Comparisons of Alternative Quasi-Monte Carlo Sequences for American Option Pricing PDF Download
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Author: Jennifer X.F. Jiang
Publisher:
ISBN:
Category :
Languages : en
Pages : 17
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Book Description
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.
Author: Jennifer X.F. Jiang
Publisher:
ISBN:
Category :
Languages : en
Pages : 17
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Book Description
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.
Author: Harald Niederreiter
Publisher: Springer Science & Business Media
ISBN: 1461216907
Category : Mathematics
Languages : en
Pages : 463
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Book Description
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: John R. Birge
Publisher:
ISBN:
Category :
Languages : en
Pages : 29
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Book Description
Author: Gianluca Fusai
Publisher: Springer Science & Business Media
ISBN: 3540499598
Category : Business & Economics
Languages : en
Pages : 606
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Book Description
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.
Author: To Wang Ng
Publisher:
ISBN:
Category :
Languages : en
Pages : 120
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Book Description
Author: Christiane Lemieux
Publisher: Springer Science & Business Media
ISBN: 038778165X
Category : Mathematics
Languages : en
Pages : 373
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Book Description
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.
Author: Silvio Galanti
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
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.
Author: Phuc Phan
Publisher:
ISBN:
Category :
Languages : en
Pages : 11
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Book Description
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.
Author: Stefano Scoleri
Publisher:
ISBN:
Category :
Languages : en
Pages : 48
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Book Description
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.
Author: Kai-Tai Fang
Publisher: Springer Science & Business Media
ISBN: 3642560466
Category : Mathematics
Languages : en
Pages : 570
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Book Description
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.
