Approving Least Squares Monte Carlo Approach for Valuing American Options PDF Download
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Author: Lei Zhang
Publisher:
ISBN:
Category : Monte Carlo method
Languages : en
Pages : 284
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Book Description
Author: Lei Zhang
Publisher:
ISBN:
Category : Monte Carlo method
Languages : en
Pages : 284
Get Book Here
Book Description
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Author: Laura Hass Thomsen
Publisher:
ISBN:
Category :
Languages : en
Pages : 97
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Author: Alberto Barola
Publisher: LAP Lambert Academic Publishing
ISBN: 9783659352607
Category :
Languages : en
Pages : 160
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Book Description
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: Lars Stentoft
Publisher:
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Category :
Languages : en
Pages :
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Author: 黃惠君
Publisher:
ISBN:
Category :
Languages : zh-CN
Pages : 102
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Author: Andries Jacobus Van Niekerk
Publisher:
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Category :
Languages : en
Pages :
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Book Description
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:
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ISBN:
Category :
Languages : en
Pages : 152
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Author:
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Category :
Languages : pt-BR
Pages :
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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: Gilles B. Desvilles
Publisher:
ISBN:
Category :
Languages : en
Pages : 14
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Book Description
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.
