Download or read book Comparisons of Alternative Quasi Monte Carlo Sequences for American Option Pricing written by Jennifer X.F. Jiang and published by . This book was released on 2004 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quasi-Monte Carlo sequences have been shown to provide accurate option price approximations for a variety of options. In this paper, we apply quasi-Monte Carlo sequences in a duality approach to value American options. We compare the results using different low discrepancy sequences and estimate error bounds and computational effort. The results demonstrate the value of sequences using expansions of irrationals.
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.
Download or read book Quasi Monte Carlo Approaches to Option Pricing written by John R. Birge and published by . This book was released on 1995 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Implementing Models in Quantitative Finance Methods and Cases written by Gianluca Fusai and published by Springer Science & Business Media. This book was released on 2007-12-20 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book puts numerical methods in action for the purpose of solving practical problems in quantitative finance. The first part develops a toolkit in numerical methods for finance. The second part proposes twenty self-contained cases covering model simulation, asset pricing and hedging, risk management, statistical estimation and model calibration. Each case develops a detailed solution to a concrete problem arising in applied financial management and guides the user towards a computer implementation. The appendices contain "crash courses" in VBA and Matlab programming languages.
Download or read book Valuing American Style Option by Quasi Monte Carlo Simulation written by To Wang Ng and published by . This book was released on 2012 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Monte Carlo and Quasi Monte Carlo Sampling written by Christiane Lemieux and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quasi–Monte Carlo methods have become an increasingly popular alternative to Monte Carlo methods over the last two decades. Their successful implementation on practical problems, especially in finance, has motivated the development of several new research areas within this field to which practitioners and researchers from various disciplines currently contribute. This book presents essential tools for using quasi–Monte Carlo sampling in practice. The first part of the book focuses on issues related to Monte Carlo methods—uniform and non-uniform random number generation, variance reduction techniques—but the material is presented to prepare the readers for the next step, which is to replace the random sampling inherent to Monte Carlo by quasi–random sampling. The second part of the book deals with this next step. Several aspects of quasi-Monte Carlo methods are covered, including constructions, randomizations, the use of ANOVA decompositions, and the concept of effective dimension. The third part of the book is devoted to applications in finance and more advanced statistical tools like Markov chain Monte Carlo and sequential Monte Carlo, with a discussion of their quasi–Monte Carlo counterpart. The prerequisites for reading this book are a basic knowledge of statistics and enough mathematical maturity to follow through the various techniques used throughout the book. This text is aimed at graduate students in statistics, management science, operations research, engineering, and applied mathematics. It should also be useful to practitioners who want to learn more about Monte Carlo and quasi–Monte Carlo methods and researchers interested in an up-to-date guide to these methods.
Download or read book Low Discrepancy Sequences written by Silvio Galanti and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Low-discrepancy (quot;quasi-randomquot;) sampling methods offer the possibility of significantly enhancing the simulation models used in derivative valuation by using non-random quot;randomquot; numbers to generate simulated price paths. The idea is that a set of randomly generated values for the stochastic variables in a simulation will tend to have clumps of values close to each other in some regions and bare spots elsewhere, so a large number may have to be generated in order to have good coverage everywhere. Low-discrepancy sequences are non-random sets of numbers designed to cover the space more evenly, which allows the simulation to produce accurate valuation with fewer generated price series. Several alternatives exist for producing such sets, including algorithms devised by Sobol, by Halton, and by Faure. In this article, the authors give a detailed explanation of how these procedures work and how the low-discrepancy sets are generated. They then provide a comparison test among them for several types of path-dependent options, finding that the Sobol set generally appears to do the best.
Download or read book Least Squares Monte Carlo and Quasi Monte Carlo Method in Pricing American Put Options Using Matlab written by Phuc Phan and published by . This book was released on 2016 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this report, we evaluate the use of the Least Squares Monte Carlo (LSM) method, which was proposed by Longstaff and Schwartz in 2001. The holder of an American option has the right to exercise the option anytime, which makes the option much more difficult to price compared to a European style option. LSM is a simple and powerful method to price American style options and utilizes the use of least squares to estimate the conditional expected payoff to the option holder from continuation value. I provide a simple version of the LSM algorithm using second degree polynomials as basis functions with working code in Matlab to price American put option. I illustrate how the model is affected when input parameter such as risk free interest rate, volatility, underlying stock price, time to maturity are perturbed. After that, I construct the quasi Monte Carlo version of the Least Square algorithm by using Halton sequence and compare the performance of both quasi Monte Carlo and Monte Carlo algorithm.
Download or read book Application of Quasi Monte Carlo and Global Sensitivity Analysis to Option Pricing and Greeks written by Stefano Scoleri and published by . This book was released on 2017 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quasi Monte Carlo (QMC) and Global Sensitivity Analysis (GSA) techniques are applied for pricing and hedging representative financial instruments of increasing complexity. We compare standard Monte Carlo (MC) vs QMC results using Sobol' low discrepancy sequences, different sampling strategies, and various analyses of performance.We find that QMC outperforms MC in most cases, including the highest-dimensional simulations, showing faster and more stable convergence. Regarding greeks computation, we compare standard approaches, based on finite differences (FD) approximations, with adjoint methods (AAD) providing evidences that, when the number of greeks is small, the FD approach combined with QMC can lead to the same accuracy as AAD, thanks to increased convergence rate and stability, thus saving a lot of implementation effort while keeping low computational cost. Using GSA, we are able to fully explain our findings in terms of reduced effective dimension of QMC simulation, allowed in most cases, but not always, by Brownian bridge discretization or PCA construction.We conclude that, beyond pricing, QMC is a very efficient technique also for computing risk measures, greeks in particular, as it allows to reduce the computational effort of high dimensional Monte Carlo simulations typical of modern risk management.
Download or read book Monte Carlo and Quasi Monte Carlo Methods 2000 written by Kai-Tai Fang and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents the refereed proceedings of the Fourth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing which was held at Hong Kong Baptist University in 2000. An important feature are invited surveys of the state-of-the-art in key areas such as multidimensional numerical integration, low-discrepancy point sets, random number generation, and applications of Monte Carlo and quasi-Monte Carlo methods. These proceedings include also carefully selected contributed papers on all aspects of Monte Carlo and quasi-Monte Carlo methods. The reader will be informed about current research in this very active field.
Download or read book Contributions to the Theory of Monte Carlo and Quasi Monte Carlo Methods written by Giray Okten and published by Universal-Publishers. This book was released on 1999 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quasi-Monte Carlo methods, which are often described as deterministic versions of Monte Carlo methods, were introduced in the 1950s by number theoreticians. They improve several deficiencies of Monte Carlo methods; such as providing estimates with deterministic bounds and avoiding the paradoxical difficulty of generating random numbers in a computer. However, they have their own drawbacks. First, although they provide faster convergence than Monte Carlo methods asymptotically, the advantage may not be practical to obtain in "high" dimensional problems. Second, there is not a practical way to measure the error of a quasi-Monte Carlo simulation. Finally, unlike Monte Carlo methods, there is a scarcity of error reduction techniques for these methods. In this dissertation, we attempt to provide remedies for the disadvantages of quasi-Monte Carlo methods mentioned above. In the first part of the dissertation, a hybrid-Monte Carlo sequence designed to obtain error reduction in high dimensions is studied. Probabilistic results on the discrepancy of this sequence as well as results obtained by applying the sequence to problems from numerical integration and mathematical finance are presented. In the second part of the dissertation, a new hybrid-Monte Carlo method is introduced, in an attempt to obtain a practical statistical error analysis using low-discrepancy sequences. It is applied to problems from mathematical finance and particle transport theory to compare its effectiveness with the conventional methods. In the last part of the dissertation, a generalized quasi-Monte Carlo integration rule is introduced. A Koksma-Hlawka type inequality for the rule is proved, using a new concept for the variation of a function. As a consequence of the rule, error reduction techniques and in particular an "importance sampling" type statement are derived. Problems from different disciplines are used as practical tests for our methods. The numerical results obtained in favor of the methods suggest the practical advantages that can be realized by their use in a wide variety of applications.
Download or read book A Comparison of Monte Carlo and Quasi Monte Carlo Methods on the Italian Options Market written by Monica Baldini (economista) and published by . This book was released on 2003 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modeling Derivatives in C written by Justin London and published by John Wiley & Sons. This book was released on 2005-01-21 with total page 922 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the definitive and most comprehensive guide to modeling derivatives in C++ today. Providing readers with not only the theory and math behind the models, as well as the fundamental concepts of financial engineering, but also actual robust object-oriented C++ code, this is a practical introduction to the most important derivative models used in practice today, including equity (standard and exotics including barrier, lookback, and Asian) and fixed income (bonds, caps, swaptions, swaps, credit) derivatives. The book provides complete C++ implementations for many of the most important derivatives and interest rate pricing models used on Wall Street including Hull-White, BDT, CIR, HJM, and LIBOR Market Model. London illustrates the practical and efficient implementations of these models in real-world situations and discusses the mathematical underpinnings and derivation of the models in a detailed yet accessible manner illustrated by many examples with numerical data as well as real market data. A companion CD contains quantitative libraries, tools, applications, and resources that will be of value to those doing quantitative programming and analysis in C++. Filled with practical advice and helpful tools, Modeling Derivatives in C++ will help readers succeed in understanding and implementing C++ when modeling all types of derivatives.
Download or read book Monte Carlo and Quasi Monte Carlo Methods in Pricing Financial Derivatives written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: ABSTRACT: In this dissertation, we discuss the generation of low discrepancy sequences, randomization of these sequences, and the transformation methods to generate normally distributed random variables. Two well known methods for generating normally distributed numbers are considered, namely; Box-Muller and inverse transformation methods. Some researchers and financial engineers have claimed that it is incorrect to use the Box-Muller method with low-discrepancy sequences, and instead, the inverse transformation method should be used. We investigate the sensitivity of various computational finance problems with respect to different normal transformation methods. Box-Muller transformation method is theoretically justified in the context of the quasi-Monte Carlo by showing that the same error bounds apply for Box-Muller transformed point sets. Furthermore, new error bounds are derived for financial derivative pricing problems and for an isotropic integration problem where the integrand is a function of the Euclidean norm. Theoretical results are derived for financial derivative pricing problems; such as European call, Asian geometric, and Binary options with a convergence rate of 1/N. A stratified Box-Muller algorithm is introduced as an alternative to Box-Muller and inverse transformation methods, and new numerical evidence is presented in favor of this method. Finally, a statistical test for pseudo-random numbers is adapted for measuring the uniformity of transformed low discrepancy sequences.
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.
Download or read book Monte Carlo Methods for American Option Pricing written by Alberto Barola and published by LAP Lambert Academic Publishing. This book was released on 2014-05-21 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Monte Carlo approach has proved to be a valuable and flexible computational tool in modern finance. A number of Monte Carlo simulation-based methods have been developed within the past years to address the American option pricing problem. The aim of this book is to present and analyze three famous simulation algorithms for pricing American style derivatives: the stochastic tree; the stochastic mesh and the least squares method (LSM). The author first presents the mathematical descriptions underlying these numerical methods. Then the selected algorithms are tested on a common set of problems in order to assess the strengths and weaknesses of each approach as a function of the problem characteristics. The results are compared and discussed on the basis of estimates precision and computation time. Overall the simulation framework seems to work considerably well in valuing American style derivative securities. When multi-dimensional problems are considered, simulation based methods seem to be the best solution to estimate prices since the general numerical procedures of finite difference and binomial trees become impractical in these specific situations.
Download or read book Distributed Quasi Monte Carlo Algorithm for Option Pricing on HNOWs Using MpC written by Gong Chen and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
