{"product_id":"foundations-of-the-pricing-of-financial-derivatives-9781394179657","title":"Foundations of the Pricing of Financial","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eAn accessible and mathematically rigorous resource for masters and PhD students In Foundations of the Pricing of Financial Derivatives: Theory and Analysis two expert finance academics with professional experience deliver a practical new text for doctoral and masters' students and also new practitioners. The book draws on the authors extensive combined experience teaching, researching, and consulting on this topic and strikes an effective balance between fine-grained quantitative detail and high-level theoretical explanations. The authors fill the gap left by books directed at masters'-level students that often lack mathematical rigor. Further, books aimed at mathematically trained graduate students often lack quantitative explanations and critical foundational materials. Thus, this book provides the technical background required to understand the more advanced mathematics used in this discipline, in class, in research, and in practice. Readers will also find: Tables, figures, line dra\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xv\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 1 Introduction and Overview 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Motivation for This Book 2\u003c\/p\u003e \u003cp\u003e1.2 What Is a Derivative? 6\u003c\/p\u003e \u003cp\u003e1.3 Options Versus Forwards, Futures, and Swaps 8\u003c\/p\u003e \u003cp\u003e1.4 Size and Scope of the Financial Derivatives Markets 9\u003c\/p\u003e \u003cp\u003e1.5 Outline and Features of the Book 12\u003c\/p\u003e \u003cp\u003e1.6 Final Thoughts and Preview 14\u003c\/p\u003e \u003cp\u003eQuestions and Problems 15\u003c\/p\u003e \u003cp\u003eNotes 15\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Basic Foundations for Derivative Pricing\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2 Boundaries, Limits, and Conditions on Option Prices 19\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Setup, Definitions, and Arbitrage 20\u003c\/p\u003e \u003cp\u003e2.2 Absolute Minimum and Maximum Values 21\u003c\/p\u003e \u003cp\u003e2.3 The Value of an American Option Relative to the Value of a European Option 22\u003c\/p\u003e \u003cp\u003e2.4 The Value of an Option at Expiration 22\u003c\/p\u003e \u003cp\u003e2.5 The Lower Bounds of European and American Options and the Optimality of Early Exercise 23\u003c\/p\u003e \u003cp\u003e2.6 Differences in Option Values by Exercise Price 31\u003c\/p\u003e \u003cp\u003e2.7 The Effect of Differences in Time to Expiration 37\u003c\/p\u003e \u003cp\u003e2.8 The Convexity Rule 38\u003c\/p\u003e \u003cp\u003e2.9 Put-Call Parity 40\u003c\/p\u003e \u003cp\u003e2.10 The Effect of Interest Rates on Option Prices 47\u003c\/p\u003e \u003cp\u003e2.11 The Effect of Volatility on Option Prices 47\u003c\/p\u003e \u003cp\u003e2.12 The Building Blocks of European Options 48\u003c\/p\u003e \u003cp\u003e2.13 Recap and Preview 49\u003c\/p\u003e \u003cp\u003eQuestions and Problems 50\u003c\/p\u003e \u003cp\u003eNotes 51\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3 Elementary Review of Mathematics for Finance 53\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Summation Notation 53\u003c\/p\u003e \u003cp\u003e3.2 Product Notation 55\u003c\/p\u003e \u003cp\u003e3.3 Logarithms and Exponentials 56\u003c\/p\u003e \u003cp\u003e3.4 Series Formulas 58\u003c\/p\u003e \u003cp\u003e3.5 Calculus Derivatives 59\u003c\/p\u003e \u003cp\u003e3.6 Integration 68\u003c\/p\u003e \u003cp\u003e3.7 Differential Equations 70\u003c\/p\u003e \u003cp\u003e3.8 Recap and Preview 71\u003c\/p\u003e \u003cp\u003eQuestions and Problems 71\u003c\/p\u003e \u003cp\u003eNotes 73\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4 Elementary Review of Probability for Finance 75\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Marginal, Conditional, and Joint Probabilities 75\u003c\/p\u003e \u003cp\u003e4.2 Expectations, Variances, and Covariances of Discrete Random Variables 80\u003c\/p\u003e \u003cp\u003e4.3 Continuous Random Variables 86\u003c\/p\u003e \u003cp\u003e4.4 Some General Results in Probability Theory 93\u003c\/p\u003e \u003cp\u003e4.5 Technical Introduction to Common Probability Distributions Used in Finance 95\u003c\/p\u003e \u003cp\u003e4.6 Recap and Preview 109\u003c\/p\u003e \u003cp\u003eQuestions and Problems 109\u003c\/p\u003e \u003cp\u003eNotes 110\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 5 Financial Applications of Probability Distributions 113\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 The Univariate Normal Probability Distribution 113\u003c\/p\u003e \u003cp\u003e5.2 Contrasting the Normal with the Lognormal Probability Distribution 119\u003c\/p\u003e \u003cp\u003e5.3 Bivariate Normal Probability Distribution 123\u003c\/p\u003e \u003cp\u003e5.4 The Bivariate Lognormal Probability Distribution 125\u003c\/p\u003e \u003cp\u003e5.5 Recap and Preview 126\u003c\/p\u003e \u003cp\u003eAppendix 5A An Excel Routine for the Bivariate Normal Probability 126\u003c\/p\u003e \u003cp\u003eQuestions and Problems 128\u003c\/p\u003e \u003cp\u003eNotes 128\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 6 Basic Concepts in Valuing Risky Assets and Derivatives 129\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Valuing Risky Assets 129\u003c\/p\u003e \u003cp\u003e6.2 Risk-Neutral Pricing in Discrete Time 130\u003c\/p\u003e \u003cp\u003e6.3 Identical Assets and the Law of One Price 133\u003c\/p\u003e \u003cp\u003e6.4 Derivative Contracts 134\u003c\/p\u003e \u003cp\u003e6.5 A First Look at Valuing Options 136\u003c\/p\u003e \u003cp\u003e6.6 A World of Risk-Averse and Risk-Neutral Investors 137\u003c\/p\u003e \u003cp\u003e6.7 Pricing Options Under Risk Aversion 138\u003c\/p\u003e \u003cp\u003e6.8 Recap and Preview 138\u003c\/p\u003e \u003cp\u003eQuestions and Problems 139\u003c\/p\u003e \u003cp\u003eNotes 139\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Discrete Time Derivatives Pricing Theory\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 7 The Binomial Model 143\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 The One-Period Binomial Model for Calls 143\u003c\/p\u003e \u003cp\u003e7.2 The One-Period Binomial Model for Puts 146\u003c\/p\u003e \u003cp\u003e7.3 Arbitraging Price Discrepancies 149\u003c\/p\u003e \u003cp\u003e7.4 The Multiperiod Model 151\u003c\/p\u003e \u003cp\u003e7.5 American Options and Early Exercise in the Binomial Framework 154\u003c\/p\u003e \u003cp\u003e7.6 Dividends and Recombination 155\u003c\/p\u003e \u003cp\u003e7.7 Path Independence and Path Dependence 159\u003c\/p\u003e \u003cp\u003e7.8 Recap and Preview 159\u003c\/p\u003e \u003cp\u003eAppendix 7A Derivation of Equation (7.9) 159\u003c\/p\u003e \u003cp\u003eAppendix 7B Pascal’s Triangle and the Binomial Model 161\u003c\/p\u003e \u003cp\u003eQuestions and Problems 163\u003c\/p\u003e \u003cp\u003eNotes 163\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 8 Calculating the Greeks in the Binomial Model 165\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Standard Approach 165\u003c\/p\u003e \u003cp\u003e8.2 An Enhanced Method for Estimating Delta and Gamma 170\u003c\/p\u003e \u003cp\u003e8.3 Numerical Examples 172\u003c\/p\u003e \u003cp\u003e8.4 Dividends 174\u003c\/p\u003e \u003cp\u003e8.5 Recap and Preview 175\u003c\/p\u003e \u003cp\u003eQuestions and Problems 175\u003c\/p\u003e \u003cp\u003eNotes 176\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 9 Convergence of the Binomial Model to the Black-Scholes-Merton Model 177\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Setting Up the Problem 177\u003c\/p\u003e \u003cp\u003e9.2 The Hsia Proof 181\u003c\/p\u003e \u003cp\u003e9.3 Put Options 187\u003c\/p\u003e \u003cp\u003e9.4 Dividends 188\u003c\/p\u003e \u003cp\u003e9.5 Recap and Preview 188\u003c\/p\u003e \u003cp\u003eQuestions and Problems 189\u003c\/p\u003e \u003cp\u003eNotes 190\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III Continuous Time Derivatives Pricing Theory\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 10 The Basics of Brownian Motion and Wiener Processes 193\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Brownian Motion 193\u003c\/p\u003e \u003cp\u003e10.2 The Wiener Process 195\u003c\/p\u003e \u003cp\u003e10.3 Properties of a Model of Asset Price Fluctuations 196\u003c\/p\u003e \u003cp\u003e10.4 Building a Model of Asset Price Fluctuations 199\u003c\/p\u003e \u003cp\u003e10.5 Simulating Brownian Motion and Wiener Processes 202\u003c\/p\u003e \u003cp\u003e10.6 Formal Statement of Wiener Process Properties 205\u003c\/p\u003e \u003cp\u003e10.7 Recap and Preview 207\u003c\/p\u003e \u003cp\u003eAppendix 10A Simulation of the Wiener Process and the Square of the Wiener Process for Successively Smaller Time Intervals 207\u003c\/p\u003e \u003cp\u003eQuestions and Problems 208\u003c\/p\u003e \u003cp\u003eNotes 209\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 11 Stochastic Calculus and Itô’s Lemma 211\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 A Result from Basic Calculus 211\u003c\/p\u003e \u003cp\u003e11.2 Introducing Stochastic Calculus and Itô’s Lemma 212\u003c\/p\u003e \u003cp\u003e11.3 Itô’s Integral 215\u003c\/p\u003e \u003cp\u003e11.4 The Integral Form of Itô’s Lemma 216\u003c\/p\u003e \u003cp\u003e11.5 Some Additional Cases of Itô’s Lemma 217\u003c\/p\u003e \u003cp\u003e11.6 Recap and Preview 219\u003c\/p\u003e \u003cp\u003eAppendix 11A Technical Stochastic Integral Results 220\u003cbr\u003e \u003ci\u003e11A.1 Selected Stochastic Integral Results 220\u003cbr\u003e 11A.2 A General Linear Theorem 224\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003eQuestions and Problems 229\u003c\/p\u003e \u003cp\u003eNotes 230\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 12 Properties of the Lognormal and Normal Diffusion Processes for Modeling Assets 231\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 A Stochastic Process for the Asset Relative Return 232\u003c\/p\u003e \u003cp\u003e12.2 A Stochastic Process for the Asset Price Change 235\u003c\/p\u003e \u003cp\u003e12.3 Solving the Stochastic Differential Equation 236\u003c\/p\u003e \u003cp\u003e12.4 Solutions to Stochastic Differential Equations Are Not Always the Same as Solutions to Corresponding Ordinary Differential Equations 237\u003c\/p\u003e \u003cp\u003e12.5 Finding the Expected Future Asset Price 238\u003c\/p\u003e \u003cp\u003e12.6 Geometric Brownian Motion or Arithmetic Brownian Motion? 240\u003c\/p\u003e \u003cp\u003e12.7 Recap and Preview 241\u003c\/p\u003e \u003cp\u003eQuestions and Problems 242\u003c\/p\u003e \u003cp\u003eNotes 242\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 13 Deriving the Black-Scholes-Merton Model 245\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Derivation of the European Call Option Pricing Formula 245\u003c\/p\u003e \u003cp\u003e13.2 The European Put Option Pricing Formula 249\u003c\/p\u003e \u003cp\u003e13.3 Deriving the Black-Scholes-Merton Model as an Expected Value 250\u003c\/p\u003e \u003cp\u003e13.4 Deriving the Black-Scholes-Merton Model as the Solution of a Partial Differential Equation 254\u003c\/p\u003e \u003cp\u003e13.5 Decomposing the Black-Scholes-Merton Model into Binary Options 258\u003c\/p\u003e \u003cp\u003e13.6 Black-Scholes-Merton Option Pricing When There Are Dividends 259\u003c\/p\u003e \u003cp\u003e13.7 Selected Black-Scholes-Merton Model Limiting Results 259\u003c\/p\u003e \u003cp\u003e13.8 Computing the Black-Scholes-Merton Option Pricing Model Values 262\u003c\/p\u003e \u003cp\u003e13.9 Recap and Preview 265\u003c\/p\u003e \u003cp\u003eAppendix 13.A Deriving the Arithmetic Brownian Motion Option Pricing Model 265\u003c\/p\u003e \u003cp\u003eQuestions and Problems 269\u003c\/p\u003e \u003cp\u003eNotes 270\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 14 The Greeks in the Black-Scholes-Merton Model 271\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Delta: The First Derivative with Respect to the Underlying Price 274\u003c\/p\u003e \u003cp\u003e14.2 Gamma: The Second Derivative with Respect to the Underlying Price 274\u003c\/p\u003e \u003cp\u003e14.3 Theta: The First Derivative with Respect to Time 275\u003c\/p\u003e \u003cp\u003e14.4 Verifying the Solution of the Partial Differential Equation 275\u003c\/p\u003e \u003cp\u003e14.5 Selected Other Partial Derivatives of the Black-Scholes-Merton Model 277\u003c\/p\u003e \u003cp\u003e14.6 Partial Derivatives of the Black-Scholes-Merton European Put Option Pricing Model 278\u003c\/p\u003e \u003cp\u003e14.7 Incorporating Dividends 279\u003c\/p\u003e \u003cp\u003e14.8 Greek Sensitivities 280\u003c\/p\u003e \u003cp\u003e14.9 Elasticities 283\u003c\/p\u003e \u003cp\u003e14.10 Extended Greeks of the Black-Scholes-Merton Option Pricing Model 284\u003c\/p\u003e \u003cp\u003e14.11 Recap and Preview 284\u003c\/p\u003e \u003cp\u003eQuestions and Problems 285\u003c\/p\u003e \u003cp\u003eNotes 286\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 15 Girsanov’s Theorem in Option Pricing 287\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 The Martingale Representation Theorem 287\u003c\/p\u003e \u003cp\u003e15.2 Introducing the Radon-Nikodym Derivative by Changing the Drift for a Single Random Variable 289\u003c\/p\u003e \u003cp\u003e15.3 A Complete Probability Space 291\u003c\/p\u003e \u003cp\u003e15.4 Formal Statement of Girsanov’s Theorem 292\u003c\/p\u003e \u003cp\u003e15.5 Changing the Drift in a Continuous Time Stochastic Process 293\u003c\/p\u003e \u003cp\u003e15.6 Changing the Drift of an Asset Price Process 297\u003c\/p\u003e \u003cp\u003e15.7 Recap and Preview 300\u003c\/p\u003e \u003cp\u003eQuestions and Problems 301\u003c\/p\u003e \u003cp\u003eNotes 302\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 16 Connecting Discrete and Continuous Brownian Motions 303\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Brownian Motion in a Discrete World 303\u003c\/p\u003e \u003cp\u003e16.2 Moving from a Discrete to a Continuous World 306\u003c\/p\u003e \u003cp\u003e16.3 Changing the Probability Measure with the Radon-Nikodym Derivative in Discrete Time 310\u003c\/p\u003e \u003cp\u003e16.4 The Kolmogorov Equations 313\u003c\/p\u003e \u003cp\u003e16.5 Recap and Preview 321\u003c\/p\u003e \u003cp\u003eQuestions and Problems 322\u003c\/p\u003e \u003cp\u003eNotes 322\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IV Extensions and Generalizations of Derivative Pricing\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 17 Applying Linear Homogeneity to Option Pricing 327\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 Introduction to Exchange Options 327\u003c\/p\u003e \u003cp\u003e17.2 Homogeneous Functions 328\u003c\/p\u003e \u003cp\u003e17.3 Euler’s Rule 330\u003c\/p\u003e \u003cp\u003e17.4 Using Linear Homogeneity and Euler’s Rule to Derive the Black-Scholes-Merton Model 330\u003c\/p\u003e \u003cp\u003e17.5 Exchange Option Pricing 333\u003c\/p\u003e \u003cp\u003e17.6 Spread Options 337\u003c\/p\u003e \u003cp\u003e17.7 Forward Start Options 339\u003c\/p\u003e \u003cp\u003e17.8 Recap and Preview 341\u003c\/p\u003e \u003cp\u003eAppendix 17A Linear Homogeneity and the Arithmetic Brownian Motion Model 342\u003c\/p\u003e \u003cp\u003eAppendix 17B Multivariate Itô’s Lemma 344\u003c\/p\u003e \u003cp\u003eAppendix 17C Greeks of the Exchange Option Model 345\u003c\/p\u003e \u003cp\u003eQuestions and Problems 347\u003c\/p\u003e \u003cp\u003eNotes 347\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 18 Compound Option Pricing 349\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 Equity as an Option 350\u003c\/p\u003e \u003cp\u003e18.2 Valuing an Option on the Equity as a Compound Option 351\u003c\/p\u003e \u003cp\u003e18.3 Compound Option Boundary Conditions and Parities 353\u003c\/p\u003e \u003cp\u003e18.4 Geske’s Approach to Valuing a Call on a Call 356\u003c\/p\u003e \u003cp\u003e18.5 Characteristics of Geske’s Call on Call Option 358\u003c\/p\u003e \u003cp\u003e18.6 Geske’s Call on Call Option Model and Linear Homogeneity 359\u003c\/p\u003e \u003cp\u003e18.7 Generalized Compound Option Pricing Model 360\u003c\/p\u003e \u003cp\u003e18.8 Installment Options 361\u003c\/p\u003e \u003cp\u003e18.9 Recap and Preview 362\u003c\/p\u003e \u003cp\u003eAppendix 18A Selected Greeks of the Compound Option 362\u003c\/p\u003e \u003cp\u003eQuestions and Problems 363\u003c\/p\u003e \u003cp\u003eNotes 363\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 19 American Call Option Pricing 365\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e19.1 Closed-Form American Call Pricing: Roll-Geske-Whaley 366\u003c\/p\u003e \u003cp\u003e19.2 The Two-Payment Case 370\u003c\/p\u003e \u003cp\u003e19.3 Recap and Preview 372\u003c\/p\u003e \u003cp\u003eAppendix 19A Numerical Example of the One-Dividend Model 373\u003c\/p\u003e \u003cp\u003eQuestions and Problems 374\u003c\/p\u003e \u003cp\u003eNotes 374\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 20 American Put Option Pricing 377\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e20.1 The Nature of the Problem of Pricing an American Put 377\u003c\/p\u003e \u003cp\u003e20.2 The American Put as a Series of Compound Options 378\u003c\/p\u003e \u003cp\u003e20.3 Recap and Preview 380\u003c\/p\u003e \u003cp\u003eQuestions and Problems 380\u003c\/p\u003e \u003cp\u003eNotes 381\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 21 Min-Max Option Pricing 383\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e21.1 Characteristics of Stulz’s Min-Max Option 383\u003c\/p\u003e \u003cp\u003e21.2 Pricing the Call on the Min 388\u003c\/p\u003e \u003cp\u003e21.3 Other Related Options 393\u003c\/p\u003e \u003cp\u003e21.4 Recap and Preview 395\u003c\/p\u003e \u003cp\u003eAppendix 21A Multivariate Feynman-Kac Theorem 395\u003c\/p\u003e \u003cp\u003eAppendix 21B An Alternative Derivation of the Min-Max Option Model 396\u003c\/p\u003e \u003cp\u003eQuestions and Problems 397\u003c\/p\u003e \u003cp\u003eNotes 397\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 22 Pricing Forwards, Futures, and Options on Forwards and Futures 399\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e22.1 Forward Contracts 399\u003c\/p\u003e \u003cp\u003e22.2 Pricing Futures Contracts 404\u003c\/p\u003e \u003cp\u003e22.3 Options on Forwards and Futures 409\u003c\/p\u003e \u003cp\u003e22.4 Recap and Preview 412\u003c\/p\u003e \u003cp\u003eQuestions and Problems 413\u003c\/p\u003e \u003cp\u003eNotes 414\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart V Numerical Methods\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 23 Monte Carlo Simulation 417\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e23.1 Standard Monte Carlo Simulation of the Lognormal Diffusion 417\u003c\/p\u003e \u003cp\u003e23.2 Reducing the Standard Error 421\u003c\/p\u003e \u003cp\u003e23.3 Simulation with More Than One Random Variable 424\u003c\/p\u003e \u003cp\u003e23.4 Recap and Preview 424\u003c\/p\u003e \u003cp\u003eQuestions and Problems 425\u003c\/p\u003e \u003cp\u003eNotes 426\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 24 Finite Difference Methods 429\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e24.1 Setting Up the Finite Difference Problem 429\u003c\/p\u003e \u003cp\u003e24.2 The Explicit Finite Difference Method 431\u003c\/p\u003e \u003cp\u003e24.3 The Implicit Finite Difference Method 434\u003c\/p\u003e \u003cp\u003e24.4 Finite Difference Put Option Pricing 435\u003c\/p\u003e \u003cp\u003e24.5 Dividends and Early Exercise 435\u003c\/p\u003e \u003cp\u003e24.6 Recap and Preview 436\u003c\/p\u003e \u003cp\u003eQuestions and Problems 436\u003c\/p\u003e \u003cp\u003eNotes 436\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart VI Interest Rate Derivatives\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 25 The Term Structure of Interest Rates 439\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e25.1 The Unbiased Expectations Hypothesis 440\u003c\/p\u003e \u003cp\u003e25.2 The Local Expectations Hypothesis 442\u003c\/p\u003e \u003cp\u003e25.3 The Difference Between the Local and Unbiased Expectations Hypotheses 446\u003c\/p\u003e \u003cp\u003e25.4 Other Term Structure of Interest Rate Hypotheses 447\u003c\/p\u003e \u003cp\u003e25.5 Recap and Preview 450\u003c\/p\u003e \u003cp\u003eQuestions and Problems 450\u003c\/p\u003e \u003cp\u003eNotes 450\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 26 Interest Rate Contracts: Forward Rate Agreements, Swaps, and Options 453\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e26.1 Interest Rate Forwards 454\u003c\/p\u003e \u003cp\u003e26.2 Interest Rate Swaps 459\u003c\/p\u003e \u003cp\u003e26.3 Interest Rate Options 469\u003c\/p\u003e \u003cp\u003e26.4 Recap and Preview 471\u003c\/p\u003e \u003cp\u003eQuestions and Problems 471\u003c\/p\u003e \u003cp\u003eNotes 472\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 27 Fitting an Arbitrage-Free Term Structure Model 475\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e27.1 Basic Structure of the HJM Model 476\u003c\/p\u003e \u003cp\u003e27.2 Discretizing the HJM Model 479\u003c\/p\u003e \u003cp\u003e27.3 Fitting a Binomial Tree to the HJM Model 481\u003c\/p\u003e \u003cp\u003e27.4 Filling in the Remainder of the HJM Binomial Tree 485\u003c\/p\u003e \u003cp\u003e27.5 Recap and Preview 489\u003c\/p\u003e \u003cp\u003eQuestions and Problems 490\u003c\/p\u003e \u003cp\u003eNotes 491\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 28 Pricing Fixed-Income Securities and Derivatives Using an Arbitrage-Free Binomial Tree 493\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e28.1 Zero-Coupon Bonds 493\u003c\/p\u003e \u003cp\u003e28.2 Coupon Bonds 496\u003c\/p\u003e \u003cp\u003e28.3 Options on Zero-Coupon Bonds 497\u003c\/p\u003e \u003cp\u003e28.4 Options on Coupon Bonds 498\u003c\/p\u003e \u003cp\u003e28.5 Callable Bonds 499\u003c\/p\u003e \u003cp\u003e28.6 Forward Rate Agreements (FRAs) 501\u003c\/p\u003e \u003cp\u003e28.7 Interest Rate Swaps 503\u003c\/p\u003e \u003cp\u003e28.8 Interest Rate Options 505\u003c\/p\u003e \u003cp\u003e28.9 Interest Rate Swaptions 506\u003c\/p\u003e \u003cp\u003e28.10 Interest Rate Futures 508\u003c\/p\u003e \u003cp\u003e28.11 Recap and Preview 510\u003c\/p\u003e \u003cp\u003eQuestions and Problems 510\u003c\/p\u003e \u003cp\u003eNotes 510\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart VII Miscellaneous Topics\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 29 Option Prices and the Prices of State-Contingent Claims 513\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e29.1 Pure Assets in the Market 514\u003c\/p\u003e \u003cp\u003e29.2 Pricing Pure and Complex Assets 514\u003c\/p\u003e \u003cp\u003e29.3 Numerical Example 518\u003c\/p\u003e \u003cp\u003e29.4 State Pricing and Options in a Binomial Framework 519\u003c\/p\u003e \u003cp\u003e29.5 State Pricing and Options in Continuous Time 522\u003c\/p\u003e \u003cp\u003e29.6 Recap and Preview 525\u003c\/p\u003e \u003cp\u003eQuestions and Problems 525\u003c\/p\u003e \u003cp\u003eNotes 526\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 30 Option Prices and Expected Returns 527\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e30.1 The Basic Framework 527\u003c\/p\u003e \u003cp\u003e30.2 Expected Returns on Options 529\u003c\/p\u003e \u003cp\u003e30.3 Volatilities of Options 531\u003c\/p\u003e \u003cp\u003e30.4 Options and the Capital Asset Pricing Model 531\u003c\/p\u003e \u003cp\u003e30.5 Options and the Sharpe Ratio 532\u003c\/p\u003e \u003cp\u003e30.6 The Stochastic Process Followed by the Option 533\u003c\/p\u003e \u003cp\u003e30.7 Recap and Preview 535\u003c\/p\u003e \u003cp\u003eQuestions and Problems 535\u003c\/p\u003e \u003cp\u003eNotes 536\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 31 Implied Volatility and the Volatility Smile 537\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e31.1 Historical Volatility and the VIX 538\u003c\/p\u003e \u003cp\u003e31.2 An Example of Implied Volatility 539\u003c\/p\u003e \u003cp\u003e31.3 The Volatility Surface 546\u003c\/p\u003e \u003cp\u003e31.4 The Perfect Substitutability of Options 547\u003c\/p\u003e \u003cp\u003e31.5 Other Attempts to Explain the Implied Volatility Smile 549\u003c\/p\u003e \u003cp\u003e31.6 How Practitioners Use the Implied Volatility Surface 550\u003c\/p\u003e \u003cp\u003e31.7 Recap and Preview 551\u003c\/p\u003e \u003cp\u003eQuestions and Problems 551\u003c\/p\u003e \u003cp\u003eNotes 553\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 32 Pricing Foreign Currency Options 555\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e32.1 Definition of Terms 556\u003c\/p\u003e \u003cp\u003e32.2 Option Payoffs 556\u003c\/p\u003e \u003cp\u003e32.3 Valuation of the Options 557\u003c\/p\u003e \u003cp\u003e32.4 Probability of Exercise 561\u003c\/p\u003e \u003cp\u003e32.5 Some Terminology Confusion 563\u003c\/p\u003e \u003cp\u003e32.6 Recap 563\u003c\/p\u003e \u003cp\u003eQuestions and Problems 564\u003c\/p\u003e \u003cp\u003eNotes 565\u003c\/p\u003e \u003cp\u003eReferences 567\u003c\/p\u003e \u003cp\u003eSymbols Used 573\u003c\/p\u003e \u003cp\u003eSymbols 573\u003c\/p\u003e \u003cp\u003eTime-Related Notation 573\u003c\/p\u003e \u003cp\u003eInstrument-Related Notation 574\u003c\/p\u003e \u003cp\u003eAbout the Website 581\u003c\/p\u003e \u003cp\u003eIndex 583\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49407597969751,"sku":"9781394179657","price":56.25,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781394179657.jpg?v=1730499884","url":"https:\/\/bookcurl.com\/products\/foundations-of-the-pricing-of-financial-derivatives-9781394179657","provider":"Book Curl","version":"1.0","type":"link"}