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On Stochastic Differential Equation And Modified Black Scholes Option Pricing Model
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Book Synopsis On Stochastic Differential Equation and Modified Black-Scholes Option Pricing Model by : Yao Zheng
Download or read book On Stochastic Differential Equation and Modified Black-Scholes Option Pricing Model written by Yao Zheng and published by . This book was released on 2016 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents a theoretical analysis for option pricing in finance markets. Two modified Black-Scholes equations models are derived based on general stochastic differential equation. It is shown that one equation characterized only by volatility coefficient but another characterized by the coefficients of both drift and volatility. The constitutive conditions for the stochastic equation can be used to describe the Black-Scholes dynamic processes are established.
Book Synopsis Mathematical Modeling and Methods of Option Pricing by : Lishang Jiang
Download or read book Mathematical Modeling and Methods of Option Pricing written by Lishang Jiang and published by World Scientific. This book was released on 2005 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the perspective of partial differential equations (PDE), this book introduces the Black-Scholes-Merton's option pricing theory. A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs.
Book Synopsis Mathematical Modeling And Methods Of Option Pricing by : Lishang Jiang
Download or read book Mathematical Modeling And Methods Of Option Pricing written by Lishang Jiang and published by World Scientific Publishing Company. This book was released on 2005-07-18 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the unique perspective of partial differential equations (PDE), this self-contained book presents a systematic, advanced introduction to the Black-Scholes-Merton's option pricing theory.A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs. In particular, the qualitative and quantitative analysis of American option pricing is treated based on free boundary problems, and the implied volatility as an inverse problem is solved in the optimal control framework of parabolic equations.
Book Synopsis Introduction to Option Pricing Theory by : Gopinath Kallianpur
Download or read book Introduction to Option Pricing Theory written by Gopinath Kallianpur and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Application of Stochastic Volatility Models in Option Pricing by : Pascal Debus
Download or read book Application of Stochastic Volatility Models in Option Pricing written by Pascal Debus and published by GRIN Verlag. This book was released on 2013-09-09 with total page 59 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bachelorarbeit aus dem Jahr 2010 im Fachbereich BWL - Investition und Finanzierung, Note: 1,2, EBS Universität für Wirtschaft und Recht, Sprache: Deutsch, Abstract: The Black-Scholes (or Black-Scholes-Merton) Model has become the standard model for the pricing of options and can surely be seen as one of the main reasons for the growth of the derivative market after the model ́s introduction in 1973. As a consequence, the inventors of the model, Robert Merton, Myron Scholes, and without doubt also Fischer Black, if he had not died in 1995, were awarded the Nobel prize for economics in 1997. The model, however, makes some strict assumptions that must hold true for accurate pricing of an option. The most important one is constant volatility, whereas empirical evidence shows that volatility is heteroscedastic. This leads to increased mispricing of options especially in the case of out of the money options as well as to a phenomenon known as volatility smile. As a consequence, researchers introduced various approaches to expand the model by allowing the volatility to be non-constant and to follow a sto-chastic process. It is the objective of this thesis to investigate if the pricing accuracy of the Black-Scholes model can be significantly improved by applying a stochastic volatility model.
Book Synopsis Non-Gaussian Merton-Black-Scholes Theory by : Svetlana I. Boyarchenko
Download or read book Non-Gaussian Merton-Black-Scholes Theory written by Svetlana I. Boyarchenko and published by World Scientific. This book was released on 2002 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces an analytically tractable and computationally effective class of non-Gaussian models for shocks (regular Lvy processes of the exponential type) and related analytical methods similar to the initial Merton-Black-Scholes approach, which the authors call the Merton-Black-Scholes theory.The authors have chosen applications interesting for financial engineers and specialists in financial economics, real options, and partial differential equations (especially pseudodifferential operators); specialists in stochastic processes will benefit from the use of the pseudodifferential operators technique in non-Gaussian situations. The authors also consider discrete time analogues of perpetual American options and the problem of the optimal choice of capital, and outline several possible directions in which the methods of the book can be developed further.Taking account of a diverse audience, the book has been written in such a way that it is simple at the beginning and more technical in further chapters, so that it is accessible to graduate students in relevant areas and mathematicians without prior knowledge of finance or economics.
Book Synopsis Numerical Solution of Stochastic Differential Equations with Jumps in Finance by : Eckhard Platen
Download or read book Numerical Solution of Stochastic Differential Equations with Jumps in Finance written by Eckhard Platen and published by Springer Science & Business Media. This book was released on 2010-07-23 with total page 868 pages. Available in PDF, EPUB and Kindle. Book excerpt: In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations (1992). The present monograph builds on the above-mentioned work and provides an introduction to stochastic differential equations with jumps, in both theory and application, emphasizing the numerical methods needed to solve such equations. It presents many new results on higher-order methods for scenario and Monte Carlo simulation, including implicit, predictor corrector, extrapolation, Markov chain and variance reduction methods, stressing the importance of their numerical stability. Furthermore, it includes chapters on exact simulation, estimation and filtering. Besides serving as a basic text on quantitative methods, it offers ready access to a large number of potential research problems in an area that is widely applicable and rapidly expanding. Finance is chosen as the area of application because much of the recent research on stochastic numerical methods has been driven by challenges in quantitative finance. Moreover, the volume introduces readers to the modern benchmark approach that provides a general framework for modeling in finance and insurance beyond the standard risk-neutral approach. It requires undergraduate background in mathematical or quantitative methods, is accessible to a broad readership, including those who are only seeking numerical recipes, and includes exercises that help the reader develop a deeper understanding of the underlying mathematics.
Book Synopsis Stochastic Processes And Applications To Mathematical Finance - Proceedings Of The Ritsumeikan International Symposium by : Jiro Akahori
Download or read book Stochastic Processes And Applications To Mathematical Finance - Proceedings Of The Ritsumeikan International Symposium written by Jiro Akahori and published by World Scientific. This book was released on 2004-07-06 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains 17 articles on stochastic processes (stochastic calculus and Malliavin calculus, functionals of Brownian motions and Lévy processes, stochastic control and optimization problems, stochastic numerics, and so on) and their applications to problems in mathematical finance.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• Index to Social Sciences & Humanities Proceedings® (ISSHP® / ISI Proceedings)• Index to Social Sciences & Humanities Proceedings (ISSHP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences
Book Synopsis Stochastic Processes and Applications to Mathematical Finance by :
Download or read book Stochastic Processes and Applications to Mathematical Finance written by and published by World Scientific. This book was released on 2004 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains 17 articles on stochastic processes (stochastic calculus and Malliavin calculus, functionals of Brownian motions and L(r)vy processes, stochastic control and optimization problems, stochastic numerics, and so on) and their applications to problems in mathematical finance.The proceedings have been selected for coverage in: OCo Index to Scientific & Technical Proceedings- (ISTP- / ISI Proceedings)OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)OCo Index to Social Sciences & Humanities Proceedings- (ISSHP- / ISI Proceedings)OCo Index to Social Sciences & Humanities Proceedings (ISSHP CDROM version / ISI Proceedings)OCo CC Proceedings OCo Engineering & Physical Sciences"
Book Synopsis Stochastic Models for Fractional Calculus by : Mark M. Meerschaert
Download or read book Stochastic Models for Fractional Calculus written by Mark M. Meerschaert and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-10-21 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional calculus is a rapidly growing field of research, at the interface between probability, differential equations, and mathematical physics. It is used to model anomalous diffusion, in which a cloud of particles spreads in a different manner than traditional diffusion. This monograph develops the basic theory of fractional calculus and anomalous diffusion, from the point of view of probability. In this book, we will see how fractional calculus and anomalous diffusion can be understood at a deep and intuitive level, using ideas from probability. It covers basic limit theorems for random variables and random vectors with heavy tails. This includes regular variation, triangular arrays, infinitely divisible laws, random walks, and stochastic process convergence in the Skorokhod topology. The basic ideas of fractional calculus and anomalous diffusion are closely connected with heavy tail limit theorems. Heavy tails are applied in finance, insurance, physics, geophysics, cell biology, ecology, medicine, and computer engineering. The goal of this book is to prepare graduate students in probability for research in the area of fractional calculus, anomalous diffusion, and heavy tails. Many interesting problems in this area remain open. This book will guide the motivated reader to understand the essential background needed to read and unerstand current research papers, and to gain the insights and techniques needed to begin making their own contributions to this rapidly growing field.
Book Synopsis On the symmetries in the generalized Black-Scholes model with variable coefficients by :
Download or read book On the symmetries in the generalized Black-Scholes model with variable coefficients written by and published by GRIN Verlag. This book was released on 2020-09-01 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pre-University Paper from the year 2020 in the subject Mathematics - Stochastics, , language: English, abstract: According to previous research, the issue on the applicability of the original Black-Scholes model to the inverse quantity of price can be formulated as the argument of the symmetry between price and its inverse, whether there exists the set of real numbers as the drift and the volatility about the inverse quantity satisfying a certain system of stochastic differential equations. As the result of solving the equations in terms of such real numbers, it is revealed that there exist symmetries between not only them but also the coefficients of two equations. The aim of this article is to reveal in which cases these symmetries exist in the generalized Black-Scholes model, where the coeficients are deterministic or stochastic processes.
Book Synopsis Theoretical Development of Option Pricing Models and Comparison of Call Option Models by : Jeong Yeon Keum
Download or read book Theoretical Development of Option Pricing Models and Comparison of Call Option Models written by Jeong Yeon Keum and published by . This book was released on 1989 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Applied Stochastic Differential Equations by : Simo Särkkä
Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Book Synopsis PDE and Martingale Methods in Option Pricing by : Andrea Pascucci
Download or read book PDE and Martingale Methods in Option Pricing written by Andrea Pascucci and published by Springer Science & Business Media. This book was released on 2011-04-15 with total page 727 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Arbitrage, Hedging, and Speculation by : Ephraim Clark
Download or read book Arbitrage, Hedging, and Speculation written by Ephraim Clark and published by Bloomsbury Publishing USA. This book was released on 2004-04-30 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explains arbitrage, hedging, and speculation from the standpoint of a participant in the foreign exchange market—whether an individual trader or an institutional trader—who possesses analytical skill, economically sound judgment, and who has access to market data. In the foreign exchange market, arbitrage involves the simultaneous purchase and sale of a currency in different markets; the profit comes from the difference in the buying and selling prices. Hedging and speculation are opposing strategies for dealing with risk; hedging is a cover, and speculation is an assumption of risk. Authors also discuss futures, swaps, forward contracts, and other strategies. For financial scholars, students, analysts, and currency traders.
Book Synopsis Stochastic Calculus for Finance II by : Steven E. Shreve
Download or read book Stochastic Calculus for Finance II written by Steven E. Shreve and published by Springer Science & Business Media. This book was released on 2004-06-03 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A wonderful display of the use of mathematical probability to derive a large set of results from a small set of assumptions. In summary, this is a well-written text that treats the key classical models of finance through an applied probability approach....It should serve as an excellent introduction for anyone studying the mathematics of the classical theory of finance." --SIAM
Book Synopsis Non-linear Modifications of Black-Scholes Pricing Model with Diminishing Marginal Transaction Cost by : Kaidi Wang
Download or read book Non-linear Modifications of Black-Scholes Pricing Model with Diminishing Marginal Transaction Cost written by Kaidi Wang and published by . This book was released on 2020 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the field of quantitative financial analysis, the Black-Scholes Model has exerted significant influence on the booming of options trading strategies. Publishing in their Nobel Prize Work in 1973, the model was generated by Black and Scholes. Using Ito’s Lemma and portfolio management methodology, they employed partial differential equation to provide a theoretical estimate of the price of European-style options. This paper is interested in deriving non-linear modifications of the Black-Scholes model with diminishing marginal transaction cost.
