Holdings: Market risk analysis

Market risk analysis: 3 Pricing, hedging and trading financial instruments

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Bibliographic Details
Main Author:	Alexander, Carol (Author)
Format:	Book
Language:	English
Published:	Chichester [u.a.] Wiley 2008
Online Access:	Inhaltsverzeichnis
Physical Description:	XXX, 386 S. graph. Darst. 1 CD-ROM (12 cm)
ISBN:	9780470997895

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adam_text	Contents List of Figures List of Tables List of Examples Foreword Preface to Volume Ш xiii xvii xix xxi xxv Ш.1 Bonds and Swaps 1 Ш.1.1 Introduction 1 Ш.1.2 Merest Rates 2 Ш. 1.2.1 Continuously Compounded Spot and Forward Rates 3 Ш. 1.2.2 Discretely Compounded Spot Rates 4 Ш. 1.2.3 Translation between Discrete Rates and Continuous Rates 6 Ш.1.2.4 Spot and Forward Rates with Discrete Compounding 6 Ш. 1.2.5 LIBOR 8 Ш.1.3 Categorization of Bonds 8 Ш. 1.3.1 Categorization by Issuer 9 Ш.1.3.2 Categorization by Coupon and Maturity 10 III. 1.4 Characteristics of Bonds and Interest Rates 10 Ш. 1.4.1 Present Value, Price and Yield 11 Ш. 1.4.2 Relationship between Price and Yield 13 Ш. 1.4.3 Yield Curves 14 Ш. 1.4.4 Behaviour of Market Interest Rates 17 Ш. 1.4.5 Characteristics of Spot and Forward Term Structures 19 Ш.1.5 Duration and Convexity 20 Ш. 1.5.1 Macaulay Duration 21 Ш. 1.5.2 Modified Duration 23 Ш. 1.5.3 Convexity 24 Ш. 1.5.4 Duration and Convexity of a Bond Portfolio 24 Ш. 1.5.5 Duration-Convexity Approximations to Bond Price Change 25 Ш. 1.5.6 Immunizing Bond Portfolios 27 Contents ТИЛ. 6 Bonds with Semi-Annual and Floating Coupons 28 Ш. 1.6.1 Semi-Annual and Quarterly Coupons 29 Ш. 1.6.2 Floating Rate Notes 31 Ш. 1.6.3 Other Floaters 33 Ш.1.7 Forward Rate Agreements and Interest Rate Swaps 33 Ш. 1.7.1 Forward Rate Agreements 34 Ш. 1.7.2 Interest Rate Swaps 35 Ш. 1.7.3 Cash Flows on Vanilla Swaps 36 Ш. 1.7.4 Cross-Currency Swaps 38 Ш. 1.7.5 Other Swaps 40 Ш.1.8 Present Value of Basis Point 41 Ш.1.8.1 PV01 and Value Duration 41 Ш.1.8.2 Approximations to Ρ VOI 44 ΠΙ. 1.8.3 Understanding Interest Rate Risk 45 Ш.1.9 Yield Curve Fitting 48 Ш. 1.9.1 Calibration Instruments 48 ΠΙ. 1.9.2 Bootstrapping 49 Ш. 1.9.3 Splines 51 Ш. 1.9.4 Parametric Models 52 ΠΙ.1.9.5 Case Study: Statistical Properties of Forward LIBOR Rates 53 Ш. 1.10 Convertible Bonds 59 Ш. 1.10.1 Characteristics of Convertible Bonds 60 ΠΙ. 1.10.2 Survey of Pricing Models for Convertible Bonds 61 Ш.1.11 Summary and Conclusions 62 III.2 Futures and Forwards 65 Ш.2.1 Introduction 65 Ш.2.2 Characteristics of Futures and Forwards 68 Ш.2.2.1 Interest Rate and Swap Futures 68 Ш.2.2.2 Bond Futures 70 Ш.2.2.3 Currency Futures and Forwards 73 ΠΙ.2.2.4 Energy and Commodity Futures 74 Ш.2.2.5 Stock Futures and Index Futures 79 Ш.2.2.6 Exchange Traded Funds and ETF Futures 80 Ш.2.2.7 New Futures Markets 82 Ш.2.3 Theoretical Relationships between Spot, Forward and Futures 87 Ш.2.3.1 No Arbitrage Pricing 87 Ш.2.3.2 Accounting for Dividends 88 Ш.2.3.3 Dividend Risk and Interest Rate Risk 90 Ш.2.3.4 Currency Forwards and the Interest Rate Differential 91 Ш.2.3.5 No Arbitrage Prices for Forwards on Bonds 92 Ш.2.3.6 Commodity Forwards, Carry Costs and Convenience Yields 93 Ш.2.3.7 Fair Values of Futures and Spot 94 ΙΠ.2.4 The Basis 95 Ш.2.4.1 No Arbitrage Range 95 Contents ix Ш.2.4.2 Correlation between Spot and Futures Returns 97 Ш.2.4.3 Introducing Basis Risk 98 111.2.4.4 Basis Risk in Commodity Markets 100 III.2.5 Hedging with Forwards and Futures 101 Ш.2.5.1 Traditional Insurance Approach 102 Ш.2.5.2 Mean-Variance Approach 104 Ш.2.5.3 Understanding the Minimum Variance Hedge Ratio 106 Ш.2.5.4 Position Risk 108 111.2.5.5 Proxy Hedging 110 Ш.2.5.6 Basket Hedging 111 III.2.5.7 Performance Measures for Hedged Portfolios 112 Ш.2.6 Hedging in Practice 113 Ш.2.6.1 Hedging Forex Risk 113 Ш.2.6.2 Hedging International Stock Portfolios 114 111.2.6.3 Case Study: Hedging an Energy Futures Portfolio 118 111.2.6.4 Hedging Bond Portfolios 124 III.2.7 Using Futures for Short Term Hedging 126 Ш.2.7.1 Regression Based Minimum Variance Hedge Ratios 127 Ш.2.7.2 Academic Literature on Minimum Variance Hedging 129 III.2.7.3 Short Term Hedging in Liquid Markets 131 ΙΠ.2.8 Summary and Conclusions 133 ШЈ Options 137 137 139 140 142 144 146 147 148 151 152 153 154 155 156 158 159 159 161 161 163 164 165 167 167 Options III.3.1 Introduction Ш.3.2 Foundations Ш.3.2.1 Arithmetic and Geometric Brownian Motion Ш.3.2.2 Risk Neutral Valuation Ш.3.2.3 Numeraire and Measure Ш.3.2.4 Market Prices and Model Prices Ш.3.2.5 Parameters and Calibration Ш.3.2.6 Option Pricing: Review of the Binomial Model IH.3.3 Characteristics of Vanilla Options Ш.3.3.1 Elementary Options Ш.3.3.2 Put-Call Parity Ш.З.З.З Moneyness Ш.3.3.4 American Options Ш.3.3.5 Early Exercise Boundary Ш.3.3.6 Pricing American Options Ш.3.4 Hedging Options Ш.3.4.1 Delta Ш.3.4.2 Delta Hedging Ш.3.4.3 Other Greeks Ш.3.4.4 Position Greeks Ш.3.4.5 Delta-Gamma Hedging Ш.3.4.6 Delta-Gamma-Vega Hedging Ш.3.5 Trading ( Options Ш.3.5.1 Bull Strategies Contents Ш.3.5.2 Bear Strategies 168 Ш.3.5.3 Other Spread Strategies 169 Ш.3.5.4 Volatility Strategies 170 Ш.3.5.5 Replication of P&L Profiles 172 Ш.3.6 The Black-Scholes-Merton Model 173 Ш.3.6.1 Assumptions 174 Ш.3.6.2 Black-Scholes-Merton PDE 175 Ш.3.6.3 Is the Underlying the Spot or the Futures Contract? 176 Ш.3.6.4 Black-Scholes-Merton Pricing Formula 178 Ш.3.6.5 Interpretation of the Black-Scholes-Merton Formula 180 Ш.3.6.6 Implied Volatility 183 Ш.3.6.7 Adjusting BSM Prices for Stochastic Volatility 183 Ш.3.7 The Black-Scholes-Merton Greeks 186 Ш.3.7.1 Delta 187 Ш.3.7.2 ThetaandRho 188 Ш.3.7.3 Gamma 189 Ш.3.7.4 Vega, Varma and Volga 190 Ш.3.7.5 Static Hedges for Standard European Options 193 Ш.3.8 Interest Rate Options 194 Ш.3.8.1 Caplets and Floorlets 195 Ш.3.8.2 Caps, Floors and their Implied Volatilities 196 Ш.3.8.3 European Swaptions 198 Ш.3.8.4 Short Rate Models 199 Ш.3.8.5 LIBOR Model 201 Ш.3.8.6 Case Study: Application of PCA to LIBOR Model Calibration 203 Ш.3.9 Pricing Exotic Options 207 Ш.3.9.1 Pay-offs to Exotic Options 208 Ш.3.9.2 Exchange Options and Best/Worst of Two Asset Options 209 Ш.3.9.3 Spread Options 211 Ш.3.9.4 Currency Protected Options 213 Ш.3.9.5 Power Options 214 Ш.3.9.6 Chooser Options and Contingent Options 214 Ш.3.9.7 Compound Options 216 Ш.3.9.8 Capped Options and Ladder Options 216 Ш.3.9.9 Look-Back and Look-Forward Options 218 Ш.3.9.10 Barrier Options 219 Ш.3.9.11 Asian Options 221 Ш.3.10 Summary and Conclusions 224 Ш.4 Volatility 227 Ш.4.1 Introduction 227 Ш.4.2 Implied Volatility 231 Ш.4.2.1 Backing Out Implied Volatility from a Market Price 231 Ш.4.2.2 Equity Index Volatility Skew 233 Ш.4.2.3 Smiles and Skews in Other Markets 236 Contents Xl Ш.4.2.4 Term Structures of Implied Volatilities 238 III.4.2.5 Implied Volatility Surfaces 239 Ш.4.2.6 Cap and Caplet Volatilities 240 III.4.2.7 Swaption Volatilities 242 Ш.4.3 Local Volatility 243 Ш.4.3.1 Forward Volatility 244 111.4.3.2 Dupire s Equation 245 Ш.4.3.3 Parametric Models of Local Volatility 248 111.4.3.4 Lognormal Mixture Diffusion 249 Ш.4.4 Modelling the Dynamics of Implied Volatility 255 Ш.4.4.1 Sticky Models 255 Ш.4.4.2 Case Study I: Principal Component Analysis of Implied Volatilities 257 111.4.4.3 Case Study II: Modelling the ATM Volatility-Index Relationship 261 Ш.4.4.4 Case Study III: Modelling the Skew Sensitivities 264 Ш.4.4.5 Applications of Implied Volatility Dynamics to Hedging Options 265 Ш.4.5 Stochastic Volatility Models 268 Ш.4.5.1 Stochastic Volatility PDE 269 III.4.5.2 Properties of Stochastic Volatility 271 Ш.4.5.3 Model Implied Volatility Surface 275 Ш.4.5.4 Model Local Volatility Surface 277 Ш.4.5.5 Heston Model 278 Ш.4.5.6 GARCH Diffusions 280 Ш.4.5.7 CEV and SABR Models 285 Ш.4.5.8 Jumps in Prices and in Stochastic Volatility 287 Ш.4.6 Scale Invariance and Hedging 289 III.4.6.1 Scale Invariance and Change of Numeraire 291 Ш.4.6.2 Definition of Scale Invariance 291 IH.4.6.3 Scale Invariance and Homogeneity 292 Ш.4.6.4 Model Free Price Hedge Ratios 294 111.4.6.5 Minimum Variance Hedging 297 Ш.4.6.6 Minimum Variance Hedge Ratios in Specific Models 299 Ш.4.6.7 Empirical Results 300 Ш.4.7 Trading Volatility 303 Ш.4.7.1 Variance Swaps and Volatility Swaps 304 Ш.4.7.2 Trading Forward Volatility 306 Ш.4.7.3 Variance Risk Premium 307 Ш.4.7.4 Construction of a Volatility Index 308 Ш.4.7.5 Effect of the Skew 309 Ш.4.7.6 Term Structures of Volatility Indices 309 Ш.4.7.7 Vix and Other Volatility Indices 311 Ш.4.7.8 Volatility Index Futures 312 Ш.4.7.9 Options on Volatility Indices 314 Ш.4.7.10 Using Realized Volatility Forecasts to Trade Volatility 315 Ш.4.8 Summary and Conclusion 316 xii Contents Ш.5 Portfolio Mapping 321 Ш.5.1 Introduction 321 Ш.5.2 Risk Factors and Risk Factor Sensitivities 323 Ш.5.2.1 Interest Rate Sensitive Portfolios 323 Ш.5.2.2 Equity Portfolios 324 Ш.5.2.3 International Exposures 327 Ш.5.2.4 Commodity Portfolios 328 Ш.5.2.5 Options Portfolios 328 Ш.5.2.6 Orthogonalization of Risk Factors 330 Ш.5.2.7 Nominal versus Percentage Risk Factors and Sensitivities 330 Ш.5.3 Cash Flow Mapping 332 Ш.5.3.1 Present Value Invariant and Duration Invariant Maps 332 Ш.5.3.2 PV01 Invariant Cash Flow Maps 333 Ш.5.3.3 Volatility Invariant Maps 334 Ш.5.3.4 Complex Cash Flow Maps 336 Ш.5.4 Applications of Cash Flow Mapping to Market Risk Management 337 Ш.5.4. 1 Risk Management of Interest Rate Sensitive Portfolios 337 Ш.5.4.2 Mapping Portfolios of Commodity Futures 338 Ш.5.5 Mapping an Options Portfolio to Price Risk Factors 340 Ш.5.5.1 Taylor Expansions 341 Ш.5.5.2 Value Delta and Value Gamma 342 Ш.5.5.3 Delta-Gamma Approximation: Single Underlying 344 Ш.5.5.4 Effect of Gamma on Portfolio Risk 346 Ш.5.5.5 Price Beta Mapping 347 Ш.5.5.6 Delta-Gamma Approximation: Several Underlyings 349 Ш.5.5.7 Including Time and Interest Rates Sensitivities 351 Ш.5.6 Mapping Implied Volatility 353 Ш.5.6.1 Vega Risk in Options Portfolios 353 Ш.5.6.2 Second Order Approximations: Vanna and Volga 354 Ш.5.6.3 Vega Bucketing 355 Ш.5.6.4 Volatility Beta Mapping 356 Ш.5.7 Case Study: Volatility Risk in FTSE 100 Options 357 Ш.5.7.1 Estimating the Volatility Betas 357 Ш.5.7.2 Model Risk of Volatility Mapping 360 Ш.5.7.3 Mapping to Term Structures of Volatility Indices 361 Ш.5.7.4 Using PCA with Volatility Betas 361 Ш.5.8 Summary and Conclusions 364 References 367 Index 377
adam_txt	Contents List of Figures List of Tables List of Examples Foreword Preface to Volume Ш xiii xvii xix xxi xxv Ш.1 Bonds and Swaps 1 Ш.1.1 Introduction 1 Ш.1.2 Merest Rates 2 Ш. 1.2.1 Continuously Compounded Spot and Forward Rates 3 Ш. 1.2.2 Discretely Compounded Spot Rates 4 Ш. 1.2.3 Translation between Discrete Rates and Continuous Rates 6 Ш.1.2.4 Spot and Forward Rates with Discrete Compounding 6 Ш. 1.2.5 LIBOR 8 Ш.1.3 Categorization of Bonds 8 Ш. 1.3.1 Categorization by Issuer 9 Ш.1.3.2 Categorization by Coupon and Maturity 10 III. 1.4 Characteristics of Bonds and Interest Rates 10 Ш. 1.4.1 Present Value, Price and Yield 11 Ш. 1.4.2 Relationship between Price and Yield 13 Ш. 1.4.3 Yield Curves 14 Ш. 1.4.4 Behaviour of Market Interest Rates 17 Ш. 1.4.5 Characteristics of Spot and Forward Term Structures 19 Ш.1.5 Duration and Convexity 20 Ш. 1.5.1 Macaulay Duration 21 Ш. 1.5.2 Modified Duration 23 Ш. 1.5.3 Convexity 24 Ш. 1.5.4 Duration and Convexity of a Bond Portfolio 24 Ш. 1.5.5 Duration-Convexity Approximations to Bond Price Change 25 Ш. 1.5.6 Immunizing Bond Portfolios 27 Contents ТИЛ. 6 Bonds with Semi-Annual and Floating Coupons 28 Ш. 1.6.1 Semi-Annual and Quarterly Coupons 29 Ш. 1.6.2 Floating Rate Notes 31 Ш. 1.6.3 Other Floaters 33 Ш.1.7 Forward Rate Agreements and Interest Rate Swaps 33 Ш. 1.7.1 Forward Rate Agreements 34 Ш. 1.7.2 Interest Rate Swaps 35 Ш. 1.7.3 Cash Flows on Vanilla Swaps 36 Ш. 1.7.4 Cross-Currency Swaps 38 Ш. 1.7.5 Other Swaps 40 Ш.1.8 Present Value of Basis Point 41 Ш.1.8.1 PV01 and Value Duration 41 Ш.1.8.2 Approximations to Ρ VOI 44 ΠΙ. 1.8.3 Understanding Interest Rate Risk 45 Ш.1.9 Yield Curve Fitting 48 Ш. 1.9.1 Calibration Instruments 48 ΠΙ. 1.9.2 Bootstrapping 49 Ш. 1.9.3 Splines 51 Ш. 1.9.4 Parametric Models 52 ΠΙ.1.9.5 Case Study: Statistical Properties of Forward LIBOR Rates 53 Ш. 1.10 Convertible Bonds 59 Ш. 1.10.1 Characteristics of Convertible Bonds 60 ΠΙ. 1.10.2 Survey of Pricing Models for Convertible Bonds 61 Ш.1.11 Summary and Conclusions 62 III.2 Futures and Forwards 65 Ш.2.1 Introduction 65 Ш.2.2 Characteristics of Futures and Forwards 68 Ш.2.2.1 Interest Rate and Swap Futures 68 Ш.2.2.2 Bond Futures 70 Ш.2.2.3 Currency Futures and Forwards 73 ΠΙ.2.2.4 Energy and Commodity Futures 74 Ш.2.2.5 Stock Futures and Index Futures 79 Ш.2.2.6 Exchange Traded Funds and ETF Futures 80 Ш.2.2.7 New Futures Markets 82 Ш.2.3 Theoretical Relationships between Spot, Forward and Futures 87 Ш.2.3.1 No Arbitrage Pricing 87 Ш.2.3.2 Accounting for Dividends 88 Ш.2.3.3 Dividend Risk and Interest Rate Risk 90 Ш.2.3.4 Currency Forwards and the Interest Rate Differential 91 Ш.2.3.5 No Arbitrage Prices for Forwards on Bonds 92 Ш.2.3.6 Commodity Forwards, Carry Costs and Convenience Yields 93 Ш.2.3.7 Fair Values of Futures and Spot 94 ΙΠ.2.4 The Basis 95 Ш.2.4.1 No Arbitrage Range 95 Contents ix Ш.2.4.2 Correlation between Spot and Futures Returns 97 Ш.2.4.3 Introducing Basis Risk 98 111.2.4.4 Basis Risk in Commodity Markets 100 III.2.5 Hedging with Forwards and Futures 101 Ш.2.5.1 Traditional 'Insurance' Approach 102 Ш.2.5.2 Mean-Variance Approach 104 Ш.2.5.3 Understanding the Minimum Variance Hedge Ratio 106 Ш.2.5.4 Position Risk 108 111.2.5.5 Proxy Hedging 110 Ш.2.5.6 Basket Hedging 111 III.2.5.7 Performance Measures for Hedged Portfolios 112 Ш.2.6 Hedging in Practice 113 Ш.2.6.1 Hedging Forex Risk 113 Ш.2.6.2 Hedging International Stock Portfolios 114 111.2.6.3 Case Study: Hedging an Energy Futures Portfolio 118 111.2.6.4 Hedging Bond Portfolios 124 III.2.7 Using Futures for Short Term Hedging 126 Ш.2.7.1 Regression Based Minimum Variance Hedge Ratios 127 Ш.2.7.2 Academic Literature on Minimum Variance Hedging 129 III.2.7.3 Short Term Hedging in Liquid Markets 131 ΙΠ.2.8 Summary and Conclusions 133 ШЈ Options 137 137 139 140 142 144 146 147 148 151 152 153 154 155 156 158 159 159 161 161 163 164 165 167 167 Options III.3.1 Introduction Ш.3.2 Foundations Ш.3.2.1 Arithmetic and Geometric Brownian Motion Ш.3.2.2 Risk Neutral Valuation Ш.3.2.3 Numeraire and Measure Ш.3.2.4 Market Prices and Model Prices Ш.3.2.5 Parameters and Calibration Ш.3.2.6 Option Pricing: Review of the Binomial Model IH.3.3 Characteristics of Vanilla Options Ш.3.3.1 Elementary Options Ш.3.3.2 Put-Call Parity Ш.З.З.З Moneyness Ш.3.3.4 American Options Ш.3.3.5 Early Exercise Boundary Ш.3.3.6 Pricing American Options Ш.3.4 Hedging Options Ш.3.4.1 Delta Ш.3.4.2 Delta Hedging Ш.3.4.3 Other Greeks Ш.3.4.4 Position Greeks Ш.3.4.5 Delta-Gamma Hedging Ш.3.4.6 Delta-Gamma-Vega Hedging Ш.3.5 Trading ( Options Ш.3.5.1 Bull Strategies Contents Ш.3.5.2 Bear Strategies 168 Ш.3.5.3 Other Spread Strategies 169 Ш.3.5.4 Volatility Strategies 170 Ш.3.5.5 Replication of P&L Profiles 172 Ш.3.6 The Black-Scholes-Merton Model 173 Ш.3.6.1 Assumptions 174 Ш.3.6.2 Black-Scholes-Merton PDE 175 Ш.3.6.3 Is the Underlying the Spot or the Futures Contract? 176 Ш.3.6.4 Black-Scholes-Merton Pricing Formula 178 Ш.3.6.5 Interpretation of the Black-Scholes-Merton Formula 180 Ш.3.6.6 Implied Volatility 183 Ш.3.6.7 Adjusting BSM Prices for Stochastic Volatility 183 Ш.3.7 The Black-Scholes-Merton Greeks 186 Ш.3.7.1 Delta 187 Ш.3.7.2 ThetaandRho 188 Ш.3.7.3 Gamma 189 Ш.3.7.4 Vega, Varma and Volga 190 Ш.3.7.5 Static Hedges for Standard European Options 193 Ш.3.8 Interest Rate Options 194 Ш.3.8.1 Caplets and Floorlets 195 Ш.3.8.2 Caps, Floors and their Implied Volatilities 196 Ш.3.8.3 European Swaptions 198 Ш.3.8.4 Short Rate Models 199 Ш.3.8.5 LIBOR Model 201 Ш.3.8.6 Case Study: Application of PCA to LIBOR Model Calibration 203 Ш.3.9 Pricing Exotic Options 207 Ш.3.9.1 Pay-offs to Exotic Options 208 Ш.3.9.2 Exchange Options and Best/Worst of Two Asset Options 209 Ш.3.9.3 Spread Options 211 Ш.3.9.4 Currency Protected Options 213 Ш.3.9.5 Power Options 214 Ш.3.9.6 Chooser Options and Contingent Options 214 Ш.3.9.7 Compound Options 216 Ш.3.9.8 Capped Options and Ladder Options 216 Ш.3.9.9 Look-Back and Look-Forward Options 218 Ш.3.9.10 Barrier Options 219 Ш.3.9.11 Asian Options 221 Ш.3.10 Summary and Conclusions 224 Ш.4 Volatility 227 Ш.4.1 Introduction 227 Ш.4.2 Implied Volatility 231 Ш.4.2.1 'Backing Out' Implied Volatility from a Market Price 231 Ш.4.2.2 Equity Index Volatility Skew 233 Ш.4.2.3 Smiles and Skews in Other Markets 236 Contents Xl Ш.4.2.4 Term Structures of Implied Volatilities 238 III.4.2.5 Implied Volatility Surfaces 239 Ш.4.2.6 Cap and Caplet Volatilities 240 III.4.2.7 Swaption Volatilities 242 Ш.4.3 Local Volatility 243 Ш.4.3.1 Forward Volatility 244 111.4.3.2 Dupire's Equation 245 Ш.4.3.3 Parametric Models of Local Volatility 248 111.4.3.4 Lognormal Mixture Diffusion 249 Ш.4.4 Modelling the Dynamics of Implied Volatility 255 Ш.4.4.1 Sticky Models 255 Ш.4.4.2 Case Study I: Principal Component Analysis of Implied Volatilities 257 111.4.4.3 Case Study II: Modelling the ATM Volatility-Index Relationship 261 Ш.4.4.4 Case Study III: Modelling the Skew Sensitivities 264 Ш.4.4.5 Applications of Implied Volatility Dynamics to Hedging Options 265 Ш.4.5 Stochastic Volatility Models 268 Ш.4.5.1 Stochastic Volatility PDE 269 III.4.5.2 Properties of Stochastic Volatility 271 Ш.4.5.3 Model Implied Volatility Surface 275 Ш.4.5.4 Model Local Volatility Surface 277 Ш.4.5.5 Heston Model 278 Ш.4.5.6 GARCH Diffusions 280 Ш.4.5.7 CEV and SABR Models 285 Ш.4.5.8 Jumps in Prices and in Stochastic Volatility 287 Ш.4.6 Scale Invariance and Hedging 289 III.4.6.1 Scale Invariance and Change of Numeraire 291 Ш.4.6.2 Definition of Scale Invariance 291 IH.4.6.3 Scale Invariance and Homogeneity 292 Ш.4.6.4 Model Free Price Hedge Ratios 294 111.4.6.5 Minimum Variance Hedging 297 Ш.4.6.6 Minimum Variance Hedge Ratios in Specific Models 299 Ш.4.6.7 Empirical Results 300 Ш.4.7 Trading Volatility 303 Ш.4.7.1 Variance Swaps and Volatility Swaps 304 Ш.4.7.2 Trading Forward Volatility 306 Ш.4.7.3 Variance Risk Premium 307 Ш.4.7.4 Construction of a Volatility Index 308 Ш.4.7.5 Effect of the Skew 309 Ш.4.7.6 Term Structures of Volatility Indices 309 Ш.4.7.7 Vix and Other Volatility Indices 311 Ш.4.7.8 Volatility Index Futures 312 Ш.4.7.9 Options on Volatility Indices 314 Ш.4.7.10 Using Realized Volatility Forecasts to Trade Volatility 315 Ш.4.8 Summary and Conclusion 316 xii Contents Ш.5 Portfolio Mapping 321 Ш.5.1 Introduction 321 Ш.5.2 Risk Factors and Risk Factor Sensitivities 323 Ш.5.2.1 Interest Rate Sensitive Portfolios 323 Ш.5.2.2 Equity Portfolios 324 Ш.5.2.3 International Exposures 327 Ш.5.2.4 Commodity Portfolios 328 Ш.5.2.5 Options Portfolios 328 Ш.5.2.6 Orthogonalization of Risk Factors 330 Ш.5.2.7 Nominal versus Percentage Risk Factors and Sensitivities 330 Ш.5.3 Cash Flow Mapping 332 Ш.5.3.1 Present Value Invariant and Duration Invariant Maps 332 Ш.5.3.2 PV01 Invariant Cash Flow Maps 333 Ш.5.3.3 Volatility Invariant Maps 334 Ш.5.3.4 Complex Cash Flow Maps 336 Ш.5.4 Applications of Cash Flow Mapping to Market Risk Management 337 Ш.5.4. 1 Risk Management of Interest Rate Sensitive Portfolios 337 Ш.5.4.2 Mapping Portfolios of Commodity Futures 338 Ш.5.5 Mapping an Options Portfolio to Price Risk Factors 340 Ш.5.5.1 Taylor Expansions 341 Ш.5.5.2 Value Delta and Value Gamma 342 Ш.5.5.3 Delta-Gamma Approximation: Single Underlying 344 Ш.5.5.4 Effect of Gamma on Portfolio Risk 346 Ш.5.5.5 Price Beta Mapping 347 Ш.5.5.6 Delta-Gamma Approximation: Several Underlyings 349 Ш.5.5.7 Including Time and Interest Rates Sensitivities 351 Ш.5.6 Mapping Implied Volatility 353 Ш.5.6.1 Vega Risk in Options Portfolios 353 Ш.5.6.2 Second Order Approximations: Vanna and Volga 354 Ш.5.6.3 Vega Bucketing 355 Ш.5.6.4 Volatility Beta Mapping 356 Ш.5.7 Case Study: Volatility Risk in FTSE 100 Options 357 Ш.5.7.1 Estimating the Volatility Betas 357 Ш.5.7.2 Model Risk of Volatility Mapping 360 Ш.5.7.3 Mapping to Term Structures of Volatility Indices 361 Ш.5.7.4 Using PCA with Volatility Betas 361 Ш.5.8 Summary and Conclusions 364 References 367 Index 377
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id	DE-604.BV023295532
illustrated	Illustrated
index_date	2024-07-02T20:44:40Z
indexdate	2024-07-09T21:15:12Z
institution	BVB
isbn	9780470997895
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-016480072
oclc_num	633206681
open_access_boolean
owner	DE-91G DE-BY-TUM DE-1050 DE-355 DE-BY-UBR DE-703 DE-11
owner_facet	DE-91G DE-BY-TUM DE-1050 DE-355 DE-BY-UBR DE-703 DE-11
physical	XXX, 386 S. graph. Darst. 1 CD-ROM (12 cm)
publishDate	2008
publishDateSearch	2008
publishDateSort	2008
publisher	Wiley
record_format	marc
spelling	Alexander, Carol Verfasser aut Market risk analysis 3 Pricing, hedging and trading financial instruments Carol Alexander Chichester [u.a.] Wiley 2008 XXX, 386 S. graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier (DE-604)BV023295503 3 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016480072&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Alexander, Carol Market risk analysis
title	Market risk analysis
title_auth	Market risk analysis
title_exact_search	Market risk analysis
title_exact_search_txtP	Market risk analysis
title_full	Market risk analysis 3 Pricing, hedging and trading financial instruments Carol Alexander
title_fullStr	Market risk analysis 3 Pricing, hedging and trading financial instruments Carol Alexander
title_full_unstemmed	Market risk analysis 3 Pricing, hedging and trading financial instruments Carol Alexander
title_short	Market risk analysis
title_sort	market risk analysis pricing hedging and trading financial instruments
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016480072&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV023295503
work_keys_str_mv	AT alexandercarol marketriskanalysis3

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