# financial-calculus

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## Financial Calculus

**Author :**Martin Baxter

**ISBN :**0521552893

**Genre :**Business & Economics

**File Size :**78. 19 MB

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A rigorous introduction to the mathematics of pricing, construction and hedging of derivative securities.

## A Course In Financial Calculus

**Author :**Alison Etheridge

**ISBN :**0521890772

**Genre :**Business & Economics

**File Size :**77. 74 MB

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## Financial Calculus With Applications

**Author :**Erio Castagnoli

**ISBN :**8823821746

**Genre :**Business & Economics

**File Size :**46. 54 MB

**Format :**PDF

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## A Course In Financial Calculus

**Author :**Alison Etheridge

**ISBN :**9781139434553

**Genre :**Mathematics

**File Size :**89. 15 MB

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Finance provides a dramatic example of the successful application of advanced mathematical techniques to the practical problem of pricing financial derivatives. This self-contained 2002 text is designed for first courses in financial calculus aimed at students with a good background in mathematics. Key concepts such as martingales and change of measure are introduced in the discrete time framework, allowing an accessible account of Brownian motion and stochastic calculus: proofs in the continuous-time world follow naturally. The Black-Scholes pricing formula is first derived in the simplest financial context. The second half of the book is then devoted to increasing the financial sophistication of the models and instruments. The final chapter introduces more advanced topics including stock price models with jumps, and stochastic volatility. A valuable feature is the large number of exercises and examples, designed to test technique and illustrate how the methods and concepts can be applied to realistic financial questions.

## Elementary Stochastic Calculus With Finance In View

**Author :**Thomas Mikosch

**ISBN :**9810235437

**Genre :**Mathematics

**File Size :**22. 86 MB

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Modelling with the Ito integral or stochastic differential equations has become increasingly important in various applied fields, including physics, biology, chemistry and finance. However, stochastic calculus is based on a deep mathematical theory. This book is suitable for the reader without a deep mathematical background. It gives an elementary introduction to that area of probability theory, without burdening the reader with a great deal of measure theory. Applications are taken from stochastic finance. In particular, the Black -- Scholes option pricing formula is derived. The book can serve as a text for a course on stochastic calculus for non-mathematicians or as elementary reading material for anyone who wants to learn about Ito calculus and/or stochastic finance.

## Financial Calculus

**Author :**Martin Baxter

**ISBN :**1139648780

**Genre :**BUSINESS & ECONOMICS

**File Size :**57. 77 MB

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The first rigorous and accessible account of the mathematics behind the pricing, construction, and hedging of derivative securities, this book explains, with mathematical precision and in a style tailored for market practitioners, such key concepts as martingales, change of measure, and the Heath-Jarrow-Morton model. A full Glossary of probabilistic and financial terms is provided along with graphical illustrations with realistic data.

## Stochastic Calculus And Financial Applications

**Author :**J. Michael Steele

**ISBN :**9781468493054

**Genre :**Mathematics

**File Size :**37. 61 MB

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Stochastic calculus has important applications to mathematical finance. This book will appeal to practitioners and students who want an elementary introduction to these areas. From the reviews: "As the preface says, ‘This is a text with an attitude, and it is designed to reflect, wherever possible and appropriate, a prejudice for the concrete over the abstract’. This is also reflected in the style of writing which is unusually lively for a mathematics book." --ZENTRALBLATT MATH

## Theory Of Financial Risk And Derivative Pricing

**Author :**Jean-Philippe Bouchaud

**ISBN :**0521819164

**Genre :**Business & Economics

**File Size :**65. 28 MB

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This 2003 book summarizes theoretical developments in statistical tools to measure financial markets, for students and professionals in econophysics and analytical markets.

## Islamic Finance

**Author :**Mahmoud A. El-Gamal

**ISBN :**9781139457163

**Genre :**Business & Economics

**File Size :**65. 56 MB

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This book provides an overview of the practice of Islamic finance and the historical roots that define its modes of operation. The focus of the book is analytical and forward-looking. It shows that Islamic finance exists mainly as a form of rent-seeking legal-arbitrage. In every aspect of finance - from personal loans to investment banking, and from market structure to corporate governance - Islamic finance aims to replicate in Islamic forms the substantive functions of contemporary financial instruments, markets, and institutions. By attempting to replicate the substance of contemporary financial practice using pre-modern contract forms, Islamic finance has arguably failed to serve the objectives of Islamic law. This book proposes refocusing Islamic finance on substance rather than form. This approach would entail abandoning the paradigm of 'Islamization' of every financial practice. It would also entail reorienting the brand-name of Islamic finance to emphasize issues of community banking, micro-finance, and socially responsible investment.

## Financial Mathematics

**Author :**Giuseppe Campolieti

**ISBN :**9781439892428

**Genre :**Business & Economics

**File Size :**21. 48 MB

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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.

## Financial Mathematics

**Author :**Yuliya Mishura

**ISBN :**9780081004883

**Genre :**Business & Economics

**File Size :**59. 55 MB

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Finance Mathematics is devoted to financial markets both with discrete and continuous time, exploring how to make the transition from discrete to continuous time in option pricing. This book features a detailed dynamic model of financial markets with discrete time, for application in real-world environments, along with Martingale measures and martingale criterion and the proven absence of arbitrage. With a focus on portfolio optimization, fair pricing, investment risk, and self-finance, the authors provide numerical methods for solutions and practical financial models, enabling you to solve problems both from mathematical and from financial point of view. Calculations of Lower and upper prices, featuring practical examples The simplest functional limit theorem proved for transition from discrete to continuous time Learn how to optimize portfolio in the presence of risk factors

## Financial Derivatives

**Author :**Robert W. Kolb

**ISBN :**9780470499108

**Genre :**Business & Economics

**File Size :**34. 71 MB

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Essential insights on the various aspects of financialderivatives If you want to understand derivatives without getting boggeddown by the mathematics surrounding their pricing and valuation,Financial Derivatives is the book for you. Through in-depthinsights gleaned from years of financial experience, Robert Kolband James Overdahl clearly explain what derivatives are and how youcan prudently use them within the context of your underlyingbusiness activities. Financial Derivatives introduces you to the wide range ofmarkets for financial derivatives. This invaluable guide offers abroad overview of the different types of derivatives-futures,options, swaps, and structured products-while focusing on theprinciples that determine market prices. This comprehensiveresource also provides a thorough introduction to financialderivatives and their importance to risk management in a corporatesetting. Filled with helpful tables and charts, FinancialDerivatives offers a wealth of knowledge on futures, options,swaps, financial engineering, and structured products. Discusses what derivatives are and how you can prudentlyimplement them within the context of your underlying businessactivities Provides thorough coverage of financial derivatives and theirrole in risk management Explores financial derivatives without getting bogged down bythe mathematics surrounding their pricing and valuation This informative guide will help you unlock the incrediblepotential of financial derivatives.

## An Introduction To Financial Mathematics

**Author :**Hugo D. Junghenn

**ISBN :**9780429558962

**Genre :**Business & Economics

**File Size :**31. 58 MB

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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/.

## Stochastic Calculus For Finance I

**Author :**Steven Shreve

**ISBN :**0387249680

**Genre :**Mathematics

**File Size :**47. 17 MB

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Developed for the professional Master's program in Computational Finance at Carnegie Mellon, the leading financial engineering program in the U.S. Has been tested in the classroom and revised over a period of several years Exercises conclude every chapter; some of these extend the theory while others are drawn from practical problems in quantitative finance

## Financial Statistics And Mathematical Finance

**Author :**Ansgar Steland

**ISBN :**9781118316566

**Genre :**Business & Economics

**File Size :**48. 46 MB

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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.

## Understanding Financial Risk Management

**Author :**Angelo Corelli

**ISBN :**9781317753827

**Genre :**Business & Economics

**File Size :**84. 65 MB

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Financial Risk Management is a topic of primary importance in financial markets and, more generally, in life. Risk can be seen as an opportunity if related to the concept of compensative return. It is therefore important to learn how to measure and control risk, in order to get exposure to as much risk as is necessary to achieve some level of compensation, without further useless exposure. This book analyses the various types of financial risk a financial institution faces in everyday operations. Each type of risk is dealt with using a rigorous mix of analytical and theoretical approach, describing all the major models available in the literature, with an innovative look at the topic. This book covers the following aspects of risks and provides introductory overviews the most relevant statistical and mathematical tools: Market Risk Interest Rate Risk Credit Risk Liquidity Risk Operational Risk Currency Risk Volatility Risk Understanding Financial Risk Management offers an innovative approach to financial risk management. With a broad view of theory and the industry, it aims at being a friendly, but serious, starting point for those who encounter risk management for the first time, as well as for more advanced users.

## Actuarial Finance

**Author :**Mathieu Boudreault

**ISBN :**9781119137009

**Genre :**Mathematics

**File Size :**79. 57 MB

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A new textbook offering a comprehensive introduction to models and techniques for the emerging field of actuarial Finance Drs. Boudreault and Renaud answer the need for a clear, application-oriented guide to the growing field of actuarial finance with this volume, which focuses on the mathematical models and techniques used in actuarial finance for the pricing and hedging of actuarial liabilities exposed to financial markets and other contingencies. With roots in modern financial mathematics, actuarial finance presents unique challenges due to the long-term nature of insurance liabilities, the presence of mortality or other contingencies and the structure and regulations of the insurance and pension markets. Motivated, designed and written for and by actuaries, this book puts actuarial applications at the forefront in addition to balancing mathematics and finance at an adequate level to actuarial undergraduates. While the classical theory of financial mathematics is discussed, the authors provide a thorough grounding in such crucial topics as recognizing embedded options in actuarial liabilities, adequately quantifying and pricing liabilities, and using derivatives and other assets to manage actuarial and financial risks. Actuarial applications are emphasized and illustrated with about 300 examples and 200 exercises. The book also comprises end-of-chapter point-form summaries to help the reader review the most important concepts. Additional topics and features include: Compares pricing in insurance and financial markets Discusses event-triggered derivatives such as weather, catastrophe and longevity derivatives and how they can be used for risk management; Introduces equity-linked insurance and annuities (EIAs, VAs), relates them to common derivatives and how to manage mortality for these products Introduces pricing and replication in incomplete markets and analyze the impact of market incompleteness on insurance and risk management; Presents immunization techniques alongside Greeks-based hedging; Covers in detail how to delta-gamma/rho/vega hedge a liability and how to rebalance periodically a hedging portfolio. This text will prove itself a firm foundation for undergraduate courses in financial mathematics or economics, actuarial mathematics or derivative markets. It is also highly applicable to current and future actuaries preparing for the exams or actuary professionals looking for a valuable addition to their reference shelf. As of 2019, the book covers significant parts of the Society of Actuaries’ Exams FM, IFM and QFI Core, and the Casualty Actuarial Society’s Exams 2 and 3F. It is assumed the reader has basic skills in calculus (differentiation and integration of functions), probability (at the level of the Society of Actuaries’ Exam P), interest theory (time value of money) and, ideally, a basic understanding of elementary stochastic processes such as random walks.

## Handbook Of Financial Econometrics Mathematics Statistics And Machine Learning In 4 Volumes

**Author :**Cheng-few Lee

**ISBN :**9789811202407

**Genre :**Business & Economics

**File Size :**69. 29 MB

**Format :**PDF, Kindle

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This four-volume handbook covers important concepts and tools used in the fields of financial econometrics, mathematics, statistics, and machine learning. Econometric methods have been applied in asset pricing, corporate finance, international finance, options and futures, risk management, and in stress testing for financial institutions. This handbook discusses a variety of econometric methods, including single equation multiple regression, simultaneous equation regression, and panel data analysis, among others. It also covers statistical distributions, such as the binomial and log normal distributions, in light of their applications to portfolio theory and asset management in addition to their use in research regarding options and futures contracts.In both theory and methodology, we need to rely upon mathematics, which includes linear algebra, geometry, differential equations, Stochastic differential equation (Ito calculus), optimization, constrained optimization, and others. These forms of mathematics have been used to derive capital market line, security market line (capital asset pricing model), option pricing model, portfolio analysis, and others.In recent times, an increased importance has been given to computer technology in financial research. Different computer languages and programming techniques are important tools for empirical research in finance. Hence, simulation, machine learning, big data, and financial payments are explored in this handbook.Led by Distinguished Professor Cheng Few Lee from Rutgers University, this multi-volume work integrates theoretical, methodological, and practical issues based on his years of academic and industry experience.

## Model Risk In Financial Markets

**Author :**Radu Tunaru

**ISBN :**9789814663427

**Genre :**Business & Economics

**File Size :**79. 2 MB

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The financial systems in most developed countries today build up a large amount of model risk on a daily basis. However, this is not particularly visible as the financial risk management agenda is still dominated by the subprime-liquidity crisis, the sovereign crises, and other major political events. Losses caused by model risk are hard to identify and even when they are internally identified, as such, they are most likely to be classified as normal losses due to market evolution. Model Risk in Financial Markets: From Financial Engineering to Risk Management seeks to change the current perspective on model innovation, implementation and validation. This book presents a wide perspective on model risk related to financial markets, running the gamut from financial engineering to risk management, from financial mathematics to financial statistics. It combines theory and practice, both the classical and modern concepts being introduced for financial modelling. Quantitative finance is a relatively new area of research and much has been written on various directions of research and industry applications. In this book the reader gradually learns to develop a critical view on the fundamental theories and new models being proposed. Contents:IntroductionFundamental RelationshipsModel Risk in Interest Rate ModellingArbitrage TheoryDerivatives Pricing Under UncertaintyPortfolio Selection Under UncertaintyProbability Pitfalls of Financial CalculusModel Risk in Risk Measures CalculationsParameter Estimation RiskComputational ProblemsPortfolio Selection Using Sharpe RatioBayesian Calibration for Low Frequency DataMCMC Estimation of Credit Risk MeasuresLast But Not Least. Can We Avoid the Next Big Systemic Financial Crisis?Notations for the Study of MLE for CIR Process Readership: Graduate students, researchers, practitioners, senior managers in financial institutions and hedge-funds, regulators and risk managers, who are keen to understand the pitfalls of financial modelling, and also those who are looking for a career in model validation, product control and risk management functions. Key Features:Some innovative results are presented for the first timeCovers a wide range of models, results and applications in financial markets to demonstrate that model risk is generally spreadKeywords:Model Risk;Risk Management;Financial Engineering;Financial Markets

## Financial Calculus In Matlab Portfolio Analysis And Optimization

**Author :**J. Perkins

**ISBN :**1983486531

**Genre :**

**File Size :**53. 56 MB

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The objective of this book is to deepen the functions for mathematical modeling and statistical analysis of financial data. You can optimize portfolios of financial instruments, optionally taking into account turnover and transaction costs. Also is possible to estimate risk, analyze interest rate levels, price equity and interest rate derivatives, and measure investment performance. Financial Toolbox cash-flow functions compute interest rates and rates of return, present or future values, depreciation streams, and annuities. Several functions calculate interest rates involved with cash flows. The toolbox includes functions to compute the present or future value of cash flows at regular or irregular time intervals with equal or unequal payments.These toolbox functions compute prices, sensitivities, and profits for portfolios of options or other equity derivatives. They use the Black-Scholes model for European options and the binomial model for American options. Such measures are useful for managing portfolios and for executing collars, hedges, and straddles.One of the factors to consider when selecting the optimal portfolio for a particular investor is the degree of risk aversion. This level of aversion to risk can be characterized by defining the investor's indifference curve. This curve consists of the family of risk/return pairs defining the trade-off between the expected return and the risk. It establishes the increment in return that a particular investor requires to make an increment in risk worthwhile.Portfolio optimization problems involve identifying portfolios that satisfy three criteria: Minimize a proxy for risk, Match or exceed a proxy for return and Satisfy basic feasibility requirements. Portfolios are points from a feasible set of assets that constitute an asset universe. A portfolio specifies either holdings or weights in each individual asset in the asset universe. The convention is to specify portfolios in terms of weights, although the portfolio optimization tools work with holdings as well. The set of feasible portfolios is necessarily a nonempty, closed, and bounded set. The proxy for risk is a function that characterizes either the variability or losses associated with portfolio choices. The proxy for return is a function that characterizes either thegross or net benefits associated with portfolio choices.