{"product_id":"inside-volatility-filtering-9781118943977","title":"Inside Volatility Filtering","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eA new, more accurate take on the classical approach to volatility evaluation    Inside Volatility Filtering presents a new approach to volatility estimation, using financial econometrics based on a more accurate estimation of the hidden state.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eForeword ix \u003cp\u003eAcknowledgments (Second Edition) xi\u003c\/p\u003e \u003cp\u003eAcknowledgments (First Edition) xiii\u003c\/p\u003e \u003cp\u003eIntroduction (Second Edition) xv\u003c\/p\u003e \u003cp\u003eIntroduction (First Edition) xvii\u003c\/p\u003e \u003cp\u003eSummary xvii\u003c\/p\u003e \u003cp\u003eContributions and Further Research xxiii\u003c\/p\u003e \u003cp\u003eData and Programs xxiv\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 1 The Volatility Problem 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 1\u003c\/p\u003e \u003cp\u003eThe Stock Market 2\u003c\/p\u003e \u003cp\u003eThe Stock Price Process 2\u003c\/p\u003e \u003cp\u003eHistoric Volatility 3\u003c\/p\u003e \u003cp\u003eThe Derivatives Market 5\u003c\/p\u003e \u003cp\u003eThe Black-Scholes Approach 5\u003c\/p\u003e \u003cp\u003eThe Cox Ross Rubinstein Approach 7\u003c\/p\u003e \u003cp\u003eJump Diffusion and Level-Dependent Volatility 8\u003c\/p\u003e \u003cp\u003eJump Diffusion 8\u003c\/p\u003e \u003cp\u003eLevel-Dependent Volatility 11\u003c\/p\u003e \u003cp\u003eLocal Volatility 14\u003c\/p\u003e \u003cp\u003eThe Dupire Approach 14\u003c\/p\u003e \u003cp\u003eThe Derman Kani Approach 17\u003c\/p\u003e \u003cp\u003eStability Issues 18\u003c\/p\u003e \u003cp\u003eCalibration Frequency 19\u003c\/p\u003e \u003cp\u003eStochastic Volatility 21\u003c\/p\u003e \u003cp\u003eStochastic Volatility Processes 21\u003c\/p\u003e \u003cp\u003eGARCH and Diffusion Limits 22\u003c\/p\u003e \u003cp\u003eThe Pricing PDE under Stochastic Volatility 26\u003c\/p\u003e \u003cp\u003eThe Market Price of Volatility Risk 26\u003c\/p\u003e \u003cp\u003eThe Two-Factor PDE 27\u003c\/p\u003e \u003cp\u003eThe Generalized Fourier Transform 28\u003c\/p\u003e \u003cp\u003eThe Transform Technique 28\u003c\/p\u003e \u003cp\u003eSpecial Cases 30\u003c\/p\u003e \u003cp\u003eThe Mixing Solution 32\u003c\/p\u003e \u003cp\u003eThe Romano Touzi Approach 32\u003c\/p\u003e \u003cp\u003eA One-Factor Monte-Carlo Technique 34\u003c\/p\u003e \u003cp\u003eThe Long-Term Asymptotic Case 35\u003c\/p\u003e \u003cp\u003eThe Deterministic Case 35\u003c\/p\u003e \u003cp\u003eThe Stochastic Case 37\u003c\/p\u003e \u003cp\u003eA Series Expansion on Volatility-of-Volatility 39\u003c\/p\u003e \u003cp\u003eLocal Volatility Stochastic Volatility Models 42\u003c\/p\u003e \u003cp\u003eStochastic Implied Volatility 43\u003c\/p\u003e \u003cp\u003eJoint SPX and VIX Dynamics 45\u003c\/p\u003e \u003cp\u003ePure-Jump Models 47\u003c\/p\u003e \u003cp\u003eVariance Gamma 47\u003c\/p\u003e \u003cp\u003eVariance Gamma with Stochastic Arrival 51\u003c\/p\u003e \u003cp\u003eVariance Gamma with Gamma Arrival Rate 53\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 2 The Inference Problem 55\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 55\u003c\/p\u003e \u003cp\u003eUsing Option Prices 58\u003c\/p\u003e \u003cp\u003eConjugate Gradient (Fletcher-Reeves-Polak-Ribiere) Method 59\u003c\/p\u003e \u003cp\u003eLevenberg-Marquardt (LM) Method 59\u003c\/p\u003e \u003cp\u003eDirection Set (Powell) Method 61\u003c\/p\u003e \u003cp\u003eNumeric Tests 62\u003c\/p\u003e \u003cp\u003eThe Distribution of the Errors 65\u003c\/p\u003e \u003cp\u003eUsing Stock Prices 65\u003c\/p\u003e \u003cp\u003eThe Likelihood Function 65\u003c\/p\u003e \u003cp\u003eFiltering 69\u003c\/p\u003e \u003cp\u003eThe Simple and Extended Kalman Filters 72\u003c\/p\u003e \u003cp\u003eThe Unscented Kalman Filter 74\u003c\/p\u003e \u003cp\u003eKushner’s Nonlinear Filter 77\u003c\/p\u003e \u003cp\u003eParameter Learning 80\u003c\/p\u003e \u003cp\u003eParameter Estimation via MLE 95\u003c\/p\u003e \u003cp\u003eDiagnostics 108\u003c\/p\u003e \u003cp\u003eParticle Filtering 111\u003c\/p\u003e \u003cp\u003eComparing Heston with Other Models 133\u003c\/p\u003e \u003cp\u003eThe Performance of the Inference Tools 141\u003c\/p\u003e \u003cp\u003eThe Bayesian Approach 158\u003c\/p\u003e \u003cp\u003eUsing the Characteristic Function 172\u003c\/p\u003e \u003cp\u003eIntroducing Jumps 174\u003c\/p\u003e \u003cp\u003ePure-Jump Models 184\u003c\/p\u003e \u003cp\u003eRecapitulation 201\u003c\/p\u003e \u003cp\u003eModel Identification 201\u003c\/p\u003e \u003cp\u003eConvergence Issues and Solutions 202\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 3 The Consistency Problem 203\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 203\u003c\/p\u003e \u003cp\u003eThe Consistency Test 206\u003c\/p\u003e \u003cp\u003eThe Setting 206\u003c\/p\u003e \u003cp\u003eThe Cross-Sectional Results 206\u003c\/p\u003e \u003cp\u003eTime-Series Results 209\u003c\/p\u003e \u003cp\u003eFinancial Interpretation 210\u003c\/p\u003e \u003cp\u003eThe “Peso” Theory 214\u003c\/p\u003e \u003cp\u003eBackground 214\u003c\/p\u003e \u003cp\u003eNumeric Results 215\u003c\/p\u003e \u003cp\u003eTrading Strategies 216\u003c\/p\u003e \u003cp\u003eSkewness Trades 216\u003c\/p\u003e \u003cp\u003eKurtosis Trades 217\u003c\/p\u003e \u003cp\u003eDirectional Risks 217\u003c\/p\u003e \u003cp\u003eAn Exact Replication 219\u003c\/p\u003e \u003cp\u003eThe Mirror Trades 220\u003c\/p\u003e \u003cp\u003eAn Example of the Skewness Trade 220\u003c\/p\u003e \u003cp\u003eMultiple Trades 225\u003c\/p\u003e \u003cp\u003eHigh Volatility-of-Volatility and High Correlation 225\u003c\/p\u003e \u003cp\u003eNon-Gaussian Case 230\u003c\/p\u003e \u003cp\u003eVGSA 232\u003c\/p\u003e \u003cp\u003eA Word of Caution 236\u003c\/p\u003e \u003cp\u003eForeign Exchange, Fixed Income, and Other Markets 237\u003c\/p\u003e \u003cp\u003eForeign Exchange 237\u003c\/p\u003e \u003cp\u003eFixed Income 238\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 4 The Quality Problem 241\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 241\u003c\/p\u003e \u003cp\u003eAn Exact Solution? 241\u003c\/p\u003e \u003cp\u003eNonlinear Filtering 242\u003c\/p\u003e \u003cp\u003eStochastic PDE 243\u003c\/p\u003e \u003cp\u003eWiener Chaos Expansion 244\u003c\/p\u003e \u003cp\u003eFirst-Order WCE 247\u003c\/p\u003e \u003cp\u003eSimulations 248\u003c\/p\u003e \u003cp\u003eSecond-Order WCE 251\u003c\/p\u003e \u003cp\u003eQuality of Observations 251\u003c\/p\u003e \u003cp\u003eHistoric Spot Prices 252\u003c\/p\u003e \u003cp\u003eHistoric Option Prices 252\u003c\/p\u003e \u003cp\u003eConclusion 262\u003c\/p\u003e \u003cp\u003eBibliography 263\u003c\/p\u003e \u003cp\u003eIndex 279\u003c\/p\u003e","brand":"John Wiley \u0026 Sons 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