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Author: Kumar Muthuraman
Publisher:
ISBN:
Category :
Languages : en
Pages : 24
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Book Description
This paper describes a method to solve the free-boundary problem that arises in the pricing of American options. Most numerical methods for American option pricing exploit the representation of the option price as the expected pay-off under the risk-neutral measure and calculate the price for a given time to expiration and stock price. They do not solve the related free-boundary problem explicitly. The advantage of solving the free-boundary problem is that it provides the entire price function as well as the optimal exercise boundary explicitly. Our approach, which we term the Moving Boundary Approach, is based on using a boundary guess and the value associated with the guess to construct an improved boundary. It is also shown that on iteration, the sequence of boundaries converge monotonically to the optimal exercise boundary. Examples illustrating the convergence behavior as well as discussions providing insight into the method are also presented. Finally, we compare run times and speeds with other methods that solve the free-boundary problem and compute the optimal boundaries explicitly, like the front-fixing method, penalty method, method based on the integral representations and the method by Brennan and Schwartz (1977).
Author: Kumar Muthuraman
Publisher:
ISBN:
Category :
Languages : en
Pages : 24
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Book Description
This paper describes a method to solve the free-boundary problem that arises in the pricing of American options. Most numerical methods for American option pricing exploit the representation of the option price as the expected pay-off under the risk-neutral measure and calculate the price for a given time to expiration and stock price. They do not solve the related free-boundary problem explicitly. The advantage of solving the free-boundary problem is that it provides the entire price function as well as the optimal exercise boundary explicitly. Our approach, which we term the Moving Boundary Approach, is based on using a boundary guess and the value associated with the guess to construct an improved boundary. It is also shown that on iteration, the sequence of boundaries converge monotonically to the optimal exercise boundary. Examples illustrating the convergence behavior as well as discussions providing insight into the method are also presented. Finally, we compare run times and speeds with other methods that solve the free-boundary problem and compute the optimal boundaries explicitly, like the front-fixing method, penalty method, method based on the integral representations and the method by Brennan and Schwartz (1977).
Author: Carl Chiarella
Publisher: World Scientific
ISBN: 9814452629
Category : Options (Finance)
Languages : en
Pages : 223
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Book Description
The early exercise opportunity of an American option makes it challenging to price and an array of approaches have been proposed in the vast literature on this topic. In The Numerical Solution of the American Option Pricing Problem, Carl Chiarella, Boda Kang and Gunter Meyer focus on two numerical approaches that have proved useful for finding all prices, hedge ratios and early exercise boundaries of an American option. One is a finite difference approach which is based on the numerical solution of the partial differential equations with the free boundary problem arising in American option pricing, including the method of lines, the component wise splitting and the finite difference with PSOR. The other approach is the integral transform approach which includes Fourier or Fourier Cosine transforms. Written in a concise and systematic manner, Chiarella, Kang and Meyer explain and demonstrate the advantages and limitations of each of them based on their and their co-workers'' experiences with these approaches over the years. Contents: Introduction; The Merton and Heston Model for a Call; American Call Options under Jump-Diffusion Processes; American Option Prices under Stochastic Volatility and Jump-Diffusion Dynamics OCo The Transform Approach; Representation and Numerical Approximation of American Option Prices under Heston; Fourier Cosine Expansion Approach; A Numerical Approach to Pricing American Call Options under SVJD; Conclusion; Bibliography; Index; About the Authors. Readership: Post-graduates/ Researchers in finance and applied mathematics with interest in numerical methods for American option pricing; mathematicians/physicists doing applied research in option pricing. Key Features: Complete discussion of different numerical methods for American options; Able to handle stochastic volatility and/or jump diffusion dynamics; Able to produce hedge ratios efficiently and accurately"
Author: Kumar Muthuraman
Publisher: Now Publishers Inc
ISBN: 1601981686
Category : Boundary value problems
Languages : en
Pages : 94
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Book Description
Outlines and explains a recent computational method that solves free boundary problems by reducing them into a sequence of fixed boundary problems which are relatively easy to solve numerically.
Author: Andreas Andrikopoulos
Publisher:
ISBN:
Category :
Languages : en
Pages : 17
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Book Description
The quadratic approximation to the valuation of american options on stocks is revisited, constructing a pricing approach based on the fact that the early exercise policy should be chosen to maximize the value of the option. At the first part of the paper, we apply this approach (boundary-optimality) in the setting of the pricing model suggested in Barone-Adesi and Whaley (1987). We enrich their original valuation setting with an additional parameter, computed with the help of a boundary-optimality boundary condition. This approach enhances the accuracy performance of the Barone-Adesi and Whaley (1987) approximation. In the second part of the paper we introduce a novel approximation approach, where option value is the product of two functions, one of the being a function of time and the other one being a function of the stock price. Applying the principle that the early exercise policy should maximize option value, this alternative option pricing technique provides accurate results for american call and put options.
Author: Matheus R. Grasselli
Publisher: World Scientific
ISBN: 9814407887
Category : Business & Economics
Languages : en
Pages : 598
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Book Description
This outstanding collection of articles includes papers presented at the Fields Institute, Toronto, as part of the Thematic Program in Quantitative Finance that took place in the first six months of the year 2010. The scope of the volume in very broad, including papers on foundational issues in mathematical finance, papers on computational finance, and papers on derivatives and risk management. Many of the articles contain path-breaking insights that are relevant to the developing new order of post-crisis financial risk management.
Author: Gregory E Fasshauer
Publisher: World Scientific Publishing Company
ISBN: 9814630152
Category : Mathematics
Languages : en
Pages : 537
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Book Description
In an attempt to introduce application scientists and graduate students to the exciting topic of positive definite kernels and radial basis functions, this book presents modern theoretical results on kernel-based approximation methods and demonstrates their implementation in various settings. The authors explore the historical context of this fascinating topic and explain recent advances as strategies to address long-standing problems. Examples are drawn from fields as diverse as function approximation, spatial statistics, boundary value problems, machine learning, surrogate modeling and finance. Researchers from those and other fields can recreate the results within using the documented MATLAB code, also available through the online library. This combination of a strong theoretical foundation and accessible experimentation empowers readers to use positive definite kernels on their own problems of interest.
Author: Dumitru Baleanu
Publisher: World Scientific
ISBN: 9814355208
Category : Mathematics
Languages : en
Pages : 426
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Book Description
This title will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods.
Author: Dongming Wang
Publisher: Springer Science & Business Media
ISBN: 3764379839
Category : Mathematics
Languages : en
Pages : 391
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Book Description
The growing demand of speed, accuracy, and reliability in scientific and engineering computing has been accelerating the merging of symbolic and numeric computations. These two types of computation coexist in mathematics yet are separated in traditional research of mathematical computation. This book presents 27 research articles on the integration and interaction of symbolic and numeric computation.
Author: Elias Tzavalis
Publisher:
ISBN:
Category :
Languages : en
Pages : 35
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Book Description
In this paper we introduce a new method of pricing an American call option by approximating its early exercise boundary based on Chebyshev polynomial functions. We implement the method to price options under the standard assumptions of the Black-Scholes model, for European options, and under stochastic volatility. For the latter, we provide an integral representation which unbundles the American call option price to Arrow-Debreu security prices. Numerical results indicate that our method is an effective alternative to other exercise boundary approximation methods under both the standard assumptions of the Black-Scholes and stochastic volatility.
Author: Lirkov Ivan Dimov
Publisher: Springer
ISBN: 3642184669
Category : Computers
Languages : en
Pages : 524
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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.
