Computation of Greeks Using the Discrete Malliavin Calculus and Binomial Tree PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Computation of Greeks Using the Discrete Malliavin Calculus and Binomial Tree PDF full book. Access full book title Computation of Greeks Using the Discrete Malliavin Calculus and Binomial Tree by Yoshifumi Muroi. Download full books in PDF and EPUB format.
Author: Yoshifumi Muroi
Publisher: Springer Nature
ISBN: 9811910731
Category : Mathematics
Languages : en
Pages : 113
Get Book Here
Book Description
This book presents new computation schemes for the sensitivity of options using the binomial tree and introduces readers to the discrete Malliavin calculus. It also shows that applications of the discrete Malliavin calculus approach to the binomial tree model offer fundamental tools for computing Greeks. The binomial tree approach is one of the most popular methods in option pricing. Although it is a fairly traditional model for option pricing, it is still widely used in financial institutions since it is tractable and easy to understand. However, the book shows that the tree approach also offers a powerful tool for deriving the Greeks for options. Greeks are quantities that represent the sensitivities of the price of derivative securities with respect to changes in the underlying asset price or parameters. The Malliavin calculus, the stochastic methods of variations, is one of the most popular tools used to derive Greeks. However, it is also very difficult to understand for most students and practitioners because it is based on complex mathematics. To help readers more easily understand the Malliavin calculus, the book introduces the discrete Malliavin calculus, a theory of the functional for the Bernoulli random walk. The discrete Malliavin calculus is significantly easier to understand, because the functional space of the Bernoulli random walk is realized in a finite dimensional space. As such, it makes this valuable tool far more accessible for a broad readership.
Author: Yoshifumi Muroi
Publisher: Springer Nature
ISBN: 9811910731
Category : Mathematics
Languages : en
Pages : 113
Get Book Here
Book Description
This book presents new computation schemes for the sensitivity of options using the binomial tree and introduces readers to the discrete Malliavin calculus. It also shows that applications of the discrete Malliavin calculus approach to the binomial tree model offer fundamental tools for computing Greeks. The binomial tree approach is one of the most popular methods in option pricing. Although it is a fairly traditional model for option pricing, it is still widely used in financial institutions since it is tractable and easy to understand. However, the book shows that the tree approach also offers a powerful tool for deriving the Greeks for options. Greeks are quantities that represent the sensitivities of the price of derivative securities with respect to changes in the underlying asset price or parameters. The Malliavin calculus, the stochastic methods of variations, is one of the most popular tools used to derive Greeks. However, it is also very difficult to understand for most students and practitioners because it is based on complex mathematics. To help readers more easily understand the Malliavin calculus, the book introduces the discrete Malliavin calculus, a theory of the functional for the Bernoulli random walk. The discrete Malliavin calculus is significantly easier to understand, because the functional space of the Bernoulli random walk is realized in a finite dimensional space. As such, it makes this valuable tool far more accessible for a broad readership.
Author: Jean-Luc Prigent
Publisher: Springer Science & Business Media
ISBN: 3540248315
Category : Business & Economics
Languages : en
Pages : 432
Get Book Here
Book Description
A comprehensive overview of weak convergence of stochastic processes and its application to the study of financial markets. Split into three parts, the first recalls the mathematics of stochastic processes and stochastic calculus with special emphasis on contiguity properties and weak convergence of stochastic integrals. The second part is devoted to the analysis of financial theory from the convergence point of view. The main problems, which include portfolio optimization, option pricing and hedging are examined, especially when considering discrete-time approximations of continuous-time dynamics. The third part deals with lattice- and tree-based computational procedures for option pricing both on stocks and stochastic bonds. More general discrete approximations are also introduced and detailed. Includes detailed examples.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 888
Get Book Here
Book Description
Author: Nicolas Privault
Publisher: Springer
ISBN: 3642023800
Category : Mathematics
Languages : en
Pages : 322
Get Book Here
Book Description
This monograph is an introduction to some aspects of stochastic analysis in the framework of normal martingales, in both discrete and continuous time. The text is mostly self-contained, except for Section 5.7 that requires some background in geometry, and should be accessible to graduate students and researchers having already received a basic training in probability. Prereq- sites are mostly limited to a knowledge of measure theory and probability, namely?-algebras,expectations,andconditionalexpectations.Ashortint- duction to stochastic calculus for continuous and jump processes is given in Chapter 2 using normal martingales, whose predictable quadratic variation is the Lebesgue measure. There already exists several books devoted to stochastic analysis for c- tinuous di?usion processes on Gaussian and Wiener spaces, cf. e.g. [51], [63], [65], [72], [83], [84], [92], [128], [134], [143], [146], [147]. The particular f- ture of this text is to simultaneously consider continuous processes and jump processes in the uni?ed framework of normal martingales.
Author: Marek Capiński
Publisher: Cambridge University Press
ISBN: 110700263X
Category : Business & Economics
Languages : en
Pages : 193
Get Book Here
Book Description
An excellent basis for further study. Suitable even for readers with no mathematical background.
Author: Alison Etheridge
Publisher: Cambridge University Press
ISBN: 9780521890779
Category : Business & Economics
Languages : en
Pages : 208
Get Book Here
Book Description
Finance provides a dramatic example of the successful application of mathematics to the practical problem of pricing financial derivatives. This self-contained text is designed for first courses in financial calculus. Key concepts are introduced in the discrete time framework: proofs in the continuous-time world follow naturally. The second half of the book is devoted to financially sophisticated models and instruments. A valuable feature is the large number of exercises and examples, designed to test technique and illustrate how the methods and concepts are applied to realistic financial questions.
Author: Andrea Pascucci
Publisher: Springer Science & Business Media
ISBN: 8847017815
Category : Mathematics
Languages : en
Pages : 727
Get Book Here
Book Description
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.
Author: Marco Avellaneda
Publisher: World Scientific
ISBN: 9789810246938
Category : Mathematics
Languages : en
Pages : 372
Get Book Here
Book Description
Contains lectures presented at the Courant Institute's Mathematical Finance Seminar.
Author: Rüdiger U. Seydel
Publisher: Springer Science & Business Media
ISBN: 1447129938
Category : Mathematics
Languages : en
Pages : 440
Get Book Here
Book Description
The disciplines of financial engineering and numerical computation differ greatly, however computational methods are used in a number of ways across the field of finance. It is the aim of this book to explain how such methods work in financial engineering; specifically the use of numerical methods as tools for computational finance. By concentrating on the field of option pricing, a core task of financial engineering and risk analysis, this book explores a wide range of computational tools in a coherent and focused manner and will be of use to the entire field of computational finance. Starting with an introductory chapter that presents the financial and stochastic background, the remainder of the book goes on to detail computational methods using both stochastic and deterministic approaches. Now in its fifth edition, Tools for Computational Finance has been significantly revised and contains: A new chapter on incomplete markets which links to new appendices on Viscosity solutions and the Dupire equation; Several new parts throughout the book such as that on the calculation of sensitivities (Sect. 3.7) and the introduction of penalty methods and their application to a two-factor model (Sect. 6.7) Additional material in the field of analytical methods including Kim’s integral representation and its computation Guidelines for comparing algorithms and judging their efficiency An extended chapter on finite elements that now includes a discussion of two-asset options Additional exercises, figures and references Written from the perspective of an applied mathematician, methods are introduced as tools within the book for immediate and straightforward application. A ‘learning by calculating’ approach is adopted throughout this book enabling readers to explore several areas of the financial world. Interdisciplinary in nature, this book will appeal to advanced undergraduate students in mathematics, engineering and other scientific disciplines as well as professionals in financial engineering.
Author: Louis Bachelier
Publisher: Princeton University Press
ISBN: 1400829305
Category : Business & Economics
Languages : en
Pages : 205
Get Book Here
Book Description
March 29, 1900, is considered by many to be the day mathematical finance was born. On that day a French doctoral student, Louis Bachelier, successfully defended his thesis Théorie de la Spéculation at the Sorbonne. The jury, while noting that the topic was "far away from those usually considered by our candidates," appreciated its high degree of originality. This book provides a new translation, with commentary and background, of Bachelier's seminal work. Bachelier's thesis is a remarkable document on two counts. In mathematical terms Bachelier's achievement was to introduce many of the concepts of what is now known as stochastic analysis. His purpose, however, was to give a theory for the valuation of financial options. He came up with a formula that is both correct on its own terms and surprisingly close to the Nobel Prize-winning solution to the option pricing problem by Fischer Black, Myron Scholes, and Robert Merton in 1973, the first decisive advance since 1900. Aside from providing an accurate and accessible translation, this book traces the twin-track intellectual history of stochastic analysis and financial economics, starting with Bachelier in 1900 and ending in the 1980s when the theory of option pricing was substantially complete. The story is a curious one. The economic side of Bachelier's work was ignored until its rediscovery by financial economists more than fifty years later. The results were spectacular: within twenty-five years the whole theory was worked out, and a multibillion-dollar global industry of option trading had emerged.
