Author: Jerome Detemple
Publisher:
ISBN:
Category :
Languages : en
Pages :
Get Book Here
Book Description
We develop lower and upper bounds on the prices of American call and put options written on a dividend paying asset. We provide two option price approximations, one based on the lower bound (term LBA) and one based on both bounds (termed LUBA). The LUBA approximation has an average accuracy comparable to a 1000-step binomial tree with a computation speed comparable to a 50-step binomial tree. We introduce a modification of the binomial method (termed BBSR) which is very simple to implement and performs remarkably well. We also conduct a careful large-scale evaluation of many recent methods for computing American option prices.
Author: Detemple, Jérôme
Publisher: Montréal : CIRANO
ISBN:
Category :
Languages : en
Pages : 30
Get Book Here
Book Description
Author: Mark Broadie
Publisher:
ISBN:
Category :
Languages : fr
Pages :
Get Book Here
Book Description
Author: Peter M.A. Sloot
Publisher: Springer Science & Business Media
ISBN: 3540435913
Category : Computers
Languages : en
Pages : 1132
Get Book Here
Book Description
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: Dmitrii S. Silvestrov
Publisher: Walter de Gruyter
ISBN: 3110329824
Category : Mathematics
Languages : en
Pages : 520
Get Book Here
Book Description
The book gives a systematical presentation of stochastic approximation methods for models of American-type options with general pay-off functions for discrete time Markov price processes. Advanced methods combining backward recurrence algorithms for computing of option rewards and general results on convergence of stochastic space skeleton and tree approximations for option rewards are applied to a variety of models of multivariate modulated Markov price processes. The principal novelty of presented results is based on consideration of multivariate modulated Markov price processes and general pay-off functions, which can depend not only on price but also an additional stochastic modulating index component, and use of minimal conditions of smoothness for transition probabilities and pay-off functions, compactness conditions for log-price processes and rate of growth conditions for pay-off functions. The book also contains an extended bibliography of works in the area. This book is the first volume of the comprehensive two volumes monograph. The second volume will present results on structural studies of optimal stopping domains, Monte Carlo based approximation reward algorithms, and convergence of American-type options for autoregressive and continuous time models, as well as results of the corresponding experimental studies.
Author: Jingtang Ma
Publisher:
ISBN:
Category :
Languages : en
Pages : 28
Get Book Here
Book Description
In this paper, we extend the lower-upper bound approximation (LUBA) idea of Broadie and Detemple [Broadie, M., Detemple, J., (1996) American option valuation: New bounds, approximations, and comparison of existing methods. Review of Financial Studies. 9(4): 1211-1250] to the Laplace space. We construct tight lower and upper bounds for the price of a finite-maturity American option when the underlying stock is modeled by a large class of stochastic processes, for which there exist closed-form expressions for the Laplace transforms of the corresponding “capped (barrier) option prices”. The method is applied to a time-homogeneous diffusion process and a jump diffusion process. The novelty of the method is to first take the Laplace transform of the price of the “capped (barrier) option” with respect to the time to maturity, and then carry out optimization procedures similar as Broadie and Detemple in the Laplace space. Finally we numerically invert the Laplace transforms to obtain the lower bound of the price of the American option, and further utilize the early exercise premium (EEP) representation in the Laplace space to obtain the upper bound. We obtain explicit expressions in the case of the constant elasticity of variance (CEV) model (Wong and Zhao) and the double-exponential jump diffusion (DEJD) model (Leippold and Vasiljevic). Numerical examples show that our lower and upper bounds are accurate and efficient compared to results in the literature. To the best of authors' knowledge, it is the first time that the LUBA idea of Broadie and Detemple is applied to a model with jumps, and this solves an open question stated on page 1181 of Kou and Wang.
Author: Lirkov Ivan Dimov
Publisher: Springer
ISBN: 3642184669
Category : Computers
Languages : en
Pages : 524
Get Book Here
Book Description
This book constitutes the thoroughly refereed post-conference proceedings of the 7th International Conference on Numerical Methods and Applications, NMA 2010, held in Borovets, Bulgaria, in August 2010. The 60 revised full papers presented together with 3 invited papers were carefully reviewed and selected from numerous submissions for inclusion in this book. The papers are organized in topical sections on Monte Carlo and quasi-Monte Carlo methods, environmental modeling, grid computing and applications, metaheuristics for optimization problems, and modeling and simulation of electrochemical processes.
Author: L. C. G. Rogers
Publisher: Cambridge University Press
ISBN: 9780521573542
Category : Business & Economics
Languages : en
Pages : 348
Get Book Here
Book Description
Numerical Methods in Finance describes a wide variety of numerical methods used in financial analysis.
Author: Jin-Chuan Duan
Publisher: Springer Science & Business Media
ISBN: 3642172547
Category : Business & Economics
Languages : en
Pages : 791
Get Book Here
Book Description
Any financial asset that is openly traded has a market price. Except for extreme market conditions, market price may be more or less than a “fair” value. Fair value is likely to be some complicated function of the current intrinsic value of tangible or intangible assets underlying the claim and our assessment of the characteristics of the underlying assets with respect to the expected rate of growth, future dividends, volatility, and other relevant market factors. Some of these factors that affect the price can be measured at the time of a transaction with reasonably high accuracy. Most factors, however, relate to expectations about the future and to subjective issues, such as current management, corporate policies and market environment, that could affect the future financial performance of the underlying assets. Models are thus needed to describe the stochastic factors and environment, and their implementations inevitably require computational finance tools.
Author: Gianluca Fusai
Publisher: Springer Science & Business Media
ISBN: 3540499598
Category : Business & Economics
Languages : en
Pages : 606
Get Book Here
Book Description
This book puts numerical methods in action for the purpose of solving practical problems in quantitative finance. The first part develops a toolkit in numerical methods for finance. The second part proposes twenty self-contained cases covering model simulation, asset pricing and hedging, risk management, statistical estimation and model calibration. Each case develops a detailed solution to a concrete problem arising in applied financial management and guides the user towards a computer implementation. The appendices contain "crash courses" in VBA and Matlab programming languages.
