**Author**: Alison Etheridge

**Publisher:** Cambridge University Press

**ISBN:**

**Category:** Business & Economics

**Page:** 196

**View:** 878

- 2002-08-15
- in Business & Economics
- Alison Etheridge

**Author**: Alison Etheridge

**Publisher:** Cambridge University Press

**ISBN:**

**Category:** Business & Economics

**Page:** 196

**View:** 878

Publisher Description

- 2011-11-23
- in Business & Economics
- Hugo D. Junghenn

*A First Course in Financial Mathematics*

**Author**: Hugo D. Junghenn

**Publisher:** CRC Press

**ISBN:**

**Category:** Business & Economics

**Page:** 266

**View:** 591

Option Valuation: A First Course in Financial Mathematics provides a straightforward introduction to the mathematics and models used in the valuation of financial derivatives. It examines the principles of option pricing in detail via standard binomial and stochastic calculus models. Developing the requisite mathematical background as needed, the text presents an introduction to probability theory and stochastic calculus suitable for undergraduate students in mathematics, economics, and finance. The first nine chapters of the book describe option valuation techniques in discrete time, focusing on the binomial model. The author shows how the binomial model offers a practical method for pricing options using relatively elementary mathematical tools. The binomial model also enables a clear, concrete exposition of fundamental principles of finance, such as arbitrage and hedging, without the distraction of complex mathematical constructs. The remaining chapters illustrate the theory in continuous time, with an emphasis on the more mathematically sophisticated Black-Scholes-Merton model. Largely self-contained, this classroom-tested text offers a sound introduction to applied probability through a mathematical finance perspective. Numerous examples and exercises help students gain expertise with financial calculus methods and increase their general mathematical sophistication. The exercises range from routine applications to spreadsheet projects to the pricing of a variety of complex financial instruments. Hints and solutions to odd-numbered problems are given in an appendix and a full solutions manual is available for qualifying instructors.

- 2013-07-23
- in Mathematics
- M V Tretyakov

**Author**: M V Tretyakov

**Publisher:** World Scientific Publishing Company

**ISBN:**

**Category:** Mathematics

**Page:** 276

**View:** 780

This book is an elementary introduction to the basic concepts of financial mathematics with a central focus on discrete models and an aim to demonstrate simple, but widely used, financial derivatives for managing market risks. Only a basic knowledge of probability, real analysis, ordinary differential equations, linear algebra and some common sense are required to understand the concepts considered in this book. Financial mathematics is an application of advanced mathematical and statistical methods to financial management and markets, with a main objective of quantifying and hedging risks. Since the book aims to present the basics of financial mathematics to the reader, only essential elements of probability and stochastic analysis are given to explain ideas concerning derivative pricing and hedging. To keep the reader intrigued and motivated, the book has a ‘sandwich’ structure: probability and stochastics are given in situ where mathematics can be readily illustrated by application to finance. The first part of the book introduces one of the main principles in finance — ‘no arbitrage pricing’. It also introduces main financial instruments such as forward and futures contracts, bonds and swaps, and options. The second part deals with pricing and hedging of European- and American-type options in the discrete-time setting. In addition, the concept of complete and incomplete markets is discussed. Elementary probability is briefly revised and discrete-time discrete-space stochastic processes used in financial modelling are considered. The third part introduces the Wiener process, Ito integrals and stochastic differential equations, but its main focus is the famous Black–Scholes formula for pricing European options. Some guidance for further study within this exciting and rapidly changing field is given in the concluding chapter. There are approximately 100 exercises interspersed throughout the book, and solutions for most problems are provided in the appendices.

- 2006-03-30
- in Business & Economics
- Kerry Back

*Introduction to Theory and Computation*

**Author**: Kerry Back

**Publisher:** Springer Science & Business Media

**ISBN:**

**Category:** Business & Economics

**Page:** 356

**View:** 714

"Deals with pricing and hedging financial derivatives.... Computational methods are introduced and the text contains the Excel VBA routines corresponding to the formulas and procedures described in the book. This is valuable since computer simulation can help readers understand the theory....The book...succeeds in presenting intuitively advanced derivative modelling... it provides a useful bridge between introductory books and the more advanced literature." --MATHEMATICAL REVIEWS

- 2014-03-12
- in Business & Economics
- Giuseppe Campolieti

*A Comprehensive Treatment*

**Author**: Giuseppe Campolieti

**Publisher:** CRC Press

**ISBN:**

**Category:** Business & Economics

**Page:** 829

**View:** 100

Versatile for Several Interrelated Courses at the Undergraduate and Graduate Levels Financial Mathematics: A Comprehensive Treatment provides a unified, self-contained account of the main theory and application of methods behind modern-day financial mathematics. Tested and refined through years of the authors’ teaching experiences, the book encompasses a breadth of topics, from introductory to more advanced ones. Accessible to undergraduate students in mathematics, finance, actuarial science, economics, and related quantitative areas, much of the text covers essential material for core curriculum courses on financial mathematics. Some of the more advanced topics, such as formal derivative pricing theory, stochastic calculus, Monte Carlo simulation, and numerical methods, can be used in courses at the graduate level. Researchers and practitioners in quantitative finance will also benefit from the combination of analytical and numerical methods for solving various derivative pricing problems. With an abundance of examples, problems, and fully worked out solutions, the text introduces the financial theory and relevant mathematical methods in a mathematically rigorous yet engaging way. Unlike similar texts in the field, this one presents multiple problem-solving approaches, linking related comprehensive techniques for pricing different types of financial derivatives. The book provides complete coverage of both discrete- and continuous-time financial models that form the cornerstones of financial derivative pricing theory. It also presents a self-contained introduction to stochastic calculus and martingale theory, which are key fundamental elements in quantitative finance.

- 2018-05-31
- in Mathematics
- Arlie O. Petters

*Understanding and Building Financial Intuition*

**Author**: Arlie O. Petters

**Publisher:** Springer

**ISBN:**

**Category:** Mathematics

**Page:** 483

**View:** 204

This textbook aims to fill the gap between those that offer a theoretical treatment without many applications and those that present and apply formulas without appropriately deriving them. The balance achieved will give readers a fundamental understanding of key financial ideas and tools that form the basis for building realistic models, including those that may become proprietary. Numerous carefully chosen examples and exercises reinforce the student’s conceptual understanding and facility with applications. The exercises are divided into conceptual, application-based, and theoretical problems, which probe the material deeper. The book is aimed toward advanced undergraduates and first-year graduate students who are new to finance or want a more rigorous treatment of the mathematical models used within. While no background in finance is assumed, prerequisite math courses include multivariable calculus, probability, and linear algebra. The authors introduce additional mathematical tools as needed. The entire textbook is appropriate for a single year-long course on introductory mathematical finance. The self-contained design of the text allows for instructor flexibility in topics courses and those focusing on financial derivatives. Moreover, the text is useful for mathematicians, physicists, and engineers who want to learn finance via an approach that builds their financial intuition and is explicit about model building, as well as business school students who want a treatment of finance that is deeper but not overly theoretical.

- 2008-05-07
- in Mathematics
- Daniel Michelbrink

**Author**: Daniel Michelbrink

**Publisher:** diplom.de

**ISBN:**

**Category:** Mathematics

**Page:** 96

**View:** 642

Inhaltsangabe:Introduction: The present paper is about continuous time stochastic calculus and its application to stochastic portfolio selection problems. The paper is divided into two parts: The first part provides the mathematical framework and consists of Chapters 1 and 2, where it gives an insight into the theory of stochastic process and the theory of stochastic calculus. The second part, consisting of Chapters 3 and 4, applies the first part to problems in stochastic portfolio theory and stochastic portfolio optimisation. Chapter 1, "Stochastic Processes", starts with the construction of stochastic process. The significance of Markovian kernels is discussed and some examples of process and emigroups will be given. The simple normal-distribution will be extended to the multi-variate normal distribution, which is needed for introducing the Brownian motion process. Finally, another class of stochastic process is introduced which plays a central role in mathematical finance: the martingale. Chapter 2, "Stochastic Calculus", begins with the introduction of the stochastic integral. This integral is different to the Lebesgue-Stieltjes integral because of the randomness of the integrand and integrator. This is followed by the probably most important theorem in stochastic calculus: It o s formula. It o s formula is of central importance and most of the proofs of Chapters 3 and 4 are not possible without it. We continue with the notion of a stochastic differential equations. We introduce strong and weak solutions and a way to solve stochastic differential equations by removing the drift. The last section of Chapter 2 applies stochastic calculus to stochastic control. We will need stochastic control to solve some portfolio problems in Chapter 4. Chapter 3, "Stochastic Portfolio Theory", deals mainly with the problem of introducing an appropriate model for stock prices and portfolios. These models will be needed in Chapter 4. The first section of Chapter 3 introduces a stock market model, portfolios, the risk-less asset, consumption and labour income processes. The second section, Section 3.2, introduces the notion of relative return as well as portfolio generating functions. Relative return finds application in Chapter 4 where we deal with benchmark optimisation. Benchmark optimisation is optimising a portfolio with respect to a given benchmark portfolio. The final section of Chapter 3 contains some considerations about the long-term behaviour of [...]

- 2019-03-14
- in Business & Economics
- Hugo D. Junghenn

*Option Valuation*

**Author**: Hugo D. Junghenn

**Publisher:** CRC Press

**ISBN:**

**Category:** Business & Economics

**Page:** 304

**View:** 629

Introduction to Financial Mathematics: Option Valuation, Second Edition is a well-rounded primer to the mathematics and models used in the valuation of financial derivatives. The book consists of fifteen chapters, the first ten of which develop option valuation techniques in discrete time, the last five describing the theory in continuous time. The first half of the textbook develops basic finance and probability. The author then treats the binomial model as the primary example of discrete-time option valuation. The final part of the textbook examines the Black-Scholes model. The book is written to provide a straightforward account of the principles of option pricing and examines these principles in detail using standard discrete and stochastic calculus models. Additionally, the second edition has new exercises and examples, and includes many tables and graphs generated by over 30 MS Excel VBA modules available on the author’s webpage https://home.gwu.edu/~hdj/.

- 2013-12-01
- in Mathematics
- Steven Roman

*From Risk Management to Options Pricing*

**Author**: Steven Roman

**Publisher:** Springer Science & Business Media

**ISBN:**

**Category:** Mathematics

**Page:** 356

**View:** 487

An elementary introduction to probability and mathematical finance including a chapter on the Capital Asset Pricing Model (CAPM), a topic that is very popular among practitioners and economists. Dr. Roman has authored 32 books, including a number of books on mathematics, such as Coding and Information Theory, Advanced Linear Algebra, and Field Theory, published by Springer-Verlag.

- 2012-06-21
- in Business & Economics
- Ansgar Steland

*Methods, Models and Applications*

**Author**: Ansgar Steland

**Publisher:** John Wiley & Sons

**ISBN:**

**Category:** Business & Economics

**Page:** 400

**View:** 514

Mathematical finance has grown into a huge area of research which requires a lot of care and a large number of sophisticated mathematical tools. Mathematically rigorous and yet accessible to advanced level practitioners and mathematicians alike, it considers various aspects of the application of statistical methods in finance and illustrates some of the many ways that statistical tools are used in financial applications. Financial Statistics and Mathematical Finance: Provides an introduction to the basics of financial statistics and mathematical finance. Explains the use and importance of statistical methods in econometrics and financial engineering. Illustrates the importance of derivatives and calculus to aid understanding in methods and results. Looks at advanced topics such as martingale theory, stochastic processes and stochastic integration. Features examples throughout to illustrate applications in mathematical and statistical finance. Is supported by an accompanying website featuring R code and data sets. Financial Statistics and Mathematical Finance introduces the financial methodology and the relevant mathematical tools in a style that is both mathematically rigorous and yet accessible to advanced level practitioners and mathematicians alike, both graduate students and researchers in statistics, finance, econometrics and business administration will benefit from this book.

- 2004-07-05
- in Mathematics
- David Applebaum

**Author**: David Applebaum

**Publisher:** Cambridge University Press

**ISBN:**

**Category:** Mathematics

**Page:** 384

**View:** 901

Publisher Description

- 2016-07-14
- in Mathematics
- Geon Ho Choe

**Author**: Geon Ho Choe

**Publisher:** Springer

**ISBN:**

**Category:** Mathematics

**Page:** 657

**View:** 911

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.

- 2017-02-27
- in Business & Economics
- Cho, Seung Mo

**Author**: Cho, Seung Mo

**Publisher:** 주식회사 부크크

**ISBN:**

**Category:** Business & Economics

**Page:** 100

**View:** 928

Modern finance theory is vast and deep with various academic bases such as microeconomics, econometrics, probability theory, stochastic calculus, psychology, sociology, political economy, etc. depending on the specific research theme. Among those bases, this book is adopting probability theory and stochastic calculus to present some of the main contents of finance in a very concise manner. As a matter of fact, the objective of this book is to show, as concisely as possible, how probability and stochastic calculus is closely related to modern mathematical finance. So the organization of the book is to present theories of probability first and then their related financial theories later within each of the chapters in the theorem-proof style. From my past experience, students with a quantitative background prefer mathematical symbols to normal English sentences especially in case they are not native speakers of English. So I have tried to minimize the use of English sentences. This book is intended for upper level undergraduate courses and introductory graduate courses in mathematical finance for a single semester. This book can also be used for self-studying students with proper prerequisite knowledge. The only prerequisite for this book is one year courses of calculus.

- 2020-03-30T16:47:00+02:00
- in Business & Economics
- Erio Castagnoli

*With Applications*

**Author**: Erio Castagnoli

**Publisher:** EGEA spa

**ISBN:**

**Category:** Business & Economics

**Page:** 226

**View:** 534

This volume deals with traditional financial mathematics, at times presented in a critical and provocative way. We are convinced that even with the recent and rapid developments of mathematical finance, the topics we consider here continue to be of interest in terms of their applications and in constructing a general framework of financial evaluation. This volume contains an introduction to two themes – interest rate term structure and financial immunization – that are more modern and market-oriented. Several exercises have also been added: their use should facilitate self-verification of learning without the need for further material.

- 2013-10-18
- in Mathematics
- Alexander D. Kolesnik

**Author**: Alexander D. Kolesnik

**Publisher:** Springer Science & Business Media

**ISBN:**

**Category:** Mathematics

**Page:** 128

**View:** 202

The telegraph process is a useful mathematical model for describing the stochastic motion of a particle that moves with finite speed on the real line and alternates between two possible directions of motion at random time instants. That is why it can be considered as the finite-velocity counterpart of the classical Einstein-Smoluchowski's model of the Brownian motion in which the infinite speed of motion and the infinite intensity of the alternating directions are assumed. The book will be interesting to specialists in the area of diffusion processes with finite speed of propagation and in financial modelling. It will also be useful for students and postgraduates who are taking their first steps in these intriguing and attractive fields.

- 2004-03
- in Business & Economics
- Frank Reize

*An Empirical Study*

**Author**: Frank Reize

**Publisher:** Springer Science & Business Media

**ISBN:**

**Category:** Business & Economics

**Page:** 241

**View:** 446

The book presents an analysis of the transition from unemployment to self-employment and its subsidisation with the so-called "bridging allowance" in Germany. On the basis of econometric models, the determinants and the success of self-employment among former unemployed are estimated at the individual as well as at the firm level. By comparing different groups of the formerly unemployed, it becomes evident that self-employment is one successful route out of unemployment, as self-employment proves to be more stable than paid-employment. Therefore, the bridging allowance reaches its aim of regaining stable employment for the unemployed. However, this programme fails to create additional employment in the newly founded firms.

- 2011-03-01
- in Business & Economics
- Riccardo Rebonato

*Pricing, Calibration and Hedging for Complex Interest-Rate Derivatives*

**Author**: Riccardo Rebonato

**Publisher:** John Wiley & Sons

**ISBN:**

**Category:** Business & Economics

**Page:** 296

**View:** 214

This book presents a major innovation in the interest rate space. It explains a financially motivated extension of the LIBOR Market model which accurately reproduces the prices for plain vanilla hedging instruments (swaptions and caplets) of all strikes and maturities produced by the SABR model. The authors show how to accurately recover the whole of the SABR smile surface using their extension of the LIBOR market model. This is not just a new model, this is a new way of option pricing that takes into account the need to calibrate as accurately as possible to the plain vanilla reference hedging instruments and the need to obtain prices and hedges in reasonable time whilst reproducing a realistic future evolution of the smile surface. It removes the hard choice between accuracy and time because the framework that the authors provide reproduces today's market prices of plain vanilla options almost exactly and simultaneously gives a reasonable future evolution for the smile surface. The authors take the SABR model as the starting point for their extension of the LMM because it is a good model for European options. The problem, however with SABR is that it treats each European option in isolation and the processes for the various underlyings (forward and swap rates) do not talk to each other so it isn't obvious how to relate these processes into the dynamics of the whole yield curve. With this new model, the authors bring the dynamics of the various forward rates and stochastic volatilities under a single umbrella. To ensure the absence of arbitrage they derive drift adjustments to be applied to both the forward rates and their volatilities. When this is completed, complex derivatives that depend on the joint realisation of all relevant forward rates can now be priced. Contents THE THEORETICAL SET-UP The Libor Market model The SABR Model The LMM-SABR Model IMPLEMENTATION AND CALIBRATION Calibrating the LMM-SABR model to Market Caplet prices Calibrating the LMM/SABR model to Market Swaption Prices Calibrating the Correlation Structure EMPIRICAL EVIDENCE The Empirical problem Estimating the volatility of the forward rates Estimating the correlation structure Estimating the volatility of the volatility HEDGING Hedging the Volatility Structure Hedging the Correlation Structure Hedging in conditions of market stress

- 2003-01-01
- in Mathematics
- Nicolas Bouleau

*The Language of Dirichlet Forms*

**Author**: Nicolas Bouleau

**Publisher:** Walter de Gruyter

**ISBN:**

**Category:** Mathematics

**Page:** 244

**View:** 930

The book deals with propagation of errors on data through mathematical models with applications in finance and physics. It is interesting for scientists and practitioners when studying the sensitivity of their models to small changes in the hypotheses. The book differs from what is usually done in sensitivity analysis because it yields powerful new tools allowing to manage errors in stochastic models as those used in modern finance.

- 2006
- in

**Author**:

**Publisher:** Rozenberg Publishers

**ISBN:**

**Category:**

**Page:** 340

**View:** 671

- 2005-05-26
- in Business & Economics
- Roy E. Bailey

**Author**: Roy E. Bailey

**Publisher:** Cambridge University Press

**ISBN:**

**Category:** Business & Economics

**Page:** 528

**View:** 466

This is a concise overview of capital markets, suitable for advanced undergraduates and for graduate students in financial economics. Following a brief overview of financial markets, the text explores how the economics of uncertainty can be applied to financial decision-making.