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Johnson W: Quantitative Finance

Quantitative Finance

Mastering Mathematical Models for Market Success

Exotic options are among the most sophisticated instruments in modern finance. This monograph provides a comprehensive mathematical framework for the pricing, hedging, and risk management of these complex derivatives. Covering a broad range of path-dependent and non-standard options, the book brings together the theoretical foundations, mathematical models, and practical techniques used in modern quantitative finance. It examines key pricing methods-including stochastic processes, risk-neutral valuation, partial differential equations (PDEs), Monte Carlo simulation, lattice methods, and numerical techniques-alongside hedging strategies, model assumptions, and practical challenges encountered in financial markets. Designed as a comprehensive review, this book serves as a valuable reference for graduate students, researchers, quantitative analysts, financial engineers, and finance professionals seeking a deeper understanding of exotic options and advanced derivative pricing. By combining mathematical rigor with practical financial applications, it offers a clear and structured overview of one of the most advanced areas of quantitative finance.

A Unified Mathematical Framework for Pricing, Hedging, and Risk Management

Exotic Options

Derivatives: Mathematical Foundations for Finance Students is written for students of finance and actuarial science who want to understand derivatives not just as formulas but as ideas that make sense. The goal is to build the mathematical foundations up step by step - starting from the familiar territory of first-year undergraduate probability and statistics and moving all the way to stochastic calculus and the principles of risk-neutral pricing, which form the heart of modern financial mathematics.This text will enable the reader to:¿ understand models of asset price behavior and apply stochastic calculus ¿ use stochastic simulations in R to investigate processes and price options ¿ price options with the binomial model ¿ derive solutions to the Black-Scholes equation using risk-neutral pricing ¿ price interest-rate derivatives using Black's model, short-rate models and the Heath-Jarrow-Morton (HJM) framework ¿ tackle quantitative finance exam questions.It incorporates a range of learning features to aid student understanding, including boxed examples, end-of-chapter summaries, selected questions from Society of Actuaries (US) Quantitative Finance examinations and further reading suggestions. The book is also supported by a suite of digital learning resources, including PowerPoint slides, multiple choice questions, instructor manual/advice document for lecturers and a test bank.This book will appeal to both undergraduate and postgraduate students who wish to understand the principles of stochastic calculus and option pricing.

Mathematical Foundations for Finance Students

Derivatives

The work carried out in many financial institutions has demonstrated that successful trading operations can be built using functional programming. However, there remains an entry barrier due to the lack of practical knowledge required to apply these techniques effectively. This book lowers that barrier by offering accessible insights that are enriched with real-world expertise.
While functional programming has been around for many decades, its benefits have become increasingly apparent in more recent years. This is due to a variety of factors, including advancements in processing speeds, the growth in the use of distributed computing, and the availability of functional programming languages on platforms which are popular in finance - particularly .NET and JVM.
The opening chapters introduce the fundamental concepts in functional programming and illustrate how these concepts are used in solving problems in the fixed income markets. As your understanding deepens, later chapters explore increasingly complex examples in areas such as valuation, risk analysis, hedging, and deal automation. The concluding chapters examine common programming patterns that arise across the solutions, including those influenced by category theory, such as functors, semigroups, monoids, and monads. At each stage, the book presents carefully selected algorithms to reinforce the practical understanding of the solutions.
In the end, this book provides an accessible introduction to the use of functional programming in the financial markets by bridging the gap between the theory of functional programming and its practical application in areas of finance.

What You Will Learn 

Develop functions for performing common financial market operations, such as valuing financial assets, calculating risks, hedging those risks, and automating buy/sell decisions.

Use functional programming to extract business insights from large datasets using numerical and statistical techniques. 

Effectively apply various functional programming features, such as recursion, higher-order functions, and list processing, in creating these solutions




Who This Book Is For
Aspiring professionals entering the financial markets; professional software engineers seeking a deeper understanding of how functional programming is utilized in modern capital markets; and finance professionals (including traders, risk managers, and other business users) who want to grasp the implementation details behind the "black box" tools they rely on in their day to day lives.

The work carried out in many financial institutions has demonstrated that successful trading operations can be built using functional programming. However, there remains an entry barrier due to the lack of practical knowledge required to apply these techniques effectively. This book lowers that barrier by offering accessible insights that are enriched with real-world expertise.While functional programming has been around for many decades, its benefits have become increasingly apparent in more recent years. This is due to a variety of factors, including advancements in processing speeds, the growth in the use of distributed computing, and the availability of functional programming languages on platforms which are popular in finance - particularly .NET and JVM.The opening chapters introduce the fundamental concepts in functional programming and illustrate how these concepts are used in solving problems in the fixed income markets. As your understanding deepens, later chapters explore increasingly complex examples in areas such as valuation, risk analysis, hedging, and deal automation. The concluding chapters examine common programming patterns that arise across the solutions, including those influenced by category theory, such as functors, semigroups, monoids, and monads. At each stage, the book presents carefully selected algorithms to reinforce the practical understanding of the solutions.In the end, this book provides an accessible introduction to the use of functional programming in the financial markets by bridging the gap between the theory of functional programming and its practical application in areas of finance.What You Will Learn&nbsp;<ul><li>Develop functions for performing common financial market operations, such as valuing financial assets, calculating risks, hedging those risks, and automating buy/sell decisions.</li><li>Use functional programming to extract business insights from large datasets using numerical and statistical techniques.&nbsp;</li><li>Effectively apply various functional programming features, such as recursion, higher-order functions, and list processing, in creating these solutions</li></ul>Who This Book Is ForAspiring professionals entering the financial markets; professional software engineers seeking a deeper understanding of how functional programming is utilized in modern capital markets; and finance professionals (including traders, risk managers, and other business users) who want to grasp the implementation details behind the "black box" tools they rely on in their day to day lives.

A Practical Guide to Solving Analytical Problems

Functional Programming in Financial Markets

ML Values Autocall Derivatives

Every twenty-four hours, more than five trillion dollars in global payments-from oil shipments and commodity trades to sovereign debt coupons-must touch a handful of clearinghouses in lower Manhattan. This invisible plumbing, the legacy of Bretton Woods and the petrodollar accord, is the foundation of the modern world economy. But what appears to be a system of elegant efficiency hides a catastrophic vulnerability: the entire architecture of global commerce flows through a single, narrow American vein.
In The Dollar Fault Line, financial analyst Josh Luberisse delivers a bracing and meticulously researched warning that the world is not merely dollar-centric; it is dollar-dependent. This dependency has created a single point of failure that exposes every nation to the whims of Federal Reserve policy, the shocks of Wall Street risk appetite, and the turmoil of American domestic politics. The next great financial rupture, he argues, will not be an American export alone but a global self-inflicted wound.
Luberisse takes readers deep inside the system's plumbing, from the real-time ledgers of Fedwire and CHIPS to the off-balance-sheet alchemy of FX swaps and repos that create trillions in "synthetic dollars" beyond regulatory radar. He reveals how this centralized architecture grants Washington extraordinary geopolitical leverage-turning sanctions into a financial chokehold -while simultaneously forcing the Federal Reserve to act as the reluctant offshore lender of last resort to the entire planet.
But this elegant design is deceptively brittle. The Dollar Fault Line demonstrates how new, non-market catalysts like climate-driven insurance losses, cyber-attacks on payment rails, and legislative gridlock over the U.S. debt ceiling can trigger liquidity cascades at lightning speed. A political showdown on Capitol Hill or a ransomware attack in New Jersey is no longer a local event; it is an instant global margin call.
Tracing the urgent, yet fledgling, search for redundancy-from China's renminbi rails and Europe's digital euro to multilateral CBDC projects like mBridge -Luberisse maps the immense "transitional pain" and political hurdles that stand in the way of a safer, multipolar system.
Authoritative, urgent, and unmissable, The Dollar Fault Line is the definitive account of the dollar's precarious dominance. It reveals a system whose unrivaled influence is now matched only by its unavoidable exposure, leaving readers with the unsettling recognition that the world's financial lifeboat is tethered to a single captain whose own vessel is navigating increasingly stormy seas.

How America's Currency Became the World's Single Point of Failure

The Dollar Fault Line

Barwertkalküle erfordern Prognosen künftiger Zahlungsströme oder Gewinne, haben sich zur vorherrschenden Bewertungsmethodik entwickelt und kommen immer häufiger zur Anwendung. In dieser Arbeit werden ausgewählte quantitative Prognoseverfahren aufgezeigt, empirisch evaluiert und daraus Empfehlungen für die Anwendung innerhalb der Rechnungslegung sowie für die Unternehmensbewertung abgeleitet. Betrachtet werden etablierte sowie neuere Methoden aus dem Bereich des maschinellen Lernens. Darüber hinaus werden die Prognosefelder der handelsrechtlichen und internationalen Rechnungslegung sowie die Auswirkungen von Rechnungslegungspolitik evaluiert. Die Untersuchungen liefern wichtige Erkenntnisse für die Unternehmensanalyse auf Basis von Daten der Finanzberichterstattung und die Ermittlung von Unternehmenswerten. Der Autor empfiehlt zudem methodische Vorgaben für Prognosen in der externen Unternehmensrechnung.

Barwertkalküle erfordern Prognosen künftiger Zahlungsströme oder Gewinne, haben sich zur vorherrschenden Bewertungsmethodik entwickelt und kommen immer häufiger zur Anwendung. In dieser Arbeit werden ausgewählte quantitative Prognoseverfahren aufgezeigt, empirisch evaluiert und daraus Empfehlungen für die Anwendung innerhalb der Rechnungslegung sowie für die Unternehmensbewertung abgeleitet. Betrachtet werden etablierte sowie neuere Methoden aus dem Bereich des maschinellen Lernens. Darüber hinaus werden die Prognosefelder der handelsrechtlichen und internationalen Rechnungslegung sowie die Auswirkungen von Rechnungslegungspolitik evaluiert. Die Untersuchungen liefern wichtige Erkenntnisse für die Unternehmensanalyse auf Basis von Daten der Finanzberichterstattung und die Ermittlung von Unternehmenswerten. Der Autor empfiehlt zudem methodische Vorgaben für Prognosen in der externen Unternehmensrechnung.&nbsp;

Methoden für die Prognose von Cashflows und Gewinnen zur Analyse und Bewertung

Quantitative Prognosen in der externen Unternehmensrechnung

Mathematics and Statistics (R0)

Syouji Nakamura

Katsushige Sawaki

Toshio Nakagawa

Including Applications to Reliability Models

Probability and Statistical Models in Operations Research, Computer and Management Sciences

Economics and Finance (R0)

&lt;p class="xparagraph" style="margin: 0cm; margin-bottom: .0001pt;"&gt;&lt;span class="xnormaltextrun"&gt;&lt;span lang="EN-GB" style="mso-ansi-language: EN-GB;"&gt;Callable mortgage bonds are utilized by individuals and companies to finance the purchase of real estate, and this asset class therefore plays a crucial role in modern society. Callable mortgage bonds constitute an enormous asset class and often offer long-term stable investments that are very attractive for pension funds.&lt;/span&gt;&lt;/span&gt;&lt;span class="xeop"&gt;&amp;nbsp;&lt;/span&gt;&lt;/p&gt;
&lt;p class="xparagraph" style="margin: 0cm; margin-bottom: .0001pt;"&gt;&amp;nbsp;&lt;/p&gt;
&lt;p class="xparagraph" style="margin: 0cm; margin-bottom: .0001pt; white-space: pre-wrap;"&gt;&lt;span style="font-variant-ligatures: none!important;"&gt;&lt;span class="xnormaltextrun"&gt;&lt;span lang="EN-GB" style="mso-ansi-language: EN-GB;"&gt;This book focuses on the pricing and calculation of risk numbers of callable fixed-rate mortgage bonds. Owing to the, from a financial perspective, irrational behaviour of borrowers, the pricing of these instruments usually requires the use of numerical solutions. Traditionally, it has been either a Monte Carlo simulation or a Finite Difference method. This book covers both methods and, in addition, the relatively new Fourier technique. This latter technique also creates a link between the interest rate derivatives market and the market for callable mortgage bonds. Finally, a chapter presenting a model for the valuation of a mortgage credit institute&amp;rsquo;s loan book is included.&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="xeop"&gt;&amp;nbsp;&lt;/span&gt;&lt;/p&gt;

Niels Rom

Numerical Methods and Valuation Models for Pricing and Risk Analysis

Callable Mortgage Bonds

Studienarbeit aus dem Jahr 2020 im Fachbereich BWL - Rechnungswesen, Bilanzierung, Steuern, Note: 1,0, Ernst-Moritz-Arndt-Universität Greifswald (Rechts- und Staatswissenschaftlichen Fakultät), Veranstaltung: Seminar zu Portofolio- und Risikomanagement, Sprache: Deutsch, Abstract: Im Rahmen des modernen Risikomanagements ist die Verarbeitung vieler korrelierender Einzelrisiken von Bedeutung. Die Copula-Theorie beschäftigt sich mit diesem Problem und ist Hauptgegenstand der vorliegenden Arbeit. Zunächst werden in Kapitel 2 mathematische Grundannahmen und Definitionen aufgezeigt, die auf den Arbeiten von Sklar und Fréchet-Hoeffding basieren. Im darauffolgenden Kapitel 3 werden die fundamentalen Copulas beschrieben, welche die verschiedenen Abhängigkeitsstrukturen modellieren. Kapitel 4 behandelt die Tail-Abhängigkeiten, bei denen die Verhaltensweisen der Copula-Funktionen an den äußeren Rändern definiert werden. Kapitel 5 betrachtet besonders wichtige Copula-Funktionen und ordnet diese der elliptischen und archimedischen Klasse zu. Dabei werden die in den vorherigen Kapiteln definierten Regeln und Eigenschaften auf spezielle Fälle angewendet. Ab-schließend werden die Erkenntnisse der Arbeit im Fazit zusammengefasst, wobei auch Kritik an Copula-Modellen angeführt wird. Hauptziel dieser Arbeit ist es, ein generelles Verständnis über die Copula-Theorie zu erlangen.

Copula-Theorie und Tail-Dependence im modernen Risikomanagement. Grundlagen, Typen und Anwendungen

Marc Henrard

Foundations, Evolution, Transition, and Implementation

Interest Rate Modelling in the Multi-Curve Framework

The Wiley Finance Series

An invaluable guide for fixed income practitioners, fully updated to incorporate the shift from LIBOR to SOFR Since its first edition in 2013, Fixed Income Relative Value Analysis: A Practitioner's Guide to the Theory, Tools, and Trades has become the gold standard for guides linking financial theories with practical analysis tools. The newly revised second edition reflects both the progress in statistical tools over the last decade and the impact of the transition to SOFR on swap spreads. You'll find a set of statistical and financial tools, a multitude of actual trades resulting from the application of these tools, as well as access to a companion website featuring spreadsheets illustrating some of the models contained in the book. This book covers: <ul> <li>Statistical models for quantitative market analysis, in particular mean reversion models and principal component analysis, now including the multivariate Ornstein-Uhlenbeck model.</li> <li>An in-depth approach to understanding swap spreads in theory and practice.</li> <li>A comprehensive discussion of the various basis swaps and their combinations.</li> <li>The incorporation of credit default swaps in yield curve analysis.</li> <li>A classification of option trades into three types and the appropriate analysis tools.</li> <li>Fitted curve techniques for identifying relative value among different bonds.</li> <li>A multi-factor delivery option model for bond future contracts.</li></ul>Fixed Income Relative Value Analysis has proven to be an indispensable desk reference for buy- and sell-side fixed income professionals, including traders, quantitative analysts, portfolio managers, financial engineers, fixed income salespeople with sophisticated clientele and risk managers.

An invaluable guide for fixed income practitioners, fully updated to incorporate the shift from LIBOR to SOFR

Since its first edition in 2013, Fixed Income Relative Value Analysis: A Practitioner's Guide to the Theory, Tools, and Trades has become the gold standard for guides linking financial theories with practical analysis tools. The newly revised second edition reflects both the progress in statistical tools over the last decade and the impact of the transition to SOFR on swap spreads.

You'll find a set of statistical and financial tools, a multitude of actual trades resulting from the application of these tools, as well as access to a companion website featuring spreadsheets illustrating some of the models contained in the book.

This book covers:
* Statistical models for quantitative market analysis, in particular mean reversion models and principal component analysis, now including the multivariate Ornstein-Uhlenbeck model.
* An in-depth approach to understanding swap spreads in theory and practice.
* A comprehensive discussion of the various basis swaps and their combinations.
* The incorporation of credit default swaps in yield curve analysis.
* A classification of option trades into three types and the appropriate analysis tools.
* Fitted curve techniques for identifying relative value among different bonds.
* A multi-factor delivery option model for bond future contracts.

Fixed Income Relative Value Analysis has proven to be an indispensable desk reference for buy- and sell-side fixed income professionals, including traders, quantitative analysts, portfolio managers, financial engineers, fixed income salespeople with sophisticated clientele and risk managers.

A Practitioner's Guide to the Theory, Tools, and Trades

Fixed Income Relative Value Analysis + Website

Das Lehrbuch behandelt Anleihen, Aktien, Immobilien sowie Optionen und weitere Produkte für die Geldanlage. Besonderes Vorwissen ist nicht vorausgesetzt. Inhalt und Aufbau entsprechen den Lehrveranstaltungen auf der Bachelor-Stufe unserer Hochschulen.
Die Kapitel 1 bis 12 stellen Grundwissen bereit. Die Themen: Geld, Werte, Liquidität, Rendite, Anleihen, Aktien, Immobilien, Finanztiefe und Finanzkrisen. Die folgenden Kapitel 13 bis 18 behandeln Themen wie Kapitalkosten, Kreditrisiken und Kapitalstruktur. Zins- und Währungsrisiken, Futures und Optionen schließen sich an.
Jedes Kapitel bietet Lernpunkte und Fragen. Das Buch endet mit einem Glossar.

utb+: Online stehen zu diesem Buch ergänzende Materialien für Dozierende sowie ein E-Learning-Kurs mit 200 Fragen und Antworten für die Prüfungsvorbereitung zur Verfügung. Erhältlich über utb.de.

Das Lehrbuch behandelt Anleihen, Aktien, Immobilien sowie Optionen und weitere Produkte für die Geldanlage. Besonderes Vorwissen ist nicht vorausgesetzt. Inhalt und Aufbau entsprechen den Lehrveranstaltungen auf der Bachelor-Stufe unserer Hochschulen.
Die Kapitel 1 bis 12 stellen Grundwissen bereit. Die Themen: Geld, Werte, Liquidität, Rendite, Anleihen, Aktien, Immobilien, Finanztiefe und Finanzkrisen. Die folgenden Kapitel 13 bis 18 behandeln Themen wie Kapitalkosten, Kreditrisiken und Kapitalstruktur. Zins- und Währungsrisiken, Futures und Optionen schließen sich an.
Jedes Kapitel bietet Lernpunkte und Fragen. Das Buch endet mit einem Glossar.


 utb+:
 Online stehen zu diesem Buch ergänzende Materialien für Dozierende sowie ein E-Learning-Kurs mit 200 Fragen und Antworten für die Prüfungsvorbereitung zur Verfügung. Erhältlich über utb.de.

Wertpapiere, Investitionen, Finanzierungen

Finanzmärkte

Quantitative Finance

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