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Essentially, the Monte Carlo method solves a problem by directly simulating the underlying (physical) process and then calculating the (average) result of the process. [ 1 ] This very general approach is valid in areas such as physics, chemistry, computer science etc. In finance, the Monte Carlo method is used to simulate the various sources of ...
Monte Carlo simulation: Drawing a large number of pseudo-random uniform variables from the interval [0,1] at one time, or once at many different times, and assigning values less than or equal to 0.50 as heads and greater than 0.50 as tails, is a Monte Carlo simulation of the behavior of repeatedly tossing a coin.
More generally though, simulation is employed for path dependent exotic derivatives, such as Asian options. In other cases, the source of uncertainty may be at a remove. For example, for bond options [3] the underlying is a bond, but the source of uncertainty is the annualized interest rate (i.e. the short rate).
Modeling and simulation (M&S) is the use of models (e.g., physical, mathematical, behavioral, or logical representation of a system, entity, phenomenon, or process) as a basis for simulations to develop data utilized for managerial or technical decision making. [ 1 ][ 2 ] In the computer application of modeling and simulation a computer is used ...
v. t. e. Data and information visualization (data viz/vis or info viz/vis) [ 2 ] is the practice of designing and creating easy-to-communicate and easy-to-understand graphic or visual representations of a large amount [ 3 ] of complex quantitative and qualitative data and information with the help of static, dynamic or interactive visual items.
Given an r-sample statistic, one can create an n-sample statistic by something similar to bootstrapping (taking the average of the statistic over all subsamples of size r). This procedure is known to have certain good properties and the result is a U-statistic. The sample mean and sample variance are of this form, for r = 1 and r = 2.
Statistics is a mathematical body of science that pertains to the collection, analysis, interpretation or explanation, and presentation of data,[5]or as a branch of mathematics.[6] Some consider statistics to be a distinct mathematical sciencerather than a branch of mathematics. While many scientific investigations make use of data, statistics ...
Financial modeling is the task of building an abstract representation (a model) of a real world financial situation. [1] This is a mathematical model designed to represent (a simplified version of) the performance of a financial asset or portfolio of a business, project, or any other investment. Typically, then, financial modeling is understood ...
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