Download or read book The Cost of Accuracy in the Least Squares Monte Carlo Approach written by Gilles B. Desvilles and published by . This book was released on 2011 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article follows in the footsteps of Longstaff and Schwartz' seminal article about the use of regressions to model expectations in the valuation of American options with Monte Carlo simulation. The article repeats the original American put pricing in order to check for estimation accuracy and computation speed.In addition the article investigates the use of the control variate technique in order to accelerate the Least Squares Monte Carlo simulation, and implements a way to get the delta sensitivity without much raising the response time. However the results underline what is believed to be the main impediment of the approach: the cost of accuracy. Performed in dimension one on a standard computer the simulations lead to conclude that pricing an option agrave; la Longstaff Schwartz is not advised when the option is simple enough to be valued with a recombining binomial tree. Indeed the response times of the binomial pricing are incomparably shorter. Moreover the standard error proposed by the method under study is not reliable both in theory and in practice. There remains a mere conjecture according to which when increasing significantly the number of trajectories then convergence to the true price is reached and the estimated standard error is negligible. But, due to the involved pathwise regressions, such an increase would lengthen considerably the response time.Finally hope comes from computer improvements, especially in the memory field. In the least resource-consuming cases running the simulation with much more trajectories on a recent computer ends up yielding the true prices with no surrounding uncertainty and in a reasonable time. Hence, for similar pricings, one can expect to rely on the estimated standard error to tell when the simulation has converged.

Download or read book Handbook of Computational Economics written by Karl Schmedders and published by Newnes. This book was released on 2013-12-31 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Computational Economics summarizes recent advances in economic thought, revealing some of the potential offered by modern computational methods. With computational power increasing in hardware and algorithms, many economists are closing the gap between economic practice and the frontiers of computational mathematics. In their efforts to accelerate the incorporation of computational power into mainstream research, contributors to this volume update the improvements in algorithms that have sharpened econometric tools, solution methods for dynamic optimization and equilibrium models, and applications to public finance, macroeconomics, and auctions. They also cover the switch to massive parallelism in the creation of more powerful computers, with advances in the development of high-power and high-throughput computing. Much more can be done to expand the value of computational modeling in economics. In conjunction with volume one (1996) and volume two (2006), this volume offers a remarkable picture of the recent development of economics as a science as well as an exciting preview of its future potential. Samples different styles and approaches, reflecting the breadth of computational economics as practiced today Focuses on problems with few well-developed solutions in the literature of other disciplines Emphasizes the potential for increasing the value of computational modeling in economics

Download or read book Assessing Least Squares Monte Carlo for the Kulatilaka Trigeorgis General Real Options Pricing Model written by Giuseppe Alesii and published by . This book was released on 2008 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: We assess the applicability of (Longstaff and Schwartz, 2001) Least Squares Monte Carlo method to the General Real Options Pricing Model of (Kulatilaka and Trigeorgis, 1994). We study LSMC under different stochastic processes: GBM, up to three dimensions, models 1, 2 and 3 in (Schwartz, 1997), benchmarking every application by lattice methods. We explore empirically a generalization of proposition 1 page 124 in (Longstaff and Schwartz, 2001) with respect to the number of discretization points, of basis functions and the number of simulated paths. We study the speed precision tradeoff of LSMC individual estimates. Finally, we show their statistical properties.

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 Approving Least Squares Monte Carlo Approach for Valuing American Options written by Lei Zhang and published by . This book was released on 2004 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical study to least squares monte carlo method for pricing american options written by 黃惠君 and published by . This book was released on 2003 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Monte Carlo Methods written by Roman Frey and published by . This book was released on 2009-10 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper provides an extensive treatment of the entire Monte Carlo simulation theory. Furthermore, the Monte Carlo technique is used for addressing the pricing of various interest rate derivatives in different term structure models by the simulation approach. With the rising complexity and diversity of upcoming derivative securities, analytically tractable or closed-form pricing methods are difficult to find or even inexistent. If the thoroughly popular lattice valuation approach additionally fails due to non-recombining characteristics, Monte Carlo simulation represents a powerful and flexible alternative pricing method. The goal of this paper is to discuss and implement the fundamentals of Monte Carlo methods and to introduce the wide use of this approach in finance, especially in interest rate derivative valuation. The paper is roughly divided into three parts. The first part focuses on random number generation and on increasing efficiency methods for Monte Carlo, such as variance reduction techniques or low-discrepancy sequences. In the following part different term structure models are developed and the link to the simulation theory is eventually established. In the third and final part some ordinary and extended Monte Carlo algorithms are implemented and corresponding simulations are run in order to analyze Bermudan swaption prices in detail. Even though Monte Carlo methods feature a relatively slow but given convergence rate, they remain a competitive tool in financial applications. They owe their rising popularity to a large extent to their flexibility and to recent progress in methods which improve their accuracy and precision in estimating quantities of interest. Moreover, some of the leading yield curve models are heavily relying on Monte Carlo techniques. Several extensions of the standard Monte Carlo approach, such as least-squares Monte Carlo, for instance, are able to overcome the early-exercise hurdle a.

Download or read book Numerische Genauigkeit Von Least Squares Monte Carlo written by Marc Furrer and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Longstaff und Schwartz (2001) haben eine einfache, aber sehr gute Methode entwickelt um amerikanische Optionen zu bewerten. Die Methode basiert auf Monte Carlo Simulationen und verwendet einfache Regressionsanalysen um die Optionen zu bewerten. Die vorliegende Arbeit untersucht die Genauigkeit der Least Squares Monte Carlo (LSM) Methode. Für die Untersuchung werden die mittels der LSM Methode erhaltenen Werte mit den analytischen Werten gemäss der Black-Scholes Formel verglichen. Die Untersuchung zeigt, dass die LSM Methode ziemlich genaue Resultate liefert.

Download or read book Practical Approach To Xva A The Evolution Of Derivatives Valuation After The Financial Crisis written by Tsuchiya Osamu and published by World Scientific. This book was released on 2019-05-16 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2008 financial crisis shook the financial derivatives market to its core, revealing a failure to fully price the cost of doing business then. As a response to this, and to cope with regulatory demands for massively increased capital and other measures with funding cost, the pre-2008 concept of Credit Valuation Adjustment (CVA) has evolved into the far more complex hybrid Cross Valuation Adjustment (XVA).This book presents a clear and concise framework and provides key considerations for the computation of myriad adjustments to the price of financial derivatives, to fully reflect costs. XVA has been of great interest recently due to heavy funding costs (FVA), initial margin (MVA) and capital requirements (KVA) required to sustain a derivatives business since 2008, in addition to the traditional concepts of cost from counterparty default or credit deterioration (CVA), and its mirror image — the cost of one own's default (DVA).The book takes a practitioner's perspective on the above concepts, and then provides a framework to implement such adjustments in practice. Models are presented too, taking note of what is computationally feasible in light of portfolios typical of investment banks, and the different instruments associated with these portfolios.

Download or read book Valuing Bermuda Asian Options by Least Squares Monte Carlo Simulation written by and published by . This book was released on 2007 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Valuing American Asian Options with Least Squares Monte Carlo and Low Discrepancy Sequences written by Andries Jacobus Van Niekerk and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: There exists no closed form approximation for arithmetically calculated Asian options, but research has shown that closed form approximations are possible for Geometrically calculated Asian options. The aim of this dissertation is to effectively price American Asian options with the least squares Monte Carlo approach (Longstaff & Schwartz, 2001), applying Low discrepancy sequences and variance reduction techniques. We evaluate how these techniques affect the pricing of American options and American Asian options in terms of accuracy, computational efficiency, and computational time used to implement these techniques. We consider the effect of, Laguerre-, weighted Laguerre- , Hermite-, and Monomial-basis functions on the Longstaff and Schwartz (2001) model. We briefly investigate GPU optimization of the Longstaff and Schwartz algorithm within Matlab. We also graph the associated implied and Local volatility surfaces of the American Asian options to assist in the practical applicability of these options.

Download or read book Monte Carlo Study of Several Methods for Estimating Linear Demand for Outdoor Recreation from Censored and Truncated Data written by Dedi M. Masykur Riyadi and published by . This book was released on 1992 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Objective of this study was to compare accuracy of several travel cost methods, by employing Monte Carlo simulations in the single site framework. Estimates from five methods were compared to the "true" travel cost coefficient and "true" consumer surplus. Each method was ranked, using the root mean squared error (RMSE) criterion. Each method was applied to one of two kinds of travel cost data: censored data that includes both users and nonusers of recreation, and truncated data from on-site surveys consisting of only users. For censored data, the Tobit (TOBIT) method and OLS (OLSALL) were used, and for truncated data, the zone average travel cost (ZATC) method, the truncated normal (TRUNCN) estimator, and OLS (OLSUSR) were employed. Two types of consumer surplus were compared: (1) Predicted (traditional) consumer surplus (TRCS) that uses predicted values of the dependent variable, and (2) "actual" or Gum-Martin consumer surplus (GMCS) that uses observed values. Hellerstein's (1992) method for computing TOBIT TRCS was used in this study, which supposedly gives better estimates of TOBIT TRCS. This improvement, however, did not always give a better RMSE ranking than ZATC or OLSALL TRCS. The smaller the proportion of non-users in the data, the better were the TOBIT estimates. When the non-users portion was larger, ZATC and OLSALL sometimes gave better estimates of consumer surplus than TOBIT. An unexpected identity of linear demand estimated by OLSALL and the classic ZATC model was discovered. An original proof of this identity is given in Appendix 1. Because of this identity, both OLSALL and ZATC gave identical TRCS estimates. However, GMCS estimates differed because of averaging involved with ZATC. For censored data, TOBIT gave the best linear demand and GMCS estimates, but for truncated (user-only) data, best estimates of consumer surplus were from the supposedly obsolete ZATC model, fitted by Bowes-Loomis weighted least squares. Another new finding was that for data suitable for ZATC, missing zero observations can be synthesized, thus permitting use of TOBIT. However, thorough testing of such a scheme was beyond the scope of this thesis.

Download or read book Theory Application and Implementation of Monte Carlo Method in Science and Technology written by Pooneh Saidi Bidokhti and published by BoD – Books on Demand. This book was released on 2019-12-18 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Monte Carlo method is a numerical technique to model the probability of all possible outcomes in a process that cannot easily be predicted due to the interference of random variables. It is a technique used to understand the impact of risk, uncertainty, and ambiguity in forecasting models. However, this technique is complicated by the amount of computer time required to achieve sufficient precision in the simulations and evaluate their accuracy. This book discusses the general principles of the Monte Carlo method with an emphasis on techniques to decrease simulation time and increase accuracy.

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 Valuing American Options by Simulation written by Laura Hass Thomsen and published by . This book was released on 2015 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Minimization Of Computational Costs Of Non analogue Monte Carlo Methods written by G A Mikhailov and published by World Scientific. This book was released on 1992-01-10 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-analogue Monte Carlo methods are useful when the direct simulation techniques are insufficient. To use the additional discretization, Monte Carlo estimates are biased and it is desirable to optimize the connection between discretization parameters and the sample size. In this connection, the book investigates variances of non-analogue Monte Carlo estimates, uniform minimization of variances by choosing a computational model and the minimization of computational cost of non-analogue Monte Carlo methods.This book is essentially new with respect to previous monographs on the Monte Carlo methods.

Download or read book Uncertainty Quantification in Laminated Composites written by Sudip Dey and published by CRC Press. This book was released on 2018-09-19 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last few decades, uncertainty quantification in composite materials and structures has gained a lot of attention from the research community as a result of industrial requirements. This book presents computationally efficient uncertainty quantification schemes following meta-model-based approaches for stochasticity in material and geometric parameters of laminated composite structures. Several metamodels have been studied and comparative results have been presented for different static and dynamic responses. Results for sensitivity analyses are provided for a comprehensive coverage of the relative importance of different material and geometric parameters in the global structural responses.