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Author : Lars Stentoft
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (471 download)
Download or read book Assessing the Least Squares Monte-Carlo Approach to American Option Valuation written by Lars Stentoft and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Lars Stentoft
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (471 download)
Download or read book Convergence of the Least Squares Monte-Carlo Approach to American Option Valuation written by Lars Stentoft and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alberto Barola
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783659352607
Total Pages : 160 pages
Book Rating : 4.3/5 (526 download)
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.
Author : Lei Zhang
Publisher :
ISBN 13 :
Total Pages : 284 pages
Book Rating : 4.:/5 (125 download)
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:
Author : Phuc Phan
Publisher :
ISBN 13 :
Total Pages : 11 pages
Book Rating : 4.:/5 (13 download)
Download or read book Least-Squares Monte Carlo and Quasi Monte Carlo Method in Pricing American Put Options Using Matlab written by Phuc Phan and published by . This book was released on 2016 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Nelson Areal
Publisher :
ISBN 13 :
Total Pages : 36 pages
Book Rating : 4.:/5 (129 download)
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.
Author : 黃惠君
Publisher :
ISBN 13 :
Total Pages : 102 pages
Book Rating : 4.:/5 (62 download)
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:
Author : Laura Hass Thomsen
Publisher :
ISBN 13 :
Total Pages : 97 pages
Book Rating : 4.:/5 (115 download)
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 Valuation of real options through the least square monte carlo approach written by and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: O presente trabalho tem como objetivo testar empiricamente a eficiência e a aplicabilidade do método dos mínimos quadrados de Monte Carlo (LSM) na avaliação de projetos envolvendo opções reais. Inicialmente, o método passoupor uma série de testes de sensibilidade para validação do mesmo. Em seguida, alguns exemplos de projetos de exploração e produção (E & P) de petróleo com opções reais foram elaborados, e seus valores determinados através do LSM. Estes resultados foram comparados aos resultados obtidos com o modelo binomial que, devido a sua simplicidade e ampla utilização, foi escolhido comobenchmark para analisar a eficiência do método LSM. Devido às semelhanças entre oportunidades de investimento em ativos financeiros e reais, muitos estudos são realizados no sentido de adaptar instrumentos financeiros para a avaliação econômica de projetos. Muitas pesquisas sobre opções reais foram desenvolvidas em exploração de recursosnaturais, em especial de E & P de petróleo. Isso ocorre devido ao porte dos investimentos que são realizados neste setor e as suas características peculiares: o mercado de petróleo é bem desenvolvido (presença de mercado futuro, instrumentos de proteção financeira, derivativos etc); os investimentos ocorrem num ambiente de incertezas econômicas e / ou técnicas; os projetos demandam uma série de flexibilidades gerenciais (prazos alternativos paraexecução dos investimentos, possibilidade de mudanças na escala do projeto, entre outras). Tais características fazem com que seja necessária uma avaliação mais cautelosa e criteriosa destes ativos reais. Uma nova ferramentadesenvolvida neste sentido é o método LSM, que consiste na avaliação de opções americanas através de simulações e de regressões simples.
Author : Nelson Areal
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book On the Dangers of a Simplistic American Option Simulation Valuation Method written by Nelson Areal and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chen and Shen (2003) argue that it is possible to improve the Least Squares Monte Carlo Method (LSMC) of Longstaff and Schwartz (2001) to value American options by removing the least squares regression module. This would make not only faster but also more accurate. We demonstrate, using a large sample of 2500 put options that the proposed algorithm - the Perfect Foresight Method (PFM) - is, as argued by the authors, faster than the LSMC algorithm but, contrary to what they state, it is not more accurate than the LSMC. In fact, the PFM algorithm incorrectly prices American options, resulting in an upward biased value of the option. We therefore, do not recommend the use of the PFM.
Author :
Publisher :
ISBN 13 :
Total Pages : 152 pages
Book Rating : 4.E/5 ( download)
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:
Author : Peter M.A. Sloot
Publisher : Springer
ISBN 13 : 3540460802
Total Pages : 1153 pages
Book Rating : 4.5/5 (44 download)
Download or read book Computational Science — ICCS 2002 written by Peter M.A. Sloot and published by Springer. This book was released on 2003-08-01 with total page 1153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Science is the scienti?c discipline that aims at the development and understanding of new computational methods and techniques to model and simulate complex systems. The area of application includes natural systems – such as biology, envir- mental and geo-sciences, physics, and chemistry – and synthetic systems such as electronics and ?nancial and economic systems. The discipline is a bridge b- ween ‘classical’ computer science – logic, complexity, architecture, algorithms – mathematics, and the use of computers in the aforementioned areas. The relevance for society stems from the numerous challenges that exist in the various science and engineering disciplines, which can be tackled by advances made in this ?eld. For instance new models and methods to study environmental issues like the quality of air, water, and soil, and weather and climate predictions through simulations, as well as the simulation-supported development of cars, airplanes, and medical and transport systems etc. Paraphrasing R. Kenway (R.D. Kenway, Contemporary Physics. 1994): ‘There is an important message to scientists, politicians, and industrialists: in the future science, the best industrial design and manufacture, the greatest medical progress, and the most accurate environmental monitoring and forecasting will be done by countries that most rapidly exploit the full potential ofcomputational science’. Nowadays we have access to high-end computer architectures and a large range of computing environments, mainly as a consequence of the enormous s- mulus from the various international programs on advanced computing, e.g.
Author : Gilles B. Desvilles
Publisher :
ISBN 13 :
Total Pages : 14 pages
Book Rating : 4.:/5 (129 download)
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.
Author : Giuseppe Alesii
Publisher :
ISBN 13 :
Total Pages : 88 pages
Book Rating : 4.:/5 (129 download)
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.
Author : Andries Jacobus Van Niekerk
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (111 download)
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.
Author : Artur Rodrigues
Publisher :
ISBN 13 :
Total Pages : 49 pages
Book Rating : 4.:/5 (129 download)
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.
Author : Qiang Liu
Publisher :
ISBN 13 :
Total Pages : 9 pages
Book Rating : 4.:/5 (129 download)
Download or read book Pricing American Options by Canonical Least-Squares Monte Carlo written by Qiang Liu and published by . This book was released on 2008 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: Options pricing and hedging under canonical valuation have recently been demonstrated to be quite effective, but unfortunately are only applicable to European options. In this paper, a variation of canonical valuation called canonical least-squares Monte Carlo is proposed to price American options, which proceeds in three stages. First, given a set of historical gross returns (or price ratios) of the underlying for a chosen time interval, a discrete risk-neutral distribution is obtained via the canonical approach. Second, from this canonical distribution independent random samples of gross returns are taken to simulate future price paths for the underlying. Third, to those paths the least-squares Monte Carlo method is then applied to compute a price for an American option. Numerical results obtained from using simulated gross returns under geometric Brownian motion (GBM) show that this new approach yields reasonably accurate prices for American put options and can be utilized as an alternative to pricing American options, whether the underlying follows GBM or not.
