Option Theory With Stochastic Analysis
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Option Theory With Stochastic Analysis
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Author : Fred Espen Benth
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-11-26
Option Theory With Stochastic Analysis written by Fred Espen Benth and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-26 with Business & Economics categories.
This is a very basic and accessible introduction to option pricing, invoking a minimum of stochastic analysis and requiring only basic mathematical skills. It covers the theory essential to the statistical modeling of stocks, pricing of derivatives with martingale theory, and computational finance including both finite-difference and Monte Carlo methods.
Option Theory With Stochastic Analysis
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Author : Fred Espen Benth
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Option Theory With Stochastic Analysis written by Fred Espen Benth and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
This is a very basic and accessible introduction to option pricing, invoking a minimum of stochastic analysis and requiring only basic mathematical skills. It covers the theory essential to the statistical modeling of stocks, pricing of derivatives with martingale theory, and computational finance including both finite-difference and Monte Carlo methods.
Introduction To Option Pricing Theory
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Author : Gopinath Kallianpur
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Option Pricing Theory written by Gopinath Kallianpur and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Since the appearance of seminal works by R. Merton, and F. Black and M. Scholes, stochastic processes have assumed an increasingly important role in the development of the mathematical theory of finance. This work examines, in some detail, that part of stochastic finance pertaining to option pricing theory. Thus the exposition is confined to areas of stochastic finance that are relevant to the theory, omitting such topics as futures and term-structure. This self-contained work begins with five introductory chapters on stochastic analysis, making it accessible to readers with little or no prior knowledge of stochastic processes or stochastic analysis. These chapters cover the essentials of Ito's theory of stochastic integration, integration with respect to semimartingales, Girsanov's Theorem, and a brief introduction to stochastic differential equations. Subsequent chapters treat more specialized topics, including option pricing in discrete time, continuous time trading, arbitrage, complete markets, European options (Black and Scholes Theory), American options, Russian options, discrete approximations, and asset pricing with stochastic volatility. In several chapters, new results are presented. A unique feature of the book is its emphasis on arbitrage, in particular, the relationship between arbitrage and equivalent martingale measures (EMM), and the derivation of necessary and sufficient conditions for no arbitrage (NA). {\it Introduction to Option Pricing Theory} is intended for students and researchers in statistics, applied mathematics, business, or economics, who have a background in measure theory and have completed probability theory at the intermediate level. The work lends itself to self-study, as well as to a one-semester course at the graduate level.
A Game Theory Analysis Of Options
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Author : Alexandre C. Ziegler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-02
A Game Theory Analysis Of Options written by Alexandre C. Ziegler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-02 with Business & Economics categories.
Modern option pricing theory was developed in the late sixties and early seventies by F. Black, R. e. Merton and M. Scholes as an analytical tool for pricing and hedging option contracts and over-the-counter warrants. How ever, already in the seminal paper by Black and Scholes, the applicability of the model was regarded as much broader. In the second part of their paper, the authors demonstrated that a levered firm's equity can be regarded as an option on the value of the firm, and thus can be priced by option valuation techniques. A year later, Merton showed how the default risk structure of cor porate bonds can be determined by option pricing techniques. Option pricing models are now used to price virtually the full range of financial instruments and financial guarantees such as deposit insurance and collateral, and to quantify the associated risks. Over the years, option pricing has evolved from a set of specific models to a general analytical framework for analyzing the production process of financial contracts and their function in the financial intermediation process in a continuous time framework. However, very few attempts have been made in the literature to integrate game theory aspects, i. e. strategic financial decisions of the agents, into the continuous time framework. This is the unique contribution of the thesis of Dr. Alexandre Ziegler. Benefiting from the analytical tractability of contin uous time models and the closed form valuation models for derivatives, Dr.
Telegraph Processes And Option Pricing
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Author : Nikita Ratanov
language : en
Publisher: Springer
Release Date : 2023-01-05
Telegraph Processes And Option Pricing written by Nikita Ratanov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-05 with Mathematics categories.
This book provides an extensive, systematic overview of the modern theory of telegraph processes and their multidimensional counterparts, together with numerous fruitful applications in financial modelling. Focusing on stochastic processes of bounded variation instead of classical diffusion, or more generally, Lévy processes, has two obvious benefits. First, the mathematical technique is much simpler, which helps to concentrate on the key problems of stochastic analysis and applications, including financial market modelling. Second, this approach overcomes some shortcomings of the (parabolic) nature of classical diffusions that contradict physical intuition, such as infinite propagation velocity and infinite total variation of paths. In this second edition, some sections of the previous text are included without any changes, while most others have been expanded and significantly revised. These are supplemented by predominantly new results concerning piecewise linear processes with arbitrary sequences of velocities, jump amplitudes, and switching intensities. The chapter on functionals of the telegraph process has been significantly expanded by adding sections on exponential functionals, telegraph meanders and running extrema, the times of the first passages of telegraph processes with alternating random jumps, and distribution of the Euclidean distance between two independent telegraph processes. A new chapter on the multidimensional counterparts of the telegraph processes is also included. The book is intended for graduate students in mathematics, probability, statistics and quantitative finance, and for researchers working at academic institutions, in industry and engineering. It can also be used by university lecturers and professionals in various applied areas.
Stochastic Analysis Stochastic Systems And Applications To Finance
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Author : Allanus Hak-Man Tsoi
language : en
Publisher: World Scientific
Release Date : 2011
Stochastic Analysis Stochastic Systems And Applications To Finance written by Allanus Hak-Man Tsoi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Business & Economics categories.
Pt. I. Stochastic analysis and systems. 1. Multidimensional Wick-Ito formula for Gaussian processes / D. Nualart and S. Ortiz-Latorre. 2. Fractional white noise multiplication / A.H. Tsoi. 3. Invariance principle of regime-switching diffusions / C. Zhu and G. Yin -- pt. II. Finance and stochastics. 4. Real options and competition / A. Bensoussan, J.D. Diltz and S.R. Hoe. 5. Finding expectations of monotone functions of binary random variables by simulation, with applications to reliability, finance, and round robin tournaments / M. Brown, E.A. Pekoz and S.M. Ross. 6. Filtering with counting process observations and other factors : applications to bond price tick data / X. Hu, D.R. Kuipers and Y. Zeng. 7. Jump bond markets some steps towards general models in applications to hedging and utility problems / M. Kohlmann and D. Xiong. 8. Recombining tree for regime-switching model : algorithm and weak convergence / R.H. Liu. 9. Optimal reinsurance under a jump diffusion model / S. Luo. 10. Applications of counting processes and martingales in survival analysis / J. Sun. 11. Stochastic algorithms and numerics for mean-reverting asset trading / Q. Zhang, C. Zhuang and G. Yin
A Stochastic Control Framework For Real Options In Strategic Evaluation
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Author : Alexander Vollert
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Stochastic Control Framework For Real Options In Strategic Evaluation written by Alexander Vollert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The theoretical foundation for real options goes back to the mid 1980s and the development of a model that forms the basis for many current applications of real option theory. Over the last decade the theory has rapidly expanded and become enriched thanks to increasing research activity. Modern real option theory may be used for the valuation of entire companies as well as for particular investment projects in the presence of uncertainty. As such, the theory of real options can serve as a tool for more practically oriented decision making, providing management with strategies maximizing its capital market value. This book is devoted to examining a new framework for classifying real options from a management and a valuation perspective, giving the advantages and disadvantages of the real option approach. Impulse control theory and the theory of optimal stopping combined with methods of mathematical finance are used to construct arbitrarily complex real option models which can be solved numerically and which yield optimal capital market strategies and values. Various examples are given to demonstrate the potential of this framework. This work will benefit the financial community, companies, as well as academics in mathematical finance by providing an important extension of real option research from both a theoretical and practical point of view.
Pde And Martingale Methods In Option Pricing
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Author : Andrea Pascucci
language : en
Publisher: Springer
Release Date : 2014-10-12
Pde And Martingale Methods In Option Pricing written by Andrea Pascucci and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-12 with Mathematics categories.
This book offers an introduction to the mathematical, probabilistic and numerical methods used in the modern theory of option pricing. The text is designed for readers with a basic mathematical background. The first part contains a presentation of the arbitrage theory in discrete time. In the second part, the theories of stochastic calculus and parabolic PDEs are developed in detail and the classical arbitrage theory is analyzed in a Markovian setting by means of of PDEs techniques. After the martingale representation theorems and the Girsanov theory have been presented, arbitrage pricing is revisited in the martingale theory optics. General tools from PDE and martingale theories are also used in the analysis of volatility modeling. The book also contains an Introduction to Lévy processes and Malliavin calculus. The last part is devoted to the description of the numerical methods used in option pricing: Monte Carlo, binomial trees, finite differences and Fourier transform.
Stochastic Analysis For Finance With Simulations
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Author : Geon Ho Choe
language : en
Publisher: Springer
Release Date : 2016-07-22
Stochastic Analysis For Finance With Simulations written by Geon Ho Choe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-22 with Mathematics categories.
This book is an introduction to stochastic analysis and quantitative finance; it includes both theoretical and computational methods. Topics covered are stochastic calculus, option pricing, optimal portfolio investment, and interest rate models. Also included are simulations of stochastic phenomena, numerical solutions of the Black–Scholes–Merton equation, Monte Carlo methods, and time series. Basic measure theory is used as a tool to describe probabilistic phenomena. The level of familiarity with computer programming is kept to a minimum. To make the book accessible to a wider audience, some background mathematical facts are included in the first part of the book and also in the appendices. This work attempts to bridge the gap between mathematics and finance by using diagrams, graphs and simulations in addition to rigorous theoretical exposition. Simulations are not only used as the computational method in quantitative finance, but they can also facilitate an intuitive and deeper understanding of theoretical concepts. Stochastic Analysis for Finance with Simulations is designed for readers who want to have a deeper understanding of the delicate theory of quantitative finance by doing computer simulations in addition to theoretical study. It will particularly appeal to advanced undergraduate and graduate students in mathematics and business, but not excluding practitioners in finance industry.