Assessing Least Squares Monte Carlo for the Kulatilaka Trigeorgis General Real Options Pricing Model PDF Download
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Author: Giuseppe Alesii
Publisher:
ISBN:
Category :
Languages : en
Pages : 88
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Book Description
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: Giuseppe Alesii
Publisher:
ISBN:
Category :
Languages : en
Pages : 88
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Book Description
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: Giuseppe Alesii
Publisher: LAP Lambert Academic Publishing
ISBN: 9783838390451
Category :
Languages : en
Pages : 96
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Book Description
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 six 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: Lars Stentoft
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author:
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ISBN:
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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: Artur Rodrigues
Publisher:
ISBN:
Category :
Languages : en
Pages : 49
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Book Description
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: 黃惠君
Publisher:
ISBN:
Category :
Languages : zh-CN
Pages : 102
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Author: Andrea Gamba
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Category :
Languages : en
Pages : 71
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This paper provides a numerical approach based on a Monte Carlo simulation for valuing dynamic capital budgeting problems with many embedded real options dependent on numerous state variables. We propose a way of decomposing a complex capital budgeting problem with many options into a set of simple options, suitably accounting for interaction and interdependence among them. The decomposition approach is numerically implemented using an extension of the Least Squares Monte Carlo algorithm, presented by Longstaff and Schwartz (2001) applied to our multi-option setting. We also provide a number of applications of our approach to well-known real options models and real life capital budgeting problems. Moreover, we present a set of numerical experiments to provide evidence for the accuracy of the proposed methodology.
Author: Lei Zhang
Publisher:
ISBN:
Category : Monte Carlo method
Languages : en
Pages : 284
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Author: Lars Stentoft
Publisher:
ISBN:
Category :
Languages : en
Pages :
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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.
