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Deterministic And Stochastic Topics In Computational Finance

Deterministic And Stochastic Topics In Computational Finance
Author: Ovidiu Calin
Publisher: World Scientific Publishing Company
Total Pages: 482
Release: 2016-11-25
Genre: Business & Economics
ISBN: 9813203102
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What distinguishes this book from other texts on mathematical finance is the use of both probabilistic and PDEs tools to price derivatives for both constant and stochastic volatility models, by which the reader has the advantage of computing explicitly a large number of prices for European, American and Asian derivatives.The book presents continuous time models for financial markets, starting from classical models such as Black-Scholes and evolving towards the most popular models today such as Heston and VAR.A key feature of the textbook is the large number of exercises, mostly solved, which are designed to help the reader to understand the material.The book is based on the author's lectures on topics on computational finance for senior and graduate students, delivered in USA (Princeton University and EMU), Taiwan and Kuwait. The prerequisites are an introductory course in stochastic calculus, as well as the usual calculus sequence.The book is addressed to undergraduate and graduate students in Masters of Finance programs as well as to those who wish to become more efficient in their practical applications.Topics covered:

Essentials of Stochastic Finance

Essentials of Stochastic Finance
Author: Albert N. Shiryaev
Publisher: World Scientific
Total Pages: 852
Release: 1999
Genre: Business & Economics
ISBN: 9810236050
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Readership: Undergraduates and researchers in probability and statistics; applied, pure and financial mathematics; economics; chaos.

Tools for Computational Finance

Tools for Computational Finance
Author: Rüdiger U. Seydel
Publisher: Springer Science & Business Media
Total Pages: 256
Release: 2013-06-29
Genre: Mathematics
ISBN: 3662225514
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Tools for Computational Finance offers a clear explanation of computational issues arising in financial mathematics. The new third edition is thoroughly revised and significantly extended, including an extensive new section on analytic methods, focused mainly on interpolation approach and quadratic approximation. Other new material is devoted to risk-neutrality, early-exercise curves, multidimensional Black-Scholes models, the integral representation of options and the derivation of the Black-Scholes equation. New figures, more exercises, and expanded background material make this guide a real must-to-have for everyone working in the world of financial engineering.

Mathematical Control Theory and Finance

Mathematical Control Theory and Finance
Author: Andrey Sarychev
Publisher: Springer Science & Business Media
Total Pages: 418
Release: 2009-03-31
Genre: Mathematics
ISBN: 354069532X
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Control theory provides a large set of theoretical and computational tools with applications in a wide range of ?elds, running from ”pure” branches of mathematics, like geometry, to more applied areas where the objective is to ?nd solutions to ”real life” problems, as is the case in robotics, control of industrial processes or ?nance. The ”high tech” character of modern business has increased the need for advanced methods. These rely heavily on mathematical techniques and seem indispensable for competitiveness of modern enterprises. It became essential for the ?nancial analyst to possess a high level of mathematical skills. C- versely, the complex challenges posed by the problems and models relevant to ?nance have, for a long time, been an important source of new research topics for mathematicians. The use of techniques from stochastic optimal control constitutes a well established and important branch of mathematical ?nance. Up to now, other branches of control theory have found comparatively less application in ?n- cial problems. To some extent, deterministic and stochastic control theories developed as di?erent branches of mathematics. However, there are many points of contact between them and in recent years the exchange of ideas between these ?elds has intensi?ed. Some concepts from stochastic calculus (e.g., rough paths) havedrawntheattentionofthedeterministiccontroltheorycommunity.Also, some ideas and tools usual in deterministic control (e.g., geometric, algebraic or functional-analytic methods) can be successfully applied to stochastic c- trol.

Recent Developments in Computational Finance

Recent Developments in Computational Finance
Author: Thomas Gerstner
Publisher: World Scientific
Total Pages: 481
Release: 2013
Genre: Business & Economics
ISBN: 9814436429
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Computational finance is an interdisciplinary field which joins financial mathematics, stochastics, numerics and scientific computing. Its task is to estimate as accurately and efficiently as possible the risks that financial instruments generate. This volume consists of a series of cutting-edge surveys of recent developments in the field written by leading international experts. These make the subject accessible to a wide readership in academia and financial businesses. The book consists of 13 chapters divided into 3 parts: foundations, algorithms and applications. Besides surveys of existing results, the book contains many new previously unpublished results.

Informal Introduction To Stochastic Calculus With Applications, An (Second Edition)

Informal Introduction To Stochastic Calculus With Applications, An (Second Edition)
Author: Ovidiu Calin
Publisher: World Scientific
Total Pages: 510
Release: 2021-11-15
Genre: Mathematics
ISBN: 9811247110
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Most branches of science involving random fluctuations can be approached by Stochastic Calculus. These include, but are not limited to, signal processing, noise filtering, stochastic control, optimal stopping, electrical circuits, financial markets, molecular chemistry, population dynamics, etc. All these applications assume a strong mathematical background, which in general takes a long time to develop. Stochastic Calculus is not an easy to grasp theory, and in general, requires acquaintance with the probability, analysis and measure theory.The goal of this book is to present Stochastic Calculus at an introductory level and not at its maximum mathematical detail. The author's goal was to capture as much as possible the spirit of elementary deterministic Calculus, at which students have been already exposed. This assumes a presentation that mimics similar properties of deterministic Calculus, which facilitates understanding of more complicated topics of Stochastic Calculus.The second edition contains several new features that improved the first edition both qualitatively and quantitatively. First, two more chapters have been added, Chapter 12 and Chapter 13, dealing with applications of stochastic processes in Electrochemistry and global optimization methods.This edition contains also a final chapter material containing fully solved review problems and provides solutions, or at least valuable hints, to all proposed problems. The present edition contains a total of about 250 exercises.This edition has also improved presentation from the first edition in several chapters, including new material.

Stochastic Geometric Analysis With Applications

Stochastic Geometric Analysis With Applications
Author: Ovidiu Calin
Publisher: World Scientific
Total Pages: 557
Release: 2023-11-21
Genre: Mathematics
ISBN: 981128329X
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This book is a comprehensive exploration of the interplay between Stochastic Analysis, Geometry, and Partial Differential Equations (PDEs). It aims to investigate the influence of geometry on diffusions induced by underlying structures, such as Riemannian or sub-Riemannian geometries, and examine the implications for solving problems in PDEs, mathematical finance, and related fields. The book aims to unify the relationships between PDEs, nonholonomic geometry, and stochastic processes, focusing on a specific condition shared by these areas known as the bracket-generating condition or Hörmander's condition. The main objectives of the book are:The intended audience for this book includes researchers and practitioners in mathematics, physics, and engineering, who are interested in stochastic techniques applied to geometry and PDEs, as well as their applications in mathematical finance and electrical circuits.

Tools for Computational Finance

Tools for Computational Finance
Author: Rüdiger U. Seydel
Publisher: Springer Science & Business Media
Total Pages: 440
Release: 2012-03-09
Genre: Mathematics
ISBN: 1447129938
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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.

Computation and Simulation for Finance

Computation and Simulation for Finance
Author: Cónall Kelly
Publisher: Springer
Total Pages: 0
Release: 2024-08-22
Genre: Mathematics
ISBN: 9783031605741
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This book offers an up-to-date introductory treatment of computational techniques applied to problems in finance, placing issues such as numerical stability, convergence and error analysis in both deterministic and stochastic settings at its core. The first part provides a welcoming but nonetheless rigorous introduction to the fundamental theory of option pricing, including European, American, and exotic options along with their hedge parameters, and combines a clear treatment of the mathematical framework with practical worked examples in Python. The second part explores the main computational methods for valuing options within the Black-Scholes framework: lattice, Monte Carlo, and finite difference methods. The third and final part covers advanced topics for the simulation of financial processes beyond the standard Black-Scholes setting. Techniques for the analysis and simulation of multidimensional financial data, including copulas, are covered and will be of interest to those studying machine learning for finance. There is also an in-depth treatment of exact and approximate sampling methods for stochastic differential equation models of interest rates and volatilities. Written for advanced undergraduate and masters-level courses, the book assumes some exposure to core mathematical topics such as linear algebra, ordinary differential equations, multivariate calculus, probability, and statistics at an undergraduate level. While familiarity with Python is not required, readers should be comfortable with basic programming constructs such as variables, loops, and conditional statements.

Computational Methods for Quantitative Finance

Computational Methods for Quantitative Finance
Author: Norbert Hilber
Publisher: Springer Science & Business Media
Total Pages: 301
Release: 2013-02-15
Genre: Mathematics
ISBN: 3642354017
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Many mathematical assumptions on which classical derivative pricing methods are based have come under scrutiny in recent years. The present volume offers an introduction to deterministic algorithms for the fast and accurate pricing of derivative contracts in modern finance. This unified, non-Monte-Carlo computational pricing methodology is capable of handling rather general classes of stochastic market models with jumps, including, in particular, all currently used Lévy and stochastic volatility models. It allows us e.g. to quantify model risk in computed prices on plain vanilla, as well as on various types of exotic contracts. The algorithms are developed in classical Black-Scholes markets, and then extended to market models based on multiscale stochastic volatility, to Lévy, additive and certain classes of Feller processes. This book is intended for graduate students and researchers, as well as for practitioners in the fields of quantitative finance and applied and computational mathematics with a solid background in mathematics, statistics or economics.​