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.
Download or read book Just in Time Monte Carlo for Path Dependent American Options written by Samir K. Dutt and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We establish simple analytical and numerical methods for propagating stochastic price processes backwards in time, step by step, to the initial value while satisfying all cross-sectional and serial requirements. This proves useful in dealing with complex path-dependent options with American triggers, where storing the history of the underlying can become computationally onerous. Examples involving the Wiener, Ornstein-Uhlenbeck, Clark, and Cox-Ingersoll-Ross processes illustrate our techniques. Our "just-in-time" method, which can be thought of as stochastic involution, extends the reach and accuracy of Monte Carlo pricing techniques beyond what has hitherto been possible.
Download or read book Handbook in Monte Carlo Simulation written by Paolo Brandimarte and published by John Wiley & Sons. This book was released on 2014-06-20 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible treatment of Monte Carlo methods, techniques, and applications in the field of finance and economics Providing readers with an in-depth and comprehensive guide, the Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics presents a timely account of the applicationsof Monte Carlo methods in financial engineering and economics. Written by an international leading expert in thefield, the handbook illustrates the challenges confronting present-day financial practitioners and provides various applicationsof Monte Carlo techniques to answer these issues. The book is organized into five parts: introduction andmotivation; input analysis, modeling, and estimation; random variate and sample path generation; output analysisand variance reduction; and applications ranging from option pricing and risk management to optimization. The Handbook in Monte Carlo Simulation features: An introductory section for basic material on stochastic modeling and estimation aimed at readers who may need a summary or review of the essentials Carefully crafted examples in order to spot potential pitfalls and drawbacks of each approach An accessible treatment of advanced topics such as low-discrepancy sequences, stochastic optimization, dynamic programming, risk measures, and Markov chain Monte Carlo methods Numerous pieces of R code used to illustrate fundamental ideas in concrete terms and encourage experimentation The Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics is a complete reference for practitioners in the fields of finance, business, applied statistics, econometrics, and engineering, as well as a supplement for MBA and graduate-level courses on Monte Carlo methods and simulation.
Download or read book Monte Carlo Simulation of Path Dependent Option Prices written by Hudson H. S. Yau and published by . This book was released on 1998 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Streamlining Monte Carlo Simulation with the Quasi analytic Method written by Giuseppe Lopomo and published by . This book was released on 1991 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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
Download or read book Addressing the Bias in Monte Carlo Pricing of Multi Asset Options with Multiple Barriers Through Discrete Sampling written by Pavel V. Shevchenko and published by . This book was released on 2014 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: An efficient conditioning technique, the so-called Brownian Bridge simulation, has previously been applied to eliminate pricing bias that arises in applications of the standard discrete-time Monte Carlo method to evaluate options written on the continuous-time extrema of an underlying asset. It is based on the simple and easy to implement analytic formulas for the distribution of one-dimensional Brownian Bridge extremes. This paper extends the technique to the valuation of multi-asset options with knock-out barriers imposed for all or some of the underlying assets. We derive formula for the unbiased option price estimator based on the joint distribution of the multi-dimensional Brownian Bridge dependent extrema. As analytic formulas are not available for the joint distribution in general, we develop upper and lower biased option price estimators based on the distribution of independent extrema and the Fréchet lower and upper bounds for the unknown distribution. All estimators are simple and easy to implement. They can always be used to bind the true value by a confidence interval. Numerical tests indicate that our biased estimators converge rapidly to the true option value as the number of time steps for the asset path simulation increases in comparison to the estimator based on the standard discrete-time method. The convergence rate depends on the correlation and barrier structures of the underlying assets.
Download or read book Monte Carlo Frameworks written by Daniel J. Duffy and published by John Wiley & Sons. This book was released on 2011-08-02 with total page 775 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is one of the first books that describe all the steps that are needed in order to analyze, design and implement Monte Carlo applications. It discusses the financial theory as well as the mathematical and numerical background that is needed to write flexible and efficient C++ code using state-of-the art design and system patterns, object-oriented and generic programming models in combination with standard libraries and tools. Includes a CD containing the source code for all examples. It is strongly advised that you experiment with the code by compiling it and extending it to suit your needs. Support is offered via a user forum on www.datasimfinancial.com where you can post queries and communicate with other purchasers of the book. This book is for those professionals who design and develop models in computational finance. This book assumes that you have a working knowledge of C ++.
Download or read book Streamlining Monte Carlo Simulation with the Quasi analytic Method written by N. K. Chidambaran and published by . This book was released on 1995 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Monte Carlo Methods written by Malvin H. Kalos and published by John Wiley & Sons. This book was released on 2008-10-20 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to Monte Carlo methods seeks to identify and study the unifying elements that underlie their effective application. Initial chapters provide a short treatment of the probability and statistics needed as background, enabling those without experience in Monte Carlo techniques to apply these ideas to their research. The book focuses on two basic themes: The first is the importance of random walks as they occur both in natural stochastic systems and in their relationship to integral and differential equations. The second theme is that of variance reduction in general and importance sampling in particular as a technique for efficient use of the methods. Random walks are introduced with an elementary example in which the modeling of radiation transport arises directly from a schematic probabilistic description of the interaction of radiation with matter. Building on this example, the relationship between random walks and integral equations is outlined. The applicability of these ideas to other problems is shown by a clear and elementary introduction to the solution of the Schrodinger equation by random walks. The text includes sample problems that readers can solve by themselves to illustrate the content of each chapter. This is the second, completely revised and extended edition of the successful monograph, which brings the treatment up to date and incorporates the many advances in Monte Carlo techniques and their applications, while retaining the original elementary but general approach.
Download or read book Handbook in Monte Carlo Simulation written by Paolo Brandimarte and published by John Wiley & Sons. This book was released on 2014-06-17 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible treatment of Monte Carlo methods, techniques, and applications in the field of finance and economics Providing readers with an in-depth and comprehensive guide, the Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics presents a timely account of the applicationsof Monte Carlo methods in financial engineering and economics. Written by an international leading expert in thefield, the handbook illustrates the challenges confronting present-day financial practitioners and provides various applicationsof Monte Carlo techniques to answer these issues. The book is organized into five parts: introduction andmotivation; input analysis, modeling, and estimation; random variate and sample path generation; output analysisand variance reduction; and applications ranging from option pricing and risk management to optimization. The Handbook in Monte Carlo Simulation features: An introductory section for basic material on stochastic modeling and estimation aimed at readers who may need a summary or review of the essentials Carefully crafted examples in order to spot potential pitfalls and drawbacks of each approach An accessible treatment of advanced topics such as low-discrepancy sequences, stochastic optimization, dynamic programming, risk measures, and Markov chain Monte Carlo methods Numerous pieces of R code used to illustrate fundamental ideas in concrete terms and encourage experimentation The Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics is a complete reference for practitioners in the fields of finance, business, applied statistics, econometrics, and engineering, as well as a supplement for MBA and graduate-level courses on Monte Carlo methods and simulation.
Download or read book Monte Carlo Simulation of the CGMY Process and Option Pricing written by Laura Ballotta and published by . This book was released on 2015 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a joint Monte Carlo-Fourier transform sampling scheme for pricing derivative products under a Carr-Geman-Madan-Yor (CGMY) model (Carr et al. [Journal of Business, 75, 305-332, 2002]) exhibiting jumps of infinite activity and finite or infinite variation. The approach relies on numerical transform inversion with computable error estimates, which allow generating the unknown cumulative distribution function of the CGMY process increments at the desired accuracy level. We use this to generate samples and simulate the entire trajectory of the process without need of truncating the process small jumps. We illustrate the computational efficiency of the proposed method by comparing to the existing methods in the literature on pricing a wide range of option contracts, including path-dependent univariate and multivariate products.
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
Download or read book Numerical Analysis and Its Applications written by Lubin Vulkov and published by Springer Science & Business Media. This book was released on 2001-03-07 with total page 803 pages. Available in PDF, EPUB and Kindle. Book excerpt: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 A. R. Ansari,A. F. HegartyandG. I. Shishkin AnAlgorithmBasedonOrthogonalPolynomialVectors forToeplitzLeastSquaresProblems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 M. VanBarel, G. Heinig andP. Kravanja FromSensitivityAnalysistoRandomFloatingPointArithmetics– ApplicationtoSylvesterEquations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 A. Barraud, S. LesecqandN. Christov ConstructionofSeminumericalSchemes: ApplicationtotheArti?cialSatelliteProblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 R. Barrio StabilityAnalysisofParallelEvaluationofFiniteSeries ofOrthogonalPolynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 R. Barrio andP. Yalamov OnSolvingLarge-ScaleWeightedLeastSquaresProblems. . . . . . . . . . . . . . . . . . 59 V.
Download or read book Multilevel Monte Carlo and Debiased Monte Carlo Methods in Financial Engineering written by Arun Kumar Polala and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation consists of two parts. In the first part we present a quasi-Monte Carlo implementation of the de-biased Monte Carlo estimator in the context of stochastic differential equations. We combine the quasi-Monte Carlo implementation with path generation techniques, and compare the accuracy of the resulting methods with the original de-biased Monte Carlo estimator when they are applied to option pricing problems under the geometric Brownian motion and Cox-Ingersoll-Ross models. In the second part we consider the application of the multilevel Monte Carlo methods to the LIBOR market model framework. The LIBOR market model is a popular interest rate model used for pricing interest rate derivatives like caplets, caps, and swaptions. Recently, long-dated interest rate derivatives have been popular in the interest rate derivative market, and the practitioners typically price them using the standard Monte Carlo method. To achieve real time pricing, practitioners often use very few Monte Carlo samples, typically in the low hundreds. We use multilevel Monte Carlo, low-discrepancy sequences, and path generation techniques to develop fast and accurate algorithms that achieve significant error reduction for small sample sizes, for pricing long-dated interest rate derivatives in the LIBOR market model framework.
Download or read book A Monte Carlo Method for Pricing American Options written by Diego Garcia and published by . This book was released on 1999 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
