION IS BASED ON: Eckhardt, Roger (1987). "Stan Ulam, John von Neumann, and the Monte Carlo method". Los Alamos Science, Special Issue (15): 131–137. FINCAD. Monte Carlo Simulation in Derivatives Valuation. http://www.fincad.com/derivatives-resources/articles/monte-carlo-simulation.aspx FINCAD Buy-Side Survey 2012. http://www.fincad.com/derivatives-resources/survey/buy-side-2012.aspx FINCAD Sell-Side Survey 2012. http://www.fincad.com/derivatives-resources/survey/sell-side-2012.aspx Fishman, G. S. (1995). Monte Carlo: Concepts, Algorithms, and Applications. New York: Springer. Metropolis, N. (1987). The Beginning of the Monte Carlo Method, Los Alamos Science (Special Issue), 125 - 130. http://library.lanl.gov/cgi-bin/getfile?00326866.pdf DISCLAIMER Your use of the information in this article is at your own risk. The information in this article is provided on an "as is" basis and without any representation, obligation, or warranty from FINCAD of any kind, whether express or implied. We hope that such information will assist you, but it should not be used or relied upon as a substitute for your own independent research.