Download or read book Improving the Least squares Monte Carlo Approach written by Nicki Søndergaard Rasmussen and published by . This book was released on 2002 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On Improving the Least Squares Monte Carlo Option Valuation Method written by Nelson Areal and published by . This book was released on 2018 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies various possible approaches to improving the least squares Monte Carlo option valuation method. We test different regression algorithms and suggest a variation to estimating the option continuation value, which can reduce the execution time of the algorithm by one third. We test the choice of varying polynomial families with different number of basis functions. We compare several variance reduction techniques, and find that using low discrepancy sequences can improve the accuracy up to four times. We also extend our analysis to compound and mutually exclusive options. For the latter, we propose an improved algorithm which is faster and more accurate.

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 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 Apply the Least Squares Monte Carlo Approach to Extremely Complex Options A Building Block Methodology written by and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Application of Monte Carlo Methods to the Evaluation of Small Sample Properties of 3 stage Least Squares Procedure written by Jugal Kishore Sharma and published by . This book was released on 1965 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Monte Carlo simulation study of model validation by least squares and ridge regression methods written by Bernard Yao-po Su and published by . This book was released on 1977 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Fast American Monte Carlo written by Claudio Moni and published by . This book was released on 2005 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: Within the American Monte Carlo framework, we present a method to combine least-squares regression with variance reduction techniques. Our method, based on constructing dynamic control variates, results in significant speed increase, as well as as higher accuracy in the exercise strategy estimation. Furthermore, we provide new results on the speed of convergence of the least-squares American Monte Carlo method.

Download or read book Enhancing Least Squares Monte Carlo with Diffusion Bridges written by Tommaso Pellegrino and published by . This book was released on 2015 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this study is to present an efficient and easy framework for the application of the Least Squares Monte Carlo methodology to the pricing of gas or power facilities as detailed in Boogert and de Jong. As mentioned in the seminal paper by Longstaff and Schwartz, the convergence of the Least Squares Monte Carlo depends on the convergence of the optimization combined with the convergence of the pure Monte Carlo method. In the context of the energy facilities, the convergence of the algorithm is more challenging in particular for the computation of sensitivities and optimal dispatched quantities. To our knowledge, an extensive study of the convergence and hence, of the reliability of the algorithm has not been performed yet, in our opinion because of the apparent infeasibility and complexity to use a very high number of simulations. We present then an easy way to simulate random trajectories by means of diffusion bridges similar to the one proposed by Kutt and Welke that is equivalent to generate a time reversal Itō diffusion. Our approach permits to perform a backward dynamic programming strategy based on a huge number of simulations without storing the whole simulated trajectory.Generally, in the valuation of energy facilities one is also interested in the forward recursion. We then design the backward and forward recursions algorithm such that one can produce the same random trajectories by the use of multiple independent random streams without storing at intermediate time steps. Finally, we show the advantages of our methodology for the valuation of virtual hydro power plants and gas storages.

Download or read book Monte Carlo Methods written by Adrian Barbu and published by Springer Nature. This book was released on 2020-02-24 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book seeks to bridge the gap between statistics and computer science. It provides an overview of Monte Carlo methods, including Sequential Monte Carlo, Markov Chain Monte Carlo, Metropolis-Hastings, Gibbs Sampler, Cluster Sampling, Data Driven MCMC, Stochastic Gradient descent, Langevin Monte Carlo, Hamiltonian Monte Carlo, and energy landscape mapping. Due to its comprehensive nature, the book is suitable for developing and teaching graduate courses on Monte Carlo methods. To facilitate learning, each chapter includes several representative application examples from various fields. The book pursues two main goals: (1) It introduces researchers to applying Monte Carlo methods to broader problems in areas such as Computer Vision, Computer Graphics, Machine Learning, Robotics, Artificial Intelligence, etc.; and (2) it makes it easier for scientists and engineers working in these areas to employ Monte Carlo methods to enhance their research.

Download or read book The Valuation of Real Options with the Least Squares Monte Carlo Simulation Method written by Artur Rodrigues and published by . This book was released on 2006 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper provides a detailed analysis of the Least Squares Monte Carlo Simulation Method (Longstaff and Schwartz, 2001) and of the extension of Gamba (2003) to value portfolios of real options. The accuracy of the method is assessed when valuing stylised real options as maximum, compound or mutually exclusive options. For the latter, we propose an improved algorithm that is faster, more accurate as well as more reliable. The analysis is carried out for a large number of call and put options. It is done comparing alternative polynomial families and simulation methods, including moment matching techniques and low-discrepancy sequences. Unlike previous analysis of the method, our results suggest that the use of weighted Laguerre polynomials, initially proposed by Longstaff and Schwartz (2001), produces more accurate estimates. We show also that the choice of the best simulation method is contingent on the problem in hand. Low-discrepancy sequences tend to produce more accurate estimates, using fewer paths than pseudo-random numbers. The accuracy of the method depends on the payoff function and seems to converge, increasing both the number of basis and the number of simulated paths.

Download or read book Explorations in Monte Carlo Methods written by Ronald W. Shonkwiler and published by Springer Nature. This book was released on with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Bias Corrected Least Squares Monte Carlo for Utility Based Optimal Stochastic Control Problems written by Johan Andreasson and published by . This book was released on 2018 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Least-Squares Monte Carlo method has gained popularity recent years due to its ability to handle multi-dimensional stochastic control problems without restrictions on the state dynamics, including problems with state variables affected by control. However, when applied to stochastic control problems in the multiperiod expected utility models, the regression t tends to contain errors which accumulate over time and typically blow up the numerical solution. In this paper we propose to transform the value function of stochastic control problems to improve the regression t, and then using either the 'Smearing Estimate' or 'Controlled Heteroskedasticity' to avoid the re-transformation bias. We also present and utilise recent improvements in Least-Squares Monte Carlo algorithms such as control randomisation with policy iteration to avoid regression errors from accumulating. Presented numerical examples demonstrate that our transformation method allows for control of disturbance terms to be handled correctly and leads to an accurate solution. In addition, in the forward simulation stage of the algorithm, we propose a re-sampling of state variables at each time step instead of simulating continuous paths, to improve the exploration of the state space that also appears to be important to obtain a stable and accurate solution for expected utility models.

Download or read book A Monte Carlo study of two robust alternatives to least squares regression estimation written by and published by . This book was released on 1974 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Comparative Evaluation of Profit Analysis and Ordinary Least Squares a Monte Carlo Approach written by Moffat Patrick Witherington and published by . This book was released on 1977 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Primer for the Monte Carlo Method written by Ilya M. Sobol and published by CRC Press. This book was released on 2018-04-24 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Monte Carlo method is a numerical method of solving mathematical problems through random sampling. As a universal numerical technique, the method became possible only with the advent of computers, and its application continues to expand with each new computer generation. A Primer for the Monte Carlo Method demonstrates how practical problems in science, industry, and trade can be solved using this method. The book features the main schemes of the Monte Carlo method and presents various examples of its application, including queueing, quality and reliability estimations, neutron transport, astrophysics, and numerical analysis. The only prerequisite to using the book is an understanding of elementary calculus.