{"product_id":"the-mathematics-of-derivatives-isbn-9780470047255","title":"The Mathematics of Derivatives","description":"\u003cb\u003ePraise for \u003ci\u003eThe Mathematics of Derivatives\u003c\/i\u003e\u003c\/b\u003e  \u003cp\u003e\"\u003ci\u003eThe Mathematics of Derivatives\u003c\/i\u003e provides a concise pedagogical discussion of both fundamental and very recent developments in mathematical finance, and is particularly well suited for readers with a science or engineering background. It is written from the point of view of a physicist focused on providing an understanding of the methodology and the assumptions behind derivative pricing. Navin has a unique and elegant viewpoint, and will help mathematically sophisticated readers rapidly get up to speed in the latest Wall Street financial innovations.\"\u003cbr\u003e —\u003cb\u003eDavid Montano\u003c\/b\u003e, Managing Director JPMorgan Securities\u003c\/p\u003e \u003cp\u003eA stylish and practical introduction to the key concepts in financial mathematics, this book tackles key fundamentals in the subject in an intuitive and refreshing manner whilst also providing detailed analytical and numerical schema for solving interesting derivatives pricing problems. If Richard Feynman wrote an introduction to financial mathematics, it might look similar. The problem and solution sets are first rate.\"\u003cbr\u003e —\u003cb\u003eBarry Ryan\u003c\/b\u003e, Partner Bhramavira Capital Partners, London\u003c\/p\u003e \u003cp\u003e\"This is a great book for anyone beginning (or contemplating), a career in financial research or analytic programming. Navin dissects a huge, complex topic into a series of discrete, concise, accessible lectures that combine the required mathematical theory with relevant applications to real-world markets. I wish this book was around when I started in finance. It would have saved me a lot of time and aggravation.\"\u003cbr\u003e —\u003cb\u003eLarry Magargal\u003c\/b\u003e\u003c\/p\u003e  Preface.  \u003cp\u003eAcknowledgments.\u003c\/p\u003e \u003cp\u003ePART I The Models.\u003c\/p\u003e \u003cp\u003eCHAPTER 1. Introduction to the Techniques of Derivative Modeling.\u003c\/p\u003e \u003cp\u003e1.1 Introduction.\u003c\/p\u003e \u003cp\u003e1.2 Models.\u003c\/p\u003e \u003cp\u003e1.2.1 What Is a Derivative?\u003c\/p\u003e \u003cp\u003e1.2.2 What Is a Model?\u003c\/p\u003e \u003cp\u003e1.2.3 Two Initial Methods for Modeling Derivatives.\u003c\/p\u003e \u003cp\u003e1.2.4 Price Processes.\u003c\/p\u003e \u003cp\u003e1.2.5 The Archetypal Security Process: Normal Returns.\u003c\/p\u003e \u003cp\u003e1.2.6 Book Outline.\u003c\/p\u003e \u003cp\u003eCHAPTER 2. Preliminary Mathematical Tools.\u003c\/p\u003e \u003cp\u003e2.1 Probability Distributions.\u003c\/p\u003e \u003cp\u003e2.2 \u003ci\u003en\u003c\/i\u003e-Dimensional Jacobians and \u003ci\u003en\u003c\/i\u003e-Form Algebra.\u003c\/p\u003e \u003cp\u003e2.3 Functional Analysis and Fourier Transforms.\u003c\/p\u003e \u003cp\u003e2.4 Normal (Central) Limit Theorem.\u003c\/p\u003e \u003cp\u003e2.5 Random Walks.\u003c\/p\u003e \u003cp\u003e2.6 Correlation.\u003c\/p\u003e \u003cp\u003e2.7 Functions of Two\/More Variables: Path Integrals.\u003c\/p\u003e \u003cp\u003e2.8 Differential Forms.\u003c\/p\u003e \u003cp\u003eCHAPTER 3. Stochastic Calculus.\u003c\/p\u003e \u003cp\u003e3.1 Wiener Process.\u003c\/p\u003e \u003cp\u003e3.2 Ito’s Lemma.\u003c\/p\u003e \u003cp\u003e3.3 Variable Changes to Get the Martingale.\u003c\/p\u003e \u003cp\u003e3.4 Other Processes: Multivariable Correlations.\u003c\/p\u003e \u003cp\u003eCHAPTER 4. Applications of Stochastic Calculus to Finance.\u003c\/p\u003e \u003cp\u003e4.1 Risk Premium Derivation.\u003c\/p\u003e \u003cp\u003e4.2 Analytic Formula for the Expected Payoff of a European Option.\u003c\/p\u003e \u003cp\u003eCHAPTER 5. From Stochastic Processes Formalism to Differential Equation Formalism.\u003c\/p\u003e \u003cp\u003e5.1 Backward and Forward Kolmogorov Equations.\u003c\/p\u003e \u003cp\u003e5.2 Derivation of Black-Scholes Equation, Risk-Neutral Pricing.\u003c\/p\u003e \u003cp\u003e5.3 Risks and Trading Strategies.\u003c\/p\u003e \u003cp\u003eCHAPTER 6. Understanding the Black-Scholes Equation.\u003c\/p\u003e \u003cp\u003e6.1 Black-Scholes Equation: A Type of Backward Kolmogorov Equation.\u003c\/p\u003e \u003cp\u003e6.1.1 Forward Price.\u003c\/p\u003e \u003cp\u003e6.2 Black-Scholes Equation: Risk-Neutral Pricing.\u003c\/p\u003e \u003cp\u003e6.3 Black-Scholes Equation: Relation to Risk Premium Definition.\u003c\/p\u003e \u003cp\u003e6.4 Black-Scholes Equation Applies to Currency Options: Hidden Symmetry 1.\u003c\/p\u003e \u003cp\u003e6.5 Black-Scholes Equation in Martingale Variables: Hidden Symmetry 2.\u003c\/p\u003e \u003cp\u003e6.6 Black-Scholes Equation with Stock as a ‘‘Derivative’’ of Option Price: Hidden Symmetry 3.\u003c\/p\u003e \u003cp\u003eCHAPTER 7. Interest Rate Hedging.\u003c\/p\u003e \u003cp\u003e7.1 Euler’s Relation.\u003c\/p\u003e \u003cp\u003e7.2 Interest Rate Dependence.\u003c\/p\u003e \u003cp\u003e7.3 Term-Structured Rates Hedging: Duration Bucketing.\u003c\/p\u003e \u003cp\u003e7.4 Algorithm for Deciding Which Hedging Instruments to Use.\u003c\/p\u003e \u003cp\u003eCHAPTER 8. Interest Rate Derivatives: HJM Models.\u003c\/p\u003e \u003cp\u003e8.1 Hull-White Model Derivation.\u003c\/p\u003e \u003cp\u003e8.1.1 Process and Pricing Equation.\u003c\/p\u003e \u003cp\u003e8.1.2 Analytic Zero-Coupon Bond Valuation.\u003c\/p\u003e \u003cp\u003e8.1.3 Analytic Bond Call Option.\u003c\/p\u003e \u003cp\u003e8.1.4 Calibration.\u003c\/p\u003e \u003cp\u003e8.2 Arbitrage-Free Pricing for Interest Rate Derivatives: HJM.\u003c\/p\u003e \u003cp\u003eCHAPTER 9. Differential Equations, Boundary Conditions, and Solutions.\u003c\/p\u003e \u003cp\u003e9.1 Boundary Conditions and Unique Solutions to Differential Equations.\u003c\/p\u003e \u003cp\u003e9.2 Solving the Black-Scholes or Heat Equation Analytically.\u003c\/p\u003e \u003cp\u003e9.2.1 Green’s Functions.\u003c\/p\u003e \u003cp\u003e9.2.2 Separation of Variables.\u003c\/p\u003e \u003cp\u003e9.3 Solving the Black-Scholes Equation Numerically.\u003c\/p\u003e \u003cp\u003e9.3.1 Finite Difference Methods: Explicit\/Implicit Methods, Variable Choice.\u003c\/p\u003e \u003cp\u003e9.3.2 Gaussian Kurtosis (and Skew = 0), Faster Convergence.\u003c\/p\u003e \u003cp\u003e9.3.3 Call\/Put Options:Grid Point Shift Factor for Higher Accuracy.\u003c\/p\u003e \u003cp\u003e9.3.4 Dividends on the Underlying Equity.\u003c\/p\u003e \u003cp\u003e9.3.5 American Exercise.\u003c\/p\u003e \u003cp\u003e9.3.6 2-D Models, Correlation and Variable Changes.\u003c\/p\u003e \u003cp\u003eCHAPTER 10. Credit Spreads.\u003c\/p\u003e \u003cp\u003e10.1 Credit Default Swaps (CDS) and the Continuous CDS Curve.\u003c\/p\u003e \u003cp\u003e10.2 Valuing Bonds Using the Continuous CDS Curve.\u003c\/p\u003e \u003cp\u003e10.3 Equations of Motion for Bonds and Credit Default Swaps.\u003c\/p\u003e \u003cp\u003eCHAPTER 11. Specific Models.\u003c\/p\u003e \u003cp\u003e11.1 Stochastic Rates and Default.\u003c\/p\u003e \u003cp\u003e11.2 Convertible Bonds.\u003c\/p\u003e \u003cp\u003e11.3 Index Options versus Single Name Options: Trading Equity Correlation.\u003c\/p\u003e \u003cp\u003e11.4 Max of \u003ci\u003en\u003c\/i\u003e Stocks: Trading Equity Correlation.\u003c\/p\u003e \u003cp\u003e11.5 Collateralized Debt Obligations (CDOs): Trading Credit Correlation.\u003c\/p\u003e \u003cp\u003e11.5.1 CDO Backed by Three Bonds.\u003c\/p\u003e \u003cp\u003e11.5.2 CDO Backed by an Arbitrary Number of Bonds.\u003c\/p\u003e \u003cp\u003ePART II Exercises and Solutions.\u003c\/p\u003e \u003cp\u003eCHAPTER 12. Exercises.\u003c\/p\u003e \u003cp\u003eCHAPTER 13. Solutions.\u003c\/p\u003e \u003cp\u003eAPPENDIX A: Central Limit Theorem-Plausibility Argument.\u003c\/p\u003e \u003cp\u003eAPPENDIX B: Solving for the Green’s Function of the Black-Scholes Equation.\u003c\/p\u003e \u003cp\u003eAPPENDIX C: Expanding the von Neumann Stability Mode for the Discretized Black-Scholes Equation.\u003c\/p\u003e \u003cp\u003eAPPENDIX D: Multiple Bond Survival Probabilities Given Correlated Default Probability Rates.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003eIndex.\u003c\/p\u003e  \u003cb\u003eROBERT L. NAVIN\u003c\/b\u003e founded Real Time Risk Systems LLC in July 2004. Prior to this, he helped set up a hedge fund in 2002 that grew to more than $1 billion in assets under management during its first year. Navin was previously at Highbridge Capital Management as head of quantitative analysis from 1997 to 2002. He graduated with an MS and a PhD in theoretical particle physics from the California Institute of Technology in 1993.   In the dynamic field of finance, where mathematics is playing an ever-greater role in decision making, understanding the mathematical underpinnings and implications of derivatives is an important endeavor.\u003cbr\u003e \u003cbr\u003e   \u003cp\u003eNobody knows this better than author Robert Navin, whose detailed knowledge of derivatives has allowed him to excel over the course of his financial career—as well as help those around him quickly grasp the mathematical techniques behind the modeling of derivatives. Now, in The Mathematics of Derivatives, he shares his expertise and experience with you.\u003c\/p\u003e \u003cp\u003eFilled with in-depth insights and practical advice, The Mathematics of Derivatives provides individuals involved in this industry—whether you're a quant-in-training with a background in economics or a software designer creating financial programs—with the information they need to succeed.\u003c\/p\u003e \u003cp\u003eDivided into two comprehensive parts, this well-rounded resource outlines the models—and the math—used to analyze the trading and risks of derivatives in Part One and then challenges you to master these methods through a variety of exercises in Part Two.\u003c\/p\u003e \u003cp\u003eAn array of topics are covered, including:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eThe Black-Scholes formula with modifications as well as more general ideas behind the derivation of the Black-Scholes formula\u003c\/li\u003e \u003cli\u003eRelevant mathematical tools—from distribution and integration definitions to n-Dimensional Jacobians, Path Integrals, and the Central Limit Theorem\u003c\/li\u003e \u003cli\u003eStochastic processes and their applicationsto finance\u003c\/li\u003e \u003cli\u003eNumerical algorithmic methods for solving parabolic partial differential equations (PDEs)\u003c\/li\u003e \u003cli\u003eThe simple default probability approach tocredit derivatives\u003c\/li\u003e \u003cli\u003eThe Heath-Jarrow-Morton (HJM) model, as well as some specific examples of modeling derivatives, such as convertible bonds and collateralizeddebt obligations\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eWith the information illustrated throughout these pages, you'll be able to implement the risk-neutral pricing paradigm correctly, design models of real-world processes using stochastic calculus, convert such models into a risk-neutral pricing equation with boundary conditions, numerically solve these equations with great accuracy, and much more.\u003c\/p\u003e \u003cp\u003eIn order to fully understand the pricing, hedging, and risk management issues associated with derivatives, you must first become familiar with the mathematical formalism that underlies them. Written in a straightforward and accessible style, The Mathematics of Derivatives provides you with a solid foundation in this field—and an opportunity to succeed in today's turbulent markets.\u003c\/p\u003e  Praise for The Mathematics of Derivatives\u003cbr\u003e \u003cbr\u003e   \u003cp\u003e\"The Mathematics of Derivatives provides a concise pedagogical discussion of both fundamental and very recent developments in mathematical finance, and is particularly well suited for readers with a science or engineering background. It is written from the point of view of a physicist focused on providing an understanding of the methodology and the assumptions behind derivative pricing. Navin has a unique and elegant viewpoint, and will help mathematically sophisticated readers rapidly get up to speed in the latest Wall Street financial innovations.\"\u003cbr\u003e —David Montano, Managing Director JPMorgan Securities\u003c\/p\u003e \u003cp\u003e\"A stylish and practical introduction to the key concepts in financial mathematics, this book tackles key fundamentals in the subject in an intuitive and refreshing manner whilst also providing detailed analytical and numerical schema for solving interesting derivatives pricing problems. If Richard Feynman wrote an introduction to financial mathematics, it might look similar. The problem and solution sets are first rate.\"\u003cbr\u003e —Barry Ryan, Partner Bhramavira Capital Partners, London\u003c\/p\u003e \u003cp\u003e\"This is a great book for anyone beginning (or contemplating), a career in financial research or analytic programming. Navin dissects a huge, complex topic into a series of discrete, concise, accessible lectures that combine the required mathematical theory with relevant applications to real-world markets. I wish this book was around when I started in finance. It would have saved me a lot of time and aggravation.\"\u003cbr\u003e —Larry Magargal\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47990285500645,"sku":"NP9780470047255","price":65.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780470047255.jpg?v=1761787203","url":"https:\/\/k12savings.com\/products\/the-mathematics-of-derivatives-isbn-9780470047255","provider":"K12savings","version":"1.0","type":"link"}