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The purpose was to explain the remarkable success of quasi-Monte Carlo (QMC) in approximating the very-high-dimensional integrals in finance. They argued that the integrands are of low effective dimension and that is why QMC is much faster than Monte Carlo (MC). The impact of the arguments of Caflisch et al. [21] was great. A number of papers ...
The Quasi-Monte Carlo method recently became popular in the area of mathematical finance or computational finance. [1] In these areas, high-dimensional numerical integrals, where the integral should be evaluated within a threshold ε, occur frequently. Hence, the Monte Carlo method and the quasi-Monte Carlo method are beneficial in these ...
Monte Carlo methods are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: [2] optimization, numerical integration, and generating draws from a probability distribution.
Monte Carlo methods are used in corporate finance and mathematical finance to value and analyze (complex) instruments, portfolios and investments by simulating the various sources of uncertainty affecting their value, and then determining the distribution of their value over the range of resultant outcomes.
A Monte Carlo simulation shows a large number and variety of possible outcomes, including the least likely as well … Continue reading → The post Understanding How the Monte Carlo Method Works ...
Conversely, however, if an analytical technique for valuing the option exists—or even a numeric technique, such as a (modified) pricing tree [10] —Monte Carlo methods will usually be too slow to be competitive. They are, in a sense, a method of last resort; [10] see further under Monte Carlo methods in finance. With faster computing ...
In 1958, Sobol’ started to work on pseudo-random numbers, then to move on developing new approaches which were later called quasi-Monte Carlo methods (QMC). [1] He was the first to use the Haar functions in mathematical applications. Sobol’ defended his D.Sc. dissertation "The Method of Haar Series in the Theory of Quadrature Formulas" in 1972.
Lattice model (finance) Margrabe's formula; Monte Carlo methods for option pricing. Monte Carlo methods in finance; Quasi-Monte Carlo methods in finance; Least Square Monte Carlo for American options; Trinomial tree; Volatility. Implied volatility; Historical volatility; Volatility smile (& Volatility surface) Stochastic volatility. Constant ...