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.
Author: Karl Schmedders
Publisher: Newnes
ISBN: 0080931782
Category : Business & Economics
Languages : en
Pages : 680
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Book Description
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
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: 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: Lei Zhang
Publisher:
ISBN:
Category : Monte Carlo method
Languages : en
Pages : 284
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Author: 黃惠君
Publisher:
ISBN:
Category :
Languages : zh-CN
Pages : 102
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Author: Roman Frey
Publisher:
ISBN: 9783639204018
Category :
Languages : en
Pages : 136
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Book Description
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.
Author: Marc Furrer
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
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.
Author: Tsuchiya Osamu
Publisher: World Scientific
ISBN: 9813272759
Category : Business & Economics
Languages : en
Pages : 340
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Book Description
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.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 152
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