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An Efficient Quasi Monte Carlo Simulation For Pricing Asian Options Under Hestons Model
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Book Synopsis An Efficient Quasi-Monte Carlo Simulation for Pricing Asian Options Under Heston's Model by : Kewei Yu
Download or read book An Efficient Quasi-Monte Carlo Simulation for Pricing Asian Options Under Heston's Model written by Kewei Yu and published by . This book was released on 2015 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: The market for path-dependent options has been expanded considerably in the financial industry. The approach for pricing the path-dependent options in this thesis is developed by Kolkiewicz (2014) based on a quasi-Monte Carlo simulation with Brownian bridges conditioning on both their terminal values and the integrals along the paths. The main contribution of this essay is an extension of the above method to price Asian options under a stochastic volatility model. A Matlab implementation of generating multi-dimensional independent Brownian paths is also included as part of the contribution. The result can be used to price path-dependent options, such as an Asian option under both stochastic interest rate model and/or stochastic volatility model. A comparison with regular Monte Carlo simulation is provided.
Book Synopsis Efficient Monte Carlo and Quasi-Monte Carlo Option Pricing Under the Variance-Gamma Model by :
Download or read book Efficient Monte Carlo and Quasi-Monte Carlo Option Pricing Under the Variance-Gamma Model written by and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop and study efficient Monte Carlo algorithms for pricing path-dependent options with the variance gamma model. The key ingredient is difference-of-gamma bridge sampling, based on the representation of a variance gamma process as the difference of two increasing gamma processes. For typical payoff structures, we obtain a pair of estimators (named low and high) with expectations that are (i) monotone along any such bridge sampler; (ii) contain the continuous-time price. These estimators provide pathwise bounds on unbiased estimators that would be more expensive to compute (infinitely expensive in some situations). By using these bounds together with extrapolation techniques, we obtain significant simulation efficiency improvements by work reduction. We then combine the gamma bridge sampling with randomized quasi-Monte Carlo to reduce the variance and thus improve the efficiency by another important factor. We illustrate the large efficiency improvements on numerical examples for Asian, lookback, and barrier options.
Book Synopsis Monte Carlo Simulation and Finance by : Don L. McLeish
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.
Book Synopsis An Accurate and Efficient Method for Pricing Asian Options by : Chuang-Chang Chang
Download or read book An Accurate and Efficient Method for Pricing Asian Options written by Chuang-Chang Chang and published by . This book was released on 2003 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we provide an accurate and efficient method for valuing Asian options that works well for the low and medium volatility as well as longer average time window. Numerical results show that our method significantly outperforms the other analytic approximation methods in the literature. The pricing errors in terms of mean square errors for calculating a bundle of Asian options are less than one percent. Our method is fast and efficient compared to the Monte Carlo benchmark method adopted as well.
Book Synopsis Contributions to the Theory of Monte Carlo and Quasi-Monte Carlo Methods by : Giray Okten
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.
Book Synopsis The Hyperbolic Model: Option Pricing Using Approximation and Quasi-Monte Carlo Methods by : Martin Predota
Download or read book The Hyperbolic Model: Option Pricing Using Approximation and Quasi-Monte Carlo Methods written by Martin Predota and published by GRIN Verlag. This book was released on 2009-04 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Doctoral Thesis / Dissertation from the year 2002 in the subject Mathematics - Stochastics, grade: 1, Technical University of Graz, language: English, abstract: Aus Sicht der Mathematik spielen Optionen eine wesentliche Rolle seit der bahnbrechenden Arbeit von Black und Scholes im Jahre 1973. Deren Modell basiert jedoch auf der unrealistischen Annahme, das log-returns von Aktienkursen normalverteilt sind. Eberlein und Keller haben 1995 gezeigt, daß solche log-returns hyperbolisch verteilt sind. Die vorliegende Arbeit baut auf dieser Annahme auf und erweitert das Optionsspektrum von Europäischen Optionen auf Asiatische, Amerikanische sowie Multi-Asset-Optionen. Weiters wird das "Standard"-Martingal-Maß, die sogenannte Esscher-Transformation, durch das Entropie-minimierende Maß erweitert. Da jedoch keine exakte Preissetzung solcher Optionen möglich ist, wird auf numerische Simulationen und Approximationen zurückgegriffen. Die verwendeten numerischen Verfahren sind die Monte Carlo-Methode mit verschiedenen Varianzreduktionstechniken und die Quasi-Monte Carlo Methode.
Book Synopsis Sustainability of the Theories Developed by Mathematical Finance and Mathematical Economics with Applications by : Wing-Keung Wong
Download or read book Sustainability of the Theories Developed by Mathematical Finance and Mathematical Economics with Applications written by Wing-Keung Wong and published by MDPI. This book was released on 2020-12-15 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topics studied in this Special Issue include a wide range of areas in finance, economics, tourism, management, marketing, and education. The topics in finance include stock market, volatility and excess returns, REIT, warrant and options, herding behavior and trading strategy, supply finance, and corporate finance. The topics in economics including economic growth, income poverty, and political economics.
Book Synopsis Monte Carlo and Quasi-Monte Carlo Sampling by : Christiane Lemieux
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.
Book Synopsis Monte Carlo and Quasi-Monte Carlo Methods 2006 by : Alexander Keller
Download or read book Monte Carlo and Quasi-Monte Carlo Methods 2006 written by Alexander Keller and published by Springer Science & Business Media. This book was released on 2007-12-30 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the refereed proceedings of the Seventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, held in Ulm, Germany, in August 2006. The proceedings include carefully selected papers on many aspects of Monte Carlo and quasi-Monte Carlo methods and their applications. They also provide information on current research in these very active areas.
Book Synopsis American-Asian Option Pricing Based on Monte Carlo Simulation Method by : Shiguang Han
Download or read book American-Asian Option Pricing Based on Monte Carlo Simulation Method written by Shiguang Han and published by . This book was released on 2012 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Second Order Discretization with Malliavin Weight and Quasi-Monte Carlo Method for Option Pricing by : Toshihiro Yamada
Download or read book A Second Order Discretization with Malliavin Weight and Quasi-Monte Carlo Method for Option Pricing written by Toshihiro Yamada and published by . This book was released on 2018 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper shows an efficient second order discretization scheme of expectations of stochastic differential equations. We introduce smart Malliavin weight which is given by a simple polynomials of Brownian motions as an improvement of the scheme of Yamada (2017). A new quasi Monte Carlo simulation is proposed to attain an efficient option pricing scheme. Numerical examples for the SABR model are shown to illustrate the validity of the scheme.
Book Synopsis Monte Carlo Methods and Path-Generation Techniques for Pricing Multi-Asset Path-Dependent Options by : Piergiacomo Sabino
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.
Book Synopsis Computational Science – ICCS 2020 by : Valeria V. Krzhizhanovskaya
Download or read book Computational Science – ICCS 2020 written by Valeria V. Krzhizhanovskaya and published by Springer Nature. This book was released on 2020-06-19 with total page 786 pages. Available in PDF, EPUB and Kindle. Book excerpt: The seven-volume set LNCS 12137, 12138, 12139, 12140, 12141, 12142, and 12143 constitutes the proceedings of the 20th International Conference on Computational Science, ICCS 2020, held in Amsterdam, The Netherlands, in June 2020.* The total of 101 papers and 248 workshop papers presented in this book set were carefully reviewed and selected from 719 submissions (230 submissions to the main track and 489 submissions to the workshops). The papers were organized in topical sections named: Part I: ICCS Main Track Part II: ICCS Main Track Part III: Advances in High-Performance Computational Earth Sciences: Applications and Frameworks; Agent-Based Simulations, Adaptive Algorithms and Solvers; Applications of Computational Methods in Artificial Intelligence and Machine Learning; Biomedical and Bioinformatics Challenges for Computer Science Part IV: Classifier Learning from Difficult Data; Complex Social Systems through the Lens of Computational Science; Computational Health; Computational Methods for Emerging Problems in (Dis-)Information Analysis Part V: Computational Optimization, Modelling and Simulation; Computational Science in IoT and Smart Systems; Computer Graphics, Image Processing and Artificial Intelligence Part VI: Data Driven Computational Sciences; Machine Learning and Data Assimilation for Dynamical Systems; Meshfree Methods in Computational Sciences; Multiscale Modelling and Simulation; Quantum Computing Workshop Part VII: Simulations of Flow and Transport: Modeling, Algorithms and Computation; Smart Systems: Bringing Together Computer Vision, Sensor Networks and Machine Learning; Software Engineering for Computational Science; Solving Problems with Uncertainties; Teaching Computational Science; UNcErtainty QUantIficatiOn for ComputationAl modeLs *The conference was canceled due to the COVID-19 pandemic. Chapter ‘APE: A Command-Line Tool and API for Automated Workflow Composition’ is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Book Synopsis Application of Quasi Monte Carlo and Global Sensitivity Analysis to Option Pricing and Greeks by : Stefano Scoleri
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.
Book Synopsis Quasi-Monte Carlo Approaches to Option Pricing by : John R. Birge
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:
Book Synopsis Implementing Quasi-Monte Carlo Simulations with Linear Transformations by : Piergiacomo Sabino
Download or read book Implementing Quasi-Monte Carlo Simulations with Linear Transformations written by Piergiacomo Sabino and published by . This book was released on 2009 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: The curse of dimensionality limits the accuracy of the Quasi-Monte Carlo (QMC) method in high-dimensional problems. Imai and Tan [9, 10, 11] have proposed a dimension reduction technique, named Linear Transformation (LT), aiming to improve the efficiency of the QMC method. We investigate this approach in detail and make it more convenient. We implement a faster QR decomposition that considerably reduces the computational burden. The efficacy of our algorithm is illustrated by considering two high-dimensional option pricing problems: Asian basket options in the Black-Scholes (BS) model and Asian options in the Cox-Ingersoll-Ross (CIR) model. We employ a QMC generator only for the components selected by the LT construction and use Latin Hypercube Sampling (LHS) for all the others. Finally, we compare our results to those obtained by different random number generators and standard algorithms; subsequently, we benchmark our computational times against those presented in Imai and Tan [11].
Book Synopsis Sinh-Acceleration by : Svetlana Boyarchenko
Download or read book Sinh-Acceleration written by Svetlana Boyarchenko and published by . This book was released on 2018 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: Characteristic functions of several popular classes of distributions and processes admit analytic continuation into unions of strips and open coni around the line of integration in the complex plane.The Fourier transform techniques reduces calculation of probability distributions and option prices to evaluation of integrals whose integrands are analytic in domains enjoying these properties.In the paper, we suggest to use changes of variables of the form $ xi= sqrt{-1} omega_1 b sinh ( sqrt{-1} omega y)$ and the simplified trapezoid rule to evaluate the integrals accurately and fast. We formulate the general scheme, and apply the scheme for calculation probability distributions and pricing European options in Lévy models, the Heston model, the CIR model, and a subordinated NTS model. We outline applications to fast and accurate calibration procedures and Monte Carlo simulations.
