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Quasi-Monte Carlo Methods In Finance
High-dimensional integrals in hundreds or thousands of variables occur commonly in finance. These integrals have to be computed numerically to within a threshold \epsilon. If the integral is of dimension d then in the worst case, where one has a guarantee of error at most \epsilon, the computational complexity is typically of order \epsilon^. That is, the problem suffers the curse of dimensionality. In 1977 P. Boyle, University of Waterloo, proposed using Monte Carlo Method, Monte Carlo (MC) to evaluate options.Boyle, P. (1977), Options: a Monte Carlo approach, J. Financial Economics, 4, 323-338. Starting in early 1992, Joseph Traub, J. F. Traub, Columbia University, and a graduate student at the time, S. Paskov, used Quasi-Monte Carlo method, quasi-Monte Carlo (QMC) to price a Collateralized mortgage obligation with parameters specified by Goldman Sachs. Even though it was believed by the world's leading experts that QMC should not be used for high-dimensional integration, Paskov and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curse Of Dimensionality
The curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience. The expression was coined by Richard E. Bellman when considering problems in dynamic programming. The curse generally refers to issues that arise when the number of datapoints is small (in a suitably defined sense) relative to the intrinsic dimension of the data. Dimensionally cursed phenomena occur in domains such as numerical analysis, sampling, combinatorics, machine learning, data mining and databases. The common theme of these problems is that when the dimensionality increases, the volume of the space increases so fast that the available data become sparse. In order to obtain a reliable result, the amount of data needed often grows exponentially with the dimensionality. Also, organizing and searching data often relies on detecting a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Barry Arthur Cipra
Barry Arthur Cipra, an American mathematician and freelance writer, regularly contributes to ''Science'' magazine and ''SIAM New''s, a monthly publication of the Society for Industrial and Applied Mathematics. Along with Dana Mackenzie and Paul Zorn he is the author of several of the volumes in the American Mathematical Society series ''What's Happening in the Mathematical Sciences'', a collection of articles about recent results in pure and applied mathematics oriented towards the undergraduate mathematics major. Biography Cipra got his Ph.D. from University of Maryland College Park in 1980. He was an instructor at The Massachusetts Institute of Technology and at Ohio State University. He was an assistant professor of mathematics at St. Olaf College in Northfield, Minnesota. Cipra received the 1991 Merten M. Hasse Prize from the Mathematical Association of America for his work on the Ising model. In 2005 he received the JPBM Communications Award. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer-Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second-largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Historical Simulation (finance)
Historical simulation in finance's value at risk (VaR) analysis is a procedure for predicting the value at risk by 'simulating' or constructing the cumulative distribution function (CDF) of assets returns over time assuming that future returns will be directly sampled from past returns. Unlike parametric VaR models, historical simulation does not assume a particular distribution of the asset returns. Also, it is relatively easy to implement. However, there are a couple of shortcomings of historical simulation. Traditional historical simulation applies equal weight to all returns of the whole period; this is inconsistent with the diminishing predictability of data that are further away from the present. Weighted historical simulation Weighted historical simulation applies decreasing weights to returns that are further away from the present, which overcomes the inconsistency of historical simulation with diminishing predictability of data that are further away from the present. H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monte Carlo Methods In Finance
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. This is usually done by help of stochastic asset models. The advantage of Monte Carlo methods over other techniques increases as the dimensions (sources of uncertainty) of the problem increase. Monte Carlo methods were first introduced to finance in 1964 by David B. Hertz through his ''Harvard Business Review'' article, discussing their application in Corporate Finance. In 1977, Phelim Boyle pioneered the use of simulation in derivative valuation in his seminal ''Journal of Financial Economics'' paper. This article discusses typical financial problems in which Monte Carlo methods are used. It also touches on the use of so-called "quasi-random" methods such as the use of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joseph F
Joseph is a common male name, derived from the Hebrew (). "Joseph" is used, along with " Josef", mostly in English, French and partially German languages. This spelling is also found as a variant in the languages of the modern-day Nordic countries. In Portuguese and Spanish, the name is "José". In Arabic, including in the Quran, the name is spelled , . In Kurdish (''Kurdî''), the name is , Persian, the name is , and in Turkish it is . In Pashto the name is spelled ''Esaf'' (ايسپ) and in Malayalam it is spelled ''Ousep'' (ഔസേപ്പ്). In Tamil, it is spelled as ''Yosepu'' (யோசேப்பு). The name has enjoyed significant popularity in its many forms in numerous countries, and ''Joseph'' was one of the two names, along with ''Robert'', to have remained in the top 10 boys' names list in the US from 1925 to 1972. It is especially common in contemporary Israel, as either "Yossi" or "Yossef", and in Italy, where the name "Giuseppe" was the most comm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phelim Boyle
Phelim P. Boyle (born 1941), is an Irish economist and distinguished professor and actuary, and a pioneer of quantitative finance. He is best known for initiating the use of Monte Carlo methods in option pricing. Biography Born on a farm in Lavey, County Londonderry, Northern Ireland, Phelim Boyle attended Dreenan School, Garron Tower and Queen's University Belfast (B.Sc.) He earned his M.Sc. in 1966 and PhD in 1970 applied mathematics, specialising in physics, from Trinity College, Dublin. He is a professor of finance in the Laurier School of Business & Economics at Wilfrid Laurier University in Canada. Until June 2006 he held the J Page R Wadsworth Chair at the University of Waterloo. He is the founder of the Master of Quantitative Finance (MQF) program there. Additional to his contributions to quantitative finance, he has published papers on actuarial science and demography. Together with his son, Feidhlim Boyle, he authored ''Derivatives: the Tools that Changed Fina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Russel E
Russel is an alternate spelling of Russell. Russel may also refer to: People with the given name * Russel Arnold (born 1973), Sri Lankan cricketer * Russel Crouse (1893–1966), American playwright * Russel Farnham (1784–1832), American frontiersman * Russel Honoré (born 1947), American general * Russel Mthembu (born 1947), South African singer * Russel Mwafulirwa (born 1983), Malawian soccer player * Russel Norman (born 1967), New Zealand politician * Russel B. Nye (1913–1993), American professor * Russel Walder (born 1959), American jazz musician * Russel Ward (1914–1995), Australian historian * Russel Wong (born 1961), Singaporean photographer * Russel Wright (1904–1976), American industrial designer People with the surname * Andrew Russel (1856–1934), American politician * Rae Russel (1925–2008), American photographer * Tony Russel (1925–2017), American actor People with the middle name *Alfred Russel Wallace (1823–1913), British naturalist Ficti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Journal Of Portfolio Management
''The Journal of Portfolio Management'' is a quarterly academic journal for finance and investing, covering topics such as asset allocation, performance measurement, market trends, risk management, and portfolio optimization. The journal was established in 1974 by Peter L. Bernstein. The editor-in-chief is Frank J. Fabozzi (Yale University). Awards The journal presents several awards to authors publishing in the journal. Bernstein Fabozzi/Jacobs Levy Award The Bernstein Fabozzi/Jacobs Levy Awards is given annually to authors of the most innovative and significant research published in the journal, as chosen by its readership. Initiated in 1999, the awards commemorate the contributions of editors Peter L. Bernstein and Frank J. Fabozzi to the field of finance, while also encouraging outstanding research in portfolio management theory and practice. Previous winners include Nobel Prize laureates ( Robert F. Engle, Merton Miller, and Robert J. Shiller), as well as Cliff Asness, John ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sobol Sequence
Sobol’ sequences (also called LPτ sequences or (''t'', ''s'') sequences in base 2) are a type of quasi-random low-discrepancy sequence. They were first introduced by the Russian mathematician Ilya M. Sobol’ (Илья Меерович Соболь) in 1967.Sobol’, I.M. (1967), "Distribution of points in a cube and approximate evaluation of integrals". ''Zh. Vych. Mat. Mat. Fiz.'' 7: 784–802 (in Russian); ''U.S.S.R Comput. Maths. Math. Phys.'' 7: 86–112 (in English). These sequences use a base of two to form successively finer uniform partitions of the unit interval and then reorder the coordinates in each dimension. Good distributions in the ''s''-dimensional unit hypercube Let be the -dimensional unit hypercube, and a real integrable function over . The original motivation of Sobol’ was to construct a sequence in so that \lim_ \frac \sum_^n f(x_i) = \int_ f and the convergence be as fast as possible. It is more or less clear that for the sum to c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monte Carlo Method
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. The name comes from the Monte Carlo Casino in Monaco, where the primary developer of the method, mathematician Stanisław Ulam, was inspired by his uncle's gambling habits. Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration, and generating draws from a probability distribution. They can also be used to model phenomena with significant uncertainty in inputs, such as calculating the risk of a nuclear power plant failure. Monte Carlo methods are often implemented using computer simulations, and they can provide approximate solutions to problems that are otherwise intractable or too complex to analyze mathematically. Monte Carlo methods are widely used in va ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
