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Author : 謝佳良
Publisher :
ISBN 13 :
Total Pages : 72 pages
Book Rating : 4.:/5 (457 download)
Download or read book Monte Carlo Approaches to Multi-asset Options written by 謝佳良 and published by . This book was released on 1999 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Piergiacomo Sabino
Publisher :
ISBN 13 :
Total Pages : 34 pages
Book Rating : 4.:/5 (129 download)
Download or read book Monte Carlo Methods and Path-Generation Techniques for Pricing Multi-Asset Path-Dependent Options written by Piergiacomo Sabino and published by . This book was released on 2007 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the problem of pricing path-dependent options on a basket of underlying assets using simulations. As an example we develop our studies using Asian options.Asian options are derivative contracts in which the underlying variable is the average price of given assets sampled over a period of time. Due to this structure, Asian options display a lower volatility and are therefore cheaper than their standard European counterparts.This paper is a survey of some recent enhancements to improve efficiency when pricing Asian options by Monte Carlo simulation in the Black-Scholes model. We analyze the dynamics with constant and time-dependent volatilities of the underlying asset returns.We present a comparison between the precision of the standard Monte Carlo method (MC) and the stratified Latin Hypercube Sampling (LHS). In particular, we discuss the use of low-discrepancy sequences, also known as Quasi-Monte Carlo method (QMC), and a randomized version of these sequences, known as Randomized Quasi Monte Carlo (RQMC). The latter has proven to be a useful variance reduction technique for both problems of up to 20 dimensions and for very high dimensions.Moreover, we present and test a new path generation approach based on a Kronecker product approximation (KPA) in the case of time-dependent volatilities. KPA proves to be a fast generation technique and reduces the computational cost of the simulation procedure.
Author : Mario Rometsch
Publisher : diplom.de
ISBN 13 : 3836615622
Total Pages : 143 pages
Book Rating : 4.8/5 (366 download)
Download or read book Quasi-Monte Carlo Methods in Finance with Application to Optimal Asset Allocation written by Mario Rometsch and published by diplom.de. This book was released on 2014-04-11 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inhaltsangabe:Introduction: Portfolio optimization is a widely studied problem in finance. The common question is, how a small investor should invest his wealth in the market to attain certain goals, like a desired payoff or some insurance against unwished events. The starting point for the mathematical treatment of this is the work of Harry Markowitz in the 1950s. His idea was to set up a relation between the mean return of a portfolio and its variance. In his terminology, an efficient portfolio has minimal variance of return among others with the same mean rate of return. Furthermore, if linear combinations of efficient portfolios and a riskless asset are allowed, this leads to the market portfolio, so that a linear combination of the risk-free asset and the market portfolio dominates any other portfolio in the mean-variance sense. Later, this theory was extended resulting in the CAPM, or capital asset pricing model, which was independently introduced by Treynor, Sharpe, Lintner and Mossin in the 1960s. In this model, every risky asset has a mean rate of return that exceeds the risk-free rate by a specific risk premium, which depends on a certain attribute of the asset, namely its _. The so-called _ in turn is the covariance of the asset return normalized by the variance of the market portfolio. The problem of the CAPM is its static nature, investments are made once and then the state of the model changes. Due to this and other simplifications, this model was and is often not found to be realistic. An impact to this research field were the two papers of Robert Merton in 1969 and 1971. He applied the theory of Ito calculus and stochastic optimal control and solved the corresponding Hamilton-Jacobi-Bellman equation. For his multiperiod model, he assumed constant coefficients and an investor with power utility. Extending the mean-variance analysis, he found that a long-term investor would prefer a portfolio that includes hedging components to protect against fluctuations in the market. Again this approach was generalized by numerous researchers and results in the problem of solving a nonlinear partial differential equation. The next milestone in this series is the work by Cox and Huang from 1989, where they solve for Optimal Consumption and Portfolio Policies when Asset Prices Follow a Diffusion Process . They apply the martingale technique to get rid of the nonlinear PDE and rather solve a linear PDE. This, with several refinements, is [...]
Author : Adam Ockman
Publisher :
ISBN 13 :
Total Pages : 33 pages
Book Rating : 4.:/5 (244 download)
Download or read book An Analysis of Multi-asset Options written by Adam Ockman and published by . This book was released on 2002 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ronald Cools
Publisher : Springer
ISBN 13 : 3319335073
Total Pages : 624 pages
Book Rating : 4.3/5 (193 download)
Download or read book Monte Carlo and Quasi-Monte Carlo Methods written by Ronald Cools and published by Springer. This book was released on 2016-06-13 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the refereed proceedings of the Eleventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of Leuven (Belgium) in April 2014. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. Offering information on the latest developments in these very active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, arising, in particular, in finance, statistics and computer graphics.
Author : Ralf Korn
Publisher : CRC Press
ISBN 13 : 1420076191
Total Pages : 485 pages
Book Rating : 4.4/5 (2 download)
Download or read book Monte Carlo Methods and Models in Finance and Insurance written by Ralf Korn and published by CRC Press. This book was released on 2010-02-26 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offering a unique balance between applications and calculations, Monte Carlo Methods and Models in Finance and Insurance incorporates the application background of finance and insurance with the theory and applications of Monte Carlo methods. It presents recent methods and algorithms, including the multilevel Monte Carlo method, the statistical Rom
Author : Chi Yan Wong
Publisher :
ISBN 13 :
Total Pages : 50 pages
Book Rating : 4.:/5 (762 download)
Download or read book Memory Reduction Methods for Option Pricing written by Chi Yan Wong and published by . This book was released on 2008 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: When pricing American-style options on d assets by Monte Carlo methods, one usually stores the simulated asset prices at all time steps on all paths in order to determine when to exercise the options. If N time steps and M paths are used; then the storage requirement is d · M · N. In this thesis, we give two simulation methods to price multi-asset American-style options, where the storage requirement only grows like (d + 1)M + N. The only additional computational cost is that we have to generate each random number twice instead of once. For machines with limited memory, we can now use larger values of M and N to improve the accuracy in pricing the options.
Author : Ali Hirsa
Publisher : Academic Press
ISBN 13 : 0123846838
Total Pages : 456 pages
Book Rating : 4.1/5 (238 download)
Download or read book An Introduction to the Mathematics of Financial Derivatives written by Ali Hirsa and published by Academic Press. This book was released on 2013-12-18 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to the Mathematics of Financial Derivatives is a popular, intuitive text that eases the transition between basic summaries of financial engineering to more advanced treatments using stochastic calculus. Requiring only a basic knowledge of calculus and probability, it takes readers on a tour of advanced financial engineering. This classic title has been revised by Ali Hirsa, who accentuates its well-known strengths while introducing new subjects, updating others, and bringing new continuity to the whole. Popular with readers because it emphasizes intuition and common sense, An Introduction to the Mathematics of Financial Derivatives remains the only "introductory" text that can appeal to people outside the mathematics and physics communities as it explains the hows and whys of practical finance problems. Facilitates readers' understanding of underlying mathematical and theoretical models by presenting a mixture of theory and applications with hands-on learning Presented intuitively, breaking up complex mathematics concepts into easily understood notions Encourages use of discrete chapters as complementary readings on different topics, offering flexibility in learning and teaching
Author : Pethuru Raj
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311134259X
Total Pages : 412 pages
Book Rating : 4.1/5 (113 download)
Download or read book Quantum Machine Learning written by Pethuru Raj and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-08-05 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum computing has shown a potential to tackle specific types of problems, especially those involving a daunting number of variables, at an exponentially faster rate compared to classical computers. This volume focuses on quantum variants of machine learning algorithms, such as quantum neural networks, quantum reinforcement learning, quantum principal component analysis, quantum support vectors, quantum Boltzmann machines, and many more.
Author : Jin-Chuan Duan
Publisher : Springer Science & Business Media
ISBN 13 : 3642172547
Total Pages : 791 pages
Book Rating : 4.6/5 (421 download)
Download or read book Handbook of Computational Finance written by Jin-Chuan Duan and published by Springer Science & Business Media. This book was released on 2011-10-25 with total page 791 pages. Available in PDF, EPUB and Kindle. Book excerpt: Any financial asset that is openly traded has a market price. Except for extreme market conditions, market price may be more or less than a “fair” value. Fair value is likely to be some complicated function of the current intrinsic value of tangible or intangible assets underlying the claim and our assessment of the characteristics of the underlying assets with respect to the expected rate of growth, future dividends, volatility, and other relevant market factors. Some of these factors that affect the price can be measured at the time of a transaction with reasonably high accuracy. Most factors, however, relate to expectations about the future and to subjective issues, such as current management, corporate policies and market environment, that could affect the future financial performance of the underlying assets. Models are thus needed to describe the stochastic factors and environment, and their implementations inevitably require computational finance tools.
Author : Paul Glasserman
Publisher : Springer Science & Business Media
ISBN 13 : 0387216170
Total Pages : 603 pages
Book Rating : 4.3/5 (872 download)
Download or read book Monte Carlo Methods in Financial Engineering written by Paul Glasserman and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "Paul Glasserman has written an astonishingly good book that bridges financial engineering and the Monte Carlo method. The book will appeal to graduate students, researchers, and most of all, practicing financial engineers [...] So often, financial engineering texts are very theoretical. This book is not." --Glyn Holton, Contingency Analysis
Author : Harald Niederreiter
Publisher : Springer Science & Business Media
ISBN 13 : 1461216907
Total Pages : 463 pages
Book Rating : 4.4/5 (612 download)
Download or read book Monte Carlo and Quasi-Monte Carlo Methods 1996 written by Harald Niederreiter and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods are numerical methods based on random sampling and quasi-Monte Carlo methods are their deterministic versions. This volume contains the refereed proceedings of the Second International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing which was held at the University of Salzburg (Austria) from July 9--12, 1996. The conference was a forum for recent progress in the theory and the applications of these methods. The topics covered in this volume range from theoretical issues in Monte Carlo and simulation methods, low-discrepancy point sets and sequences, lattice rules, and pseudorandom number generation to applications such as numerical integration, numerical linear algebra, integral equations, binary search, global optimization, computational physics, mathematical finance, and computer graphics. These proceedings will be of interest to graduate students and researchers in Monte Carlo and quasi-Monte Carlo methods, to numerical analysts, and to practitioners of simulation methods.
Author : Don L. McLeish
Publisher : John Wiley & Sons
ISBN 13 : 1118160940
Total Pages : 308 pages
Book Rating : 4.1/5 (181 download)
Download or read book Monte Carlo Simulation and Finance written by Don L. McLeish and published by John Wiley & Sons. This book was released on 2011-09-13 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods have been used for decades in physics, engineering, statistics, and other fields. Monte Carlo Simulation and Finance explains the nuts and bolts of this essential technique used to value derivatives and other securities. Author and educator Don McLeish examines this fundamental process, and discusses important issues, including specialized problems in finance that Monte Carlo and Quasi-Monte Carlo methods can help solve and the different ways Monte Carlo methods can be improved upon. This state-of-the-art book on Monte Carlo simulation methods is ideal for finance professionals and students. Order your copy today.
Author : Julien Guyon
Publisher : CRC Press
ISBN 13 : 1466570334
Total Pages : 486 pages
Book Rating : 4.4/5 (665 download)
Download or read book Nonlinear Option Pricing written by Julien Guyon and published by CRC Press. This book was released on 2013-12-19 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: New Tools to Solve Your Option Pricing Problems For nonlinear PDEs encountered in quantitative finance, advanced probabilistic methods are needed to address dimensionality issues. Written by two leaders in quantitative research—including Risk magazine’s 2013 Quant of the Year—Nonlinear Option Pricing compares various numerical methods for solving high-dimensional nonlinear problems arising in option pricing. Designed for practitioners, it is the first authored book to discuss nonlinear Black-Scholes PDEs and compare the efficiency of many different methods. Real-World Solutions for Quantitative Analysts The book helps quants develop both their analytical and numerical expertise. It focuses on general mathematical tools rather than specific financial questions so that readers can easily use the tools to solve their own nonlinear problems. The authors build intuition through numerous real-world examples of numerical implementation. Although the focus is on ideas and numerical examples, the authors introduce relevant mathematical notions and important results and proofs. The book also covers several original approaches, including regression methods and dual methods for pricing chooser options, Monte Carlo approaches for pricing in the uncertain volatility model and the uncertain lapse and mortality model, the Markovian projection method and the particle method for calibrating local stochastic volatility models to market prices of vanilla options with/without stochastic interest rates, the a + bλ technique for building local correlation models that calibrate to market prices of vanilla options on a basket, and a new stochastic representation of nonlinear PDE solutions based on marked branching diffusions.
Author : A. Bruaset
Publisher : Springer Science & Business Media
ISBN 13 : 1461219868
Total Pages : 387 pages
Book Rating : 4.4/5 (612 download)
Download or read book Modern Software Tools for Scientific Computing written by A. Bruaset and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Looking back at the years that have passed since the realization of the very first electronic, multi-purpose computers, one observes a tremendous growth in hardware and software performance. Today, researchers and engi neers have access to computing power and software that can solve numerical problems which are not fully understood in terms of existing mathemati cal theory. Thus, computational sciences must in many respects be viewed as experimental disciplines. As a consequence, there is a demand for high quality, flexible software that allows, and even encourages, experimentation with alternative numerical strategies and mathematical models. Extensibil ity is then a key issue; the software must provide an efficient environment for incorporation of new methods and models that will be required in fu ture problem scenarios. The development of such kind of flexible software is a challenging and expensive task. One way to achieve these goals is to in vest much work in the design and implementation of generic software tools which can be used in a wide range of application fields. In order to provide a forum where researchers could present and discuss their contributions to the described development, an International Work shop on Modern Software Tools for Scientific Computing was arranged in Oslo, Norway, September 16-18, 1996. This workshop, informally referred to as Sci Tools '96, was a collaboration between SINTEF Applied Mathe matics and the Departments of Informatics and Mathematics at the Uni versity of Oslo.
Author : George Levy
Publisher : Emerald Group Publishing
ISBN 13 : 178743527X
Total Pages : 344 pages
Book Rating : 4.7/5 (874 download)
Download or read book Energy Power Risk written by George Levy and published by Emerald Group Publishing. This book was released on 2018-12-10 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book describes both mathematical and computational tools for energy and power risk management, deriving from first principles stochastic models for simulating commodity risk and how to design robust C++ to implement these models.
Author : Luc Devroye
Publisher : Springer Science & Business Media
ISBN 13 : 3790825980
Total Pages : 242 pages
Book Rating : 4.7/5 (98 download)
Download or read book Recent Developments in Applied Probability and Statistics written by Luc Devroye and published by Springer Science & Business Media. This book was released on 2010-05-19 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to Professor Jürgen Lehn, who passed away on September 29, 2008, at the age of 67. It contains invited papers that were presented at the Wo- shop on Recent Developments in Applied Probability and Statistics Dedicated to the Memory of Professor Jürgen Lehn, Middle East Technical University (METU), Ankara, April 23–24, 2009, which was jointly organized by the Technische Univ- sität Darmstadt (TUD) and METU. The papers present surveys on recent devel- ments in the area of applied probability and statistics. In addition, papers from the Panel Discussion: Impact of Mathematics in Science, Technology and Economics are included. Jürgen Lehn was born on the 28th of April, 1941 in Karlsruhe. From 1961 to 1968 he studied mathematics in Freiburg and Karlsruhe, and obtained a Diploma in Mathematics from the University of Karlsruhe in 1968. He obtained his Ph.D. at the University of Regensburg in 1972, and his Habilitation at the University of Karlsruhe in 1978. Later in 1978, he became a C3 level professor of Mathematical Statistics at the University of Marburg. In 1980 he was promoted to a C4 level professorship in mathematics at the TUD where he was a researcher until his death.
