{"product_id":"volatility-and-correlation-isbn-9780470091395","title":"Volatility and Correlation","description":"In \u003ci\u003eVolatility and Correlation 2\u003csup\u003end\u003c\/sup\u003e edition: The Perfect Hedger and the Fox\u003c\/i\u003e, Rebonato looks at derivatives pricing from the angle of volatility and correlation. With both practical and theoretical applications, this is a thorough update of the highly successful \u003ci\u003eVolatility \u0026amp; Correlation\u003c\/i\u003e – with over \u003cb\u003e80% new or fully reworked\u003c\/b\u003e material and is a must have both for practitioners and for students.  \u003cp\u003eThe new and updated material includes a critical examination of the ‘perfect-replication’ approach to derivatives pricing, with special attention given to exotic options; a thorough analysis of the role of quadratic variation in derivatives pricing and hedging; a discussion of the informational efficiency of markets in commonly-used calibration and hedging practices. Treatment of new models including Variance Gamma, displaced diffusion, stochastic volatility for interest-rate smiles and equity\/FX options.\u003c\/p\u003e \u003cp\u003eThe book is split into four parts. Part I deals with a Black world without smiles, sets out the author’s ‘philosophical’ approach and covers deterministic volatility. Part II looks at smiles in equity and FX worlds. It begins with a review of relevant empirical information about smiles, and provides coverage of local-stochastic-volatility, general-stochastic-volatility, jump-diffusion and Variance-Gamma processes. Part II concludes with an important chapter that discusses if and to what extent one can dispense with an explicit specification of a model, and can directly prescribe the dynamics of the smile surface.\u003c\/p\u003e \u003cp\u003ePart III focusses on interest rates when the volatility is deterministic. Part IV extends this setting in order to account for smiles in a financially motivated and computationally tractable manner. In this final part the author deals with CEV processes, with diffusive stochastic volatility and with Markov-chain processes.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePraise for the First Edition:\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e“In this book, Dr Rebonato brings his penetrating eye to bear on option pricing and hedging.… The book is a must-read for those who already know the basics of options and are looking for an edge in applying the more sophisticated approaches that have recently been developed.”\u003cbr\u003e —Professor Ian Cooper, London Business School\u003c\/p\u003e \u003cp\u003e“Volatility and correlation are at the very core of all option pricing and hedging. In this book, Riccardo Rebonato presents the subject in his characteristically elegant and simple fashion…A rare combination of intellectual insight and practical common sense.”\u003cbr\u003e —Anthony Neuberger, London Business School\u003c\/p\u003e \u003cp\u003ePreface xxi\u003c\/p\u003e \u003cp\u003e0.1 Why a Second Edition? xxi\u003c\/p\u003e \u003cp\u003e0.2 What This Book Is Not About xxiii\u003c\/p\u003e \u003cp\u003e0.3 Structure of the Book xxiv\u003c\/p\u003e \u003cp\u003e0.4 The New Subtitle xxiv\u003c\/p\u003e \u003cp\u003eAcknowledgements xxvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003eI Foundations 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Theory and Practice of Option Modelling 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 The Role of Models in Derivatives Pricing 3\u003c\/p\u003e \u003cp\u003e1.2 The Efficient Market Hypothesis and Why It Matters for Option Pricing 9\u003c\/p\u003e \u003cp\u003e1.3 Market Practice 14\u003c\/p\u003e \u003cp\u003e1.4 The Calibration Debate 17\u003c\/p\u003e \u003cp\u003e1.5 Across-Markets Comparison of Pricing and Modelling Practices 27\u003c\/p\u003e \u003cp\u003e1.6 Using Models 30\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Option Replication 31\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 The Bedrock of Option Pricing 31\u003c\/p\u003e \u003cp\u003e2.2 The Analytic (PDE) Approach 32\u003c\/p\u003e \u003cp\u003e2.3 Binomial Replication 38\u003c\/p\u003e \u003cp\u003e2.4 Justifying the Two-State Branching Procedure 65\u003c\/p\u003e \u003cp\u003e2.5 The Nature of the Transformation between Measures: Girsanov’s Theorem 69\u003c\/p\u003e \u003cp\u003e2.6 Switching Between the PDE, the Expectation and the Binomial Replication Approaches 73\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 The Building Blocks 75\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction and Plan of the Chapter 75\u003c\/p\u003e \u003cp\u003e3.2 Definition of Market Terms 75\u003c\/p\u003e \u003cp\u003e3.3 Hedging Forward Contracts Using Spot Quantities 77\u003c\/p\u003e \u003cp\u003e3.4 Hedging Options: Volatility of Spot and Forward Processes 80\u003c\/p\u003e \u003cp\u003e3.5 The Link Between Root-Mean-Squared Volatilities and the Time-Dependence of Volatility 84\u003c\/p\u003e \u003cp\u003e3.6 Admissibility of a Series of Root-Mean-Squared Volatilities 85\u003c\/p\u003e \u003cp\u003e3.7 Summary of the Definitions So Far 87\u003c\/p\u003e \u003cp\u003e3.8 Hedging an Option with a Forward-Setting Strike 89\u003c\/p\u003e \u003cp\u003e3.9 Quadratic Variation: First Approach 95\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Variance and Mean Reversion in the Real and the Risk-Adjusted Worlds 101\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction and Plan of the Chapter 101\u003c\/p\u003e \u003cp\u003e4.2 Hedging a Plain-Vanilla Option: General Framework 102\u003c\/p\u003e \u003cp\u003e4.3 Hedging Plain-Vanilla Options: Constant Volatility 106\u003c\/p\u003e \u003cp\u003e4.4 Hedging Plain-Vanilla Options: Time-Dependent Volatility 116\u003c\/p\u003e \u003cp\u003e4.5 Hedging Behaviour In Practice 121\u003c\/p\u003e \u003cp\u003e4.6 Robustness of the Black-and-Scholes Model 127\u003c\/p\u003e \u003cp\u003e4.7 Is the Total Variance All That Matters? 130\u003c\/p\u003e \u003cp\u003e4.8 Hedging Plain-Vanilla Options: Mean-Reverting Real-World Drift 131\u003c\/p\u003e \u003cp\u003e4.9 Hedging Plain-Vanilla Options: Finite Re-Hedging Intervals Again 135\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Instantaneous and Terminal Correlation 141\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Correlation, Co-Integration and Multi-Factor Models 141\u003c\/p\u003e \u003cp\u003e5.2 The Stochastic Evolution of Imperfectly Correlated Variables 146\u003c\/p\u003e \u003cp\u003e5.3 The Role of Terminal Correlation in the Joint Evolution of Stochastic Variables 151\u003c\/p\u003e \u003cp\u003e5.4 Generalizing the Results 162\u003c\/p\u003e \u003cp\u003e5.5 Moving Ahead 164\u003c\/p\u003e \u003cp\u003e\u003cb\u003eII Smiles – Equity and FX 165\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Pricing Options in the Presence of Smiles 167\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Plan of the Chapter 167\u003c\/p\u003e \u003cp\u003e6.2 Background and Definition of the Smile 168\u003c\/p\u003e \u003cp\u003e6.3 Hedging with a Compensated Process: Plain-Vanilla and Binary Options 169\u003c\/p\u003e \u003cp\u003e6.4 Hedge Ratios for Plain-Vanilla Options in the Presence of Smiles 173\u003c\/p\u003e \u003cp\u003e6.5 Smile Tale 1: ‘Sticky’ Smiles 180\u003c\/p\u003e \u003cp\u003e6.6 Smile Tale 2: ‘Floating’ Smiles 182\u003c\/p\u003e \u003cp\u003e6.7 When Does Risk Aversion Make a Difference? 184\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Empirical Facts About Smiles 201\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 What is this Chapter About? 201\u003c\/p\u003e \u003cp\u003e7.2 Market Information About Smiles 203\u003c\/p\u003e \u003cp\u003e7.3 Equities 206\u003c\/p\u003e \u003cp\u003e7.4 Interest Rates 222\u003c\/p\u003e \u003cp\u003e7.5 FX Rates 227\u003c\/p\u003e \u003cp\u003e7.6 Conclusions 235\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 General Features of Smile-Modelling Approaches 237\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Fully-Stochastic-Volatility Models 237\u003c\/p\u003e \u003cp\u003e8.2 Local-Volatility (Restricted-Stochastic-Volatility) Models 239\u003c\/p\u003e \u003cp\u003e8.3 Jump–Diffusion Models 241\u003c\/p\u003e \u003cp\u003e8.4 Variance–Gamma Models 243\u003c\/p\u003e \u003cp\u003e8.5 Mixing Processes 243\u003c\/p\u003e \u003cp\u003e8.6 Other Approaches 245\u003c\/p\u003e \u003cp\u003e8.7 The Importance of the Quadratic Variation (Take 2) 246\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 The Input Data: Fitting an Exogenous Smile Surface 249\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 What is This Chapter About? 249\u003c\/p\u003e \u003cp\u003e9.2 Analytic Expressions for Calls vs Process Specification 249\u003c\/p\u003e \u003cp\u003e9.3 Direct Use of Market Prices: Pros and Cons 250\u003c\/p\u003e \u003cp\u003e9.4 Statement of the Problem 251\u003c\/p\u003e \u003cp\u003e9.5 Fitting Prices 252\u003c\/p\u003e \u003cp\u003e9.6 Fitting Transformed Prices 254\u003c\/p\u003e \u003cp\u003e9.7 Fitting the Implied Volatilities 255\u003c\/p\u003e \u003cp\u003e9.8 Fitting the Risk-Neutral Density Function – General 256\u003c\/p\u003e \u003cp\u003e9.9 Fitting the Risk-Neutral Density Function: Mixture of Normals 259\u003c\/p\u003e \u003cp\u003e9.10 Numerical Results 265\u003c\/p\u003e \u003cp\u003e9.11 Is the Term \u003ci\u003e∂C\/∂\u003c\/i\u003e\u003ci\u003eS\u003c\/i\u003e Really a Delta? 275\u003c\/p\u003e \u003cp\u003e9.12 Fitting the Risk-Neutral Density Function: The Generalized-Beta Approach 277\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Quadratic Variation and Smiles 293\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Why This Approach Is Interesting 293\u003c\/p\u003e \u003cp\u003e10.2 The BJN Framework for Bounding Option Prices 293\u003c\/p\u003e \u003cp\u003e10.3 The BJN Approach – Theoretical Development 294\u003c\/p\u003e \u003cp\u003e10.4 The BJN Approach: Numerical Implementation 300\u003c\/p\u003e \u003cp\u003e10.5 Discussion of the Results 312\u003c\/p\u003e \u003cp\u003e10.6 Conclusions (or, Limitations of Quadratic Variation) 316\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Local-Volatility Models: the Derman-and-Kani Approach 319\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 General Considerations on Stochastic-Volatility Models 319\u003c\/p\u003e \u003cp\u003e11.2 Special Cases of Restricted-Stochastic-Volatility Models 321\u003c\/p\u003e \u003cp\u003e11.3 The Dupire, Rubinstein and Derman-and-Kani Approaches 321\u003c\/p\u003e \u003cp\u003e11.4 Green’s Functions (Arrow–Debreu Prices) in the DK Construction 322\u003c\/p\u003e \u003cp\u003e11.5 The Derman-and-Kani Tree Construction 326\u003c\/p\u003e \u003cp\u003e11.6 Numerical Aspects of the Implementation of the DK Construction 331\u003c\/p\u003e \u003cp\u003e11.7 Implementation Results 334\u003c\/p\u003e \u003cp\u003e11.8 Estimating Instantaneous Volatilities from Prices as an Inverse Problem 343\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Extracting the Local Volatility from Option Prices 345\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 345\u003c\/p\u003e \u003cp\u003e12.2 The Modelling Framework 347\u003c\/p\u003e \u003cp\u003e12.3 A Computational Method 349\u003c\/p\u003e \u003cp\u003e12.4 Computational Results 355\u003c\/p\u003e \u003cp\u003e12.5 The Link Between Implied and Local-Volatility Surfaces 357\u003c\/p\u003e \u003cp\u003e12.6 Gaining an Intuitive Understanding 368\u003c\/p\u003e \u003cp\u003e12.7 What Local-Volatility Models Imply about Sticky and Floating Smiles 373\u003c\/p\u003e \u003cp\u003e12.8 No-Arbitrage Conditions on the Current Implied Volatility Smile Surface 375\u003c\/p\u003e \u003cp\u003e12.9 Empirical Performance 385\u003c\/p\u003e \u003cp\u003e12.10 Appendix I: Proof that \u003ci\u003e∂\u003c\/i\u003e\u003csup\u003e2\u003c\/sup\u003e\u003ci\u003eCall\u003c\/i\u003e(\u003ci\u003eSt, K, T, t\u003c\/i\u003e)\/\u003ci\u003e∂k\u003c\/i\u003e\u003csup\u003e2\u003c\/sup\u003e = \u003ci\u003eφ\u003c\/i\u003e(\u003ci\u003eS\u003csub\u003eT\u003c\/sub\u003e\u003c\/i\u003e)|\u003ci\u003e\u003csub\u003eK\u003c\/sub\u003e\u003c\/i\u003e 386\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Stochastic-Volatility Processes 389\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Plan of the Chapter 389\u003c\/p\u003e \u003cp\u003e13.2 Portfolio Replication in the Presence of Stochastic Volatility 389\u003c\/p\u003e \u003cp\u003e13.3 Mean-Reverting Stochastic Volatility 401\u003c\/p\u003e \u003cp\u003e13.4 Qualitative Features of Stochastic-Volatility Smiles 405\u003c\/p\u003e \u003cp\u003e13.5 The Relation Between Future Smiles and Future Stock Price Levels 416\u003c\/p\u003e \u003cp\u003e13.6 Portfolio Replication in Practice: The Stochastic-Volatility Case 418\u003c\/p\u003e \u003cp\u003e13.7 Actual Fitting to Market Data 427\u003c\/p\u003e \u003cp\u003e13.8 Conclusions 436\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Jump–Diffusion Processes 439\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Introduction 439\u003c\/p\u003e \u003cp\u003e14.2 The Financial Model: Smile Tale 2 Revisited 441\u003c\/p\u003e \u003cp\u003e14.3 Hedging and Replicability in the Presence of Jumps: First Considerations 444\u003c\/p\u003e \u003cp\u003e14.4 Analytic Description of Jump–Diffusions 449\u003c\/p\u003e \u003cp\u003e14.5 Hedging with Jump–Diffusion Processes 455\u003c\/p\u003e \u003cp\u003e14.6 The Pricing Formula for Log-Normal Amplitude Ratios 470\u003c\/p\u003e \u003cp\u003e14.7 The Pricing Formula in the Finite-Amplitude-Ratio Case 472\u003c\/p\u003e \u003cp\u003e14.8 The Link Between the Price Density and the Smile Shape 485\u003c\/p\u003e \u003cp\u003e14.9 Qualitative Features of Jump–Diffusion Smiles 494\u003c\/p\u003e \u003cp\u003e14.10 Jump–Diffusion Processes and Market Completeness Revisited 500\u003c\/p\u003e \u003cp\u003e14.11 Portfolio Replication in Practice: The Jump–Diffusion Case 502\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Variance–Gamma 511\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Who Can Make Best Use of the Variance–Gamma Approach? 511\u003c\/p\u003e \u003cp\u003e15.2 The Variance–Gamma Process 513\u003c\/p\u003e \u003cp\u003e15.3 Statistical Properties of the Price Distribution 522\u003c\/p\u003e \u003cp\u003e15.4 Features of the Smile 523\u003c\/p\u003e \u003cp\u003e15.5 Conclusions 527\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Displaced Diffusions and Generalizations 529\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Introduction 529\u003c\/p\u003e \u003cp\u003e16.2 Gaining Intuition 530\u003c\/p\u003e \u003cp\u003e16.3 Evolving the Underlying with Displaced Diffusions 531\u003c\/p\u003e \u003cp\u003e16.4 Option Prices with Displaced Diffusions 532\u003c\/p\u003e \u003cp\u003e16.5 Matching At-The-Money Prices with Displaced Diffusions 533\u003c\/p\u003e \u003cp\u003e16.6 The Smile Produced by Displaced Diffusions 553\u003c\/p\u003e \u003cp\u003e16.7 Extension to Other Processes 560\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 No-Arbitrage Restrictions on the Dynamics of Smile Surfaces 563\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 A Worked-Out Example: Pricing Continuous Double Barriers 564\u003c\/p\u003e \u003cp\u003e17.2 Analysis of the Cost of Unwinding 571\u003c\/p\u003e \u003cp\u003e17.3 The Trader’s Dream 575\u003c\/p\u003e \u003cp\u003e17.4 Plan of the Remainder of the Chapter 581\u003c\/p\u003e \u003cp\u003e17.5 Conditions of No-Arbitrage for the Stochastic Evolution of Future Smile Surfaces 582\u003c\/p\u003e \u003cp\u003e17.6 Deterministic Smile Surfaces 585\u003c\/p\u003e \u003cp\u003e17.7 Stochastic Smiles 593\u003c\/p\u003e \u003cp\u003e17.8 The Strength of the Assumptions 597\u003c\/p\u003e \u003cp\u003e17.9 Limitations and Conclusions 598\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIII Interest Rates – Deterministic Volatilities 601\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Mean Reversion in Interest-Rate Models 603\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 Introduction and Plan of the Chapter 603\u003c\/p\u003e \u003cp\u003e18.2 Why Mean Reversion Matters in the Case of Interest-Rate Models 604\u003c\/p\u003e \u003cp\u003e18.3 A Common Fallacy Regarding Mean Reversion 608\u003c\/p\u003e \u003cp\u003e18.4 The BDT Mean-Reversion Paradox 610\u003c\/p\u003e \u003cp\u003e18.5 The Unconditional Variance of the Short Rate in BDT – the Discrete Case 612\u003c\/p\u003e \u003cp\u003e18.6 The Unconditional Variance of the Short Rate in BDT–the Continuous-Time Equivalent 616\u003c\/p\u003e \u003cp\u003e18.7 Mean Reversion in Short-Rate Lattices: Recombining vs Bushy Trees 617\u003c\/p\u003e \u003cp\u003e18.8 Extension to More General Interest-Rate Models 620\u003c\/p\u003e \u003cp\u003e18.9 Appendix I: Evaluation of the Variance of the Logarithm of the Instantaneous Short Rate 622\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Volatility and Correlation in the LIBOR Market Model 625\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e19.1 Introduction 625\u003c\/p\u003e \u003cp\u003e19.2 Specifying the Forward-Rate Dynamics in the LIBOR Market Model 626\u003c\/p\u003e \u003cp\u003e19.3 Link with the Principal Component Analysis 631\u003c\/p\u003e \u003cp\u003e19.4 Worked-Out Example 1: Caplets and a Two-Period Swaption 632\u003c\/p\u003e \u003cp\u003e19.5 Worked-Out Example 2: Serial Options 635\u003c\/p\u003e \u003cp\u003e19.6 Plan of the Work Ahead 636\u003c\/p\u003e \u003cp\u003e\u003cb\u003e20 Calibration Strategies for the LIBOR Market Model 639\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e20.1 Plan of the Chapter 639\u003c\/p\u003e \u003cp\u003e20.2 The Setting 639\u003c\/p\u003e \u003cp\u003e20.3 Fitting an Exogenous Correlation Function 643\u003c\/p\u003e \u003cp\u003e20.4 Numerical Results 646\u003c\/p\u003e \u003cp\u003e20.5 Analytic Expressions to Link Swaption and Caplet Volatilities 659\u003c\/p\u003e \u003cp\u003e20.6 Optimal Calibration to Co-Terminal Swaptions 662\u003c\/p\u003e \u003cp\u003e\u003cb\u003e21 Specifying the Instantaneous Volatility of Forward Rates 667\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e21.1 Introduction and Motivation 667\u003c\/p\u003e \u003cp\u003e21.2 The Link between Instantaneous Volatilities and the Future Term Structure of Volatilities 668\u003c\/p\u003e \u003cp\u003e21.3 A Functional Form for the Instantaneous Volatility Function 671\u003c\/p\u003e \u003cp\u003e21.4 Ensuring Correct Caplet Pricing 673\u003c\/p\u003e \u003cp\u003e21.5 Fitting the Instantaneous Volatility Function: Imposing Time Homogeneity of the Term Structure of Volatilities 677\u003c\/p\u003e \u003cp\u003e21.6 Is a Time-Homogeneous Solution Always Possible? 679\u003c\/p\u003e \u003cp\u003e21.7 Fitting the Instantaneous Volatility Function: The Information from the Swaption Market 680\u003c\/p\u003e \u003cp\u003e21.8 Conclusions 686\u003c\/p\u003e \u003cp\u003e\u003cb\u003e22 Specifying the Instantaneous Correlation Among Forward Rates 687\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e22.1 Why Is Estimating Correlation So Difficult? 687\u003c\/p\u003e \u003cp\u003e22.2 What Shape Should We Expect for the Correlation Surface? 688\u003c\/p\u003e \u003cp\u003e22.3 Features of the Simple Exponential Correlation Function 689\u003c\/p\u003e \u003cp\u003e22.4 Features of the Modified Exponential Correlation Function 691\u003c\/p\u003e \u003cp\u003e22.5 Features of the Square-Root Exponential Correlation Function 694\u003c\/p\u003e \u003cp\u003e22.6 Further Comparisons of Correlation Models 697\u003c\/p\u003e \u003cp\u003e22.7 Features of the Schonmakers–Coffey Approach 697\u003c\/p\u003e \u003cp\u003e22.8 Does It Make a Difference (and When)? 698\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIV Interest Rates – Smiles 701\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e23 How to Model Interest-Rate Smiles 703\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e23.1 What Do We Want to Capture? A Hierarchy of Smile-Producing Mechanisms 703\u003c\/p\u003e \u003cp\u003e23.2 Are Log-Normal Co-Ordinates the Most Appropriate? 704\u003c\/p\u003e \u003cp\u003e23.3 Description of the Market Data 706\u003c\/p\u003e \u003cp\u003e23.4 Empirical Study I: Transforming the Log-Normal Co-ordinates 715\u003c\/p\u003e \u003cp\u003e23.5 The Computational Experiments 718\u003c\/p\u003e \u003cp\u003e23.6 The Computational Results 719\u003c\/p\u003e \u003cp\u003e23.7 Empirical Study II: The Log-Linear Exponent 721\u003c\/p\u003e \u003cp\u003e23.8 Combining the Theoretical and Experimental Results 725\u003c\/p\u003e \u003cp\u003e23.9 Where Do We Go From Here? 725\u003c\/p\u003e \u003cp\u003e\u003cb\u003e24 (CEV) Processes in the Context of the LMM 729\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e24.1 Introduction and Financial Motivation 729\u003c\/p\u003e \u003cp\u003e24.2 Analytical Characterization of CEV Processes 730\u003c\/p\u003e \u003cp\u003e24.3 Financial Desirability of CEV Processes 732\u003c\/p\u003e \u003cp\u003e24.4 Numerical Problems with CEV Processes 734\u003c\/p\u003e \u003cp\u003e24.5 Approximate Numerical Solutions 735\u003c\/p\u003e \u003cp\u003e24.6 Problems with the Predictor–Corrector Approximation for the LMM 747\u003c\/p\u003e \u003cp\u003e\u003cb\u003e25 Stochastic-Volatility Extensions of the LMM 751\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e25.1 Plan of the Chapter 751\u003c\/p\u003e \u003cp\u003e25.2 What is the Dog and What is the Tail? 753\u003c\/p\u003e \u003cp\u003e25.3 Displaced Diffusion vs CEV 754\u003c\/p\u003e \u003cp\u003e25.4 The Approach 754\u003c\/p\u003e \u003cp\u003e25.5 Implementing and Calibrating the Stochastic-Volatility LMM 756\u003c\/p\u003e \u003cp\u003e25.6 Suggestions and Plan of the Work Ahead 764\u003c\/p\u003e \u003cp\u003e\u003cb\u003e26 The Dynamics of the Swaption Matrix 765\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e26.1 Plan of the Chapter 765\u003c\/p\u003e \u003cp\u003e26.2 Assessing the Quality of a Model 766\u003c\/p\u003e \u003cp\u003e26.3 The Empirical Analysis 767\u003c\/p\u003e \u003cp\u003e26.4 Extracting the Model-Implied Principal Components 776\u003c\/p\u003e \u003cp\u003e26.5 Discussion, Conclusions and Suggestions for Future Work 781\u003c\/p\u003e \u003cp\u003e\u003cb\u003e27 Stochastic-Volatility Extension of the LMM: Two-Regime Instantaneous Volatility 783\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e27.1 The Relevance of the Proposed Approach 783\u003c\/p\u003e \u003cp\u003e27.2 The Proposed Extension 783\u003c\/p\u003e \u003cp\u003e27.3 An Aside: Some Simple Properties of Markov Chains 785\u003c\/p\u003e \u003cp\u003e27.4 Empirical Tests 788\u003c\/p\u003e \u003cp\u003e27.5 How Important Is the Two-Regime Feature? 798\u003c\/p\u003e \u003cp\u003e27.6 Conclusions 801\u003c\/p\u003e \u003cp\u003eBibliography 805\u003c\/p\u003e \u003cp\u003eIndex 813\u003c\/p\u003e  \u003cb\u003eRiccardo Rebonato\u003c\/b\u003e is Head of Group Market Risk for the Royal Bank of Scotland Group, and Head of The Royal Bank of Scotland Group Quantitative Research Centre. He is also a Visiting Lecturer at Oxford University for the Mathematical Finance Diploma and MSc. He holds Doctorates in Nuclear Engineering and Science of Materials\/Solid State Physics. He sits on the Board of Directors of ISDA and on the Board of Trustees of GARP.\u003cbr\u003e Prior to joining the Royal Bank of Scotland, he was Head of Complex Derivatives Trading Europe and Head of Derivatives Research at Barclays Capital (BZW), where he worked for nine years.\u003cbr\u003e Before that he was a Research Fellow in Physics at Corpus Christi College, Oxford, UK. He is the author of three books, \u003ci\u003eModern Pricing of Interest-Rate Derivatives\u003c\/i\u003e, \u003ci\u003eVolatility and Correlation in Option Pricing\u003c\/i\u003e and \u003ci\u003eInterest-Rate Option Models\u003c\/i\u003e. He has published several papers on finance in academic journals, and is on the editorial board of several journals. He is a regular speaker at conferences worldwide.  The new edition of \u003ci\u003eVolatility and Correlation\u003c\/i\u003e has been thoroughly updated and expanded with over 80% new or reworked material, reflecting the changes and developments that have taken place in the field. The new and updated material includes: empirical and theoretical analysis of the smile dynamics; examination of the perfect-replication model in relation to exotic options; treatment of additional important models, namely, Variance Gamma, displaced diffusion, CEV, stochastic volatility for interest-rate smiles and equity\/FX options; questioning of the informational efficiency of markets in commonly-used calibration and hedging practices.  \u003cp\u003eThe book is split into four sections. Part I deals with a deterministic-volatility Black world (no smiles), and sets out the author's 'philosophical' approach to option pricing. Part II deals with smiles in the equity and FX worlds. Beginning with a review of relevant empirical information about smiles, this part provides coverage of local-stochastic-volatility, general-stochastic-volatility, jump-diffusion and Variance-Gamma processes. Part II concludes with an important chapter that discusses if and to what extent one can dispense with an explicit specification of a process-based model, and can directly prescribe the dynamics of the smile surface. Part III focuses on interest rates, and part IV extends the setting used for the deterministic-volatility LIBOR market model in order to account for interest-rate smiles in a financially-motivated and computationally-tractable manner. In this final part the author deals, in increasing levels of complexity, with CEV processes, with diffusive stochastic volatility and with Markov-chain processes.\u003c\/p\u003e \u003cp\u003eCovering FX, equity and interest-rate products, \u003ci\u003eVolatility and Correlation\u003c\/i\u003e is a blend of theoretical and practical material and is designed for traders, risk managers, financial professionals and students.\u003c\/p\u003e \u003cp\u003e‘The second edition is even more comprehensive than the first, and ideally suited to quantitatively oriented traders and risk managers. Rebonato has a knack for distilling the essence from a wide range of complex option pricing models.’ \u003cb\u003eDarrell Duffie, Stanford University, USA\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e‘The author has greatly extended the first edition of this book, whose main merit remains its courage to deal with relevant issues for practitioners. Rather than concentrating on fictional problems stemming from the need to give financial ground to one’s favourite theories, the author moves from problems posed by the market. At times a colloquial stance is privileged over mathematical rigor and formalism, allowing a larger public to benefit from this book.’ \u003cb\u003eDamiano Brigo, Head of Credit Models, Banca IMI, author of \u003ci\u003eInterest Rate Models: Theory and Practice.\u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e‘This book is about equity, FX and interest-rate option pricing at its best. It combines rigorous theory with practical knowledge of markets and models. Riccardo Rebonato uses his technical mastery to make the theory clear, and his wealth of experience to give insights into applications. Whatever your level of knowledge of these markets, you will learn from him.’ \u003cb\u003eIan Cooper, Professor of Finance, London Business School\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e‘In this book, Riccardo Rebonato discloses his invaluable expertise, shedding light over the gloomy path of modern model selection for pricing and hedging derivatives. Both practitioners and academics will benefit from his teachings and advice.’ \u003cb\u003eFabio Mercurio, Head of Financial Models, Banca IMI, Milan, Italy\u003c\/b\u003e\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47990461890789,"sku":"NP9780470091395","price":188.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780470091395.jpg?v=1761787923","url":"https:\/\/k12savings.com\/es\/products\/volatility-and-correlation-isbn-9780470091395","provider":"K12savings","version":"1.0","type":"link"}