Market Risk Analysis, Pricing, Hedging and Trading Financial Instruments

by Alexander, Carol

• ISBN13: 9780470997895
• ISBN10: 0470997893
• Edition: 1st
• Format: Hardcover
• Copyright: 2008-06-09
• Publisher: Wiley

Summary

Volume III: MODELLING FINANCIAL INSTRUMENTS As a set these books are a radical update and revision of Market Models: a Guide to Financial Data Analysis. They provide a rigorous explanation of the key theoretical ideas that market model developers are faced with, in practical, clear terms. Developers are faced with many decisions, about the pricing, the data, the statistical methodology and the calibration and testing of the model prior to implementation therefore these books help risk managers, quantitative traders and investment analysts make the right decisions. The emphasis throughout is in understanding concepts and implementing solutions, assisted by the use of real-world examples both in the text and, interactively, on the accompanying CDs. All of the CD's contain VBA code & C++ code, plus VBA with Excel interface Modelling Financial Instruments is a radical update and revision of the Volatility and Correlation sections covered in Market Models: A Guide to Financial Data Analysis creating a new, stand-alone book forming Part II of the four-volume set on market risk analysis.. Modelling Financial Instruments covers advanced volatility analysis and hedging options portfolios, which are essential for market risk practitioners, taking the reader from the basics (assuming zero knowledge) right through to the more advanced concepts, in a concise, practical manner. The emphasis is on theory and calibration of these models appropriate to different markets and significantly builds on the strengths of Market Models Part I, covering in-depth analysis of Bonds and Cash Flows; factor models for Equity Portfolios; Futures and Forwards; Options; modelling Volatility and hedging Options Portfolios. All material is supported by real-world case studies using Excel spreadsheets and an accompanying CD so that the reader is provided with complete solutions.

Author Biography

Carol Alexander is a Professor of Risk Management at the ICMA Centre, University of Reading, and Chair of the Academic Advisory Council of the Professional Risk Manager’s International Association (PRMIA). She is the author of Market Models: A Guide to Financial Data Analysis(John Wiley & Sons Ltd, 2001) and has been editor and contributor of a very large number of books in finance and mathematics, including the multi-volume Professional Risk Manager’s Handbook(McGraw-Hill, 2008 and PRMIA Publications). Carol has published nearly 100 academic journal articles, book chapters and books, the majority of which focus on financial risk management and mathematical finance. Professor Alexander is one of the world’s leading authorities on market risk analysis. For further details, see www.icmacentre.rdg.ac.uk/alexander

Table of Contents

List of Figures	p. xiii
List of Tables	p. xvii
List of Examples	p. xix
Foreword	p. xxi
Preface to Volume III	p. xxv
Bonds and Swaps	p. 1
Introduction	p. 1
Interest Rates	p. 2
Continuously Compounded Spot and Forward Rates	p. 3
Discretely Compounded Spot Rates	p. 4
Translation between Discrete Rates and Continuous Rates	p. 6
Spot and Forward Rates with Discrete Compounding	p. 6
LIBOR	p. 8
Categorization of Bonds	p. 8
Categorization by Issuer	p. 9
Categorization by Coupon and Maturity	p. 10
Characteristics of Bonds and Interest Rates	p. 10
Present Value, Price and Yield	p. 11
Relationship between Price and Yield	p. 13
Yield Curves	p. 14
Behaviour of Market Interest Rates	p. 17
Characteristics of Spot and Forward Term Structures	p. 19
Duration and Convexity	p. 20
Macaulay Duration	p. 21
Modified Duration	p. 23
Convexity	p. 24
Duration and Convexity of a Bond Portfolio	p. 24
Duration-Convexity Approximations to Bond Price Change	p. 25
Immunizing Bond Portfolios	p. 27
Bonds with Semi-Annual and Floating Coupons	p. 28
Semi-Annual and Quarterly Coupons	p. 29
Floating Rate Notes	p. 31
Other Floaters	p. 33
Forward Rate Agreements and Interest Rate Swaps	p. 33
Forward Rate Agreements	p. 34
Interest Rate Swaps	p. 35
Cash Flows on Vanilla Swaps	p. 36
Cross-Currency Swaps	p. 38
Other Swaps	p. 40
Present Value of Basis Point	p. 41
PV01 and Value Duration	p. 41
Approximations to PV01	p. 44
Understanding Interest Rate Risk	p. 45
Yield Curve Fitting	p. 48
Calibration Instruments	p. 48
Bootstrapping	p. 49
Splines	p. 51
Parametric Models	p. 52
Case Study: Statistical Properties of Forward LIBOR Rates	p. 53
Convertible Bonds	p. 59
Characteristics of Convertible Bonds	p. 60
Survey of Pricing Models for Convertible Bonds	p. 61
Summary and Conclusions	p. 62
Futures and Forwards	p. 65
Introduction	p. 65
Characteristics of Futures and Forwards	p. 68
Interest Rate and Swap Futures	p. 68
Bond Futures	p. 70
Currency Futures and Forwards	p. 73
Energy and Commodity Futures	p. 74
Stock Futures and Index Futures	p. 79
Exchange Traded Funds and ETF Futures	p. 80
New Futures Markets	p. 82
Theoretical Relationships between Spot, Forward and Futures	p. 87
No Arbitrage Pricing	p. 87
Accounting for Dividends	p. 88
Dividend Risk and Interest Rate Risk	p. 90
Currency Forwards and the Interest Rate Differential	p. 91
No Arbitrage Prices for Forwards on Bonds	p. 92
Commodity Forwards, Carry Costs and Convenience Yields	p. 93
Fair Values of Futures and Spot	p. 94
The Basis	p. 95
No Arbitrage Range	p. 95
Correlation between Spot and Futures Returns	p. 97
Introducing Basis Risk	p. 98
Basis Risk in Commodity Markets	p. 100
Hedging with Forwards and Futures	p. 101
Traditional 'Insurance' Approach	p. 102
Mean-Variance Approach	p. 104
Understanding the Minimum Variance Hedge Ratio	p. 106
Position Risk	p. 108
Proxy Hedging	p. 110
Basket Hedging	p. 111
Performance Measures for Hedged Portfolios	p. 112
Hedging in Practice	p. 113
Hedging Forex Risk	p. 113
Hedging International Stock Portfolios	p. 114
Case Study: Hedging an Energy Futures Portfolio	p. 118
Hedging Bond Portfolios	p. 124
Using Futures for Short Term Hedging	p. 126
Regression Based Minimum Variance Hedge Ratios	p. 127
Academic Literature on Minimum Variance Hedging	p. 129
Short Term Hedging in Liquid Markets	p. 131
Summary and Conclusions	p. 133
Options	p. 137
Introduction	p. 137
Foundations	p. 139
Arithmetic and Geometric Brownian Motion	p. 140
Risk Neutral Valuation	p. 142
Numeraire and Measure	p. 144
Market Prices and Model Prices	p. 146
Parameters and Calibration	p. 147
Option Pricing: Review of the Binomial Model	p. 148
Characteristics of Vanilla Options	p. 151
Elementary Options	p. 152
Put-Call Parity	p. 153
Moneyness	p. 154
American Options	p. 155
Early Exercise Boundary	p. 156
Pricing American Options	p. 158
Hedging Options	p. 159
Delta	p. 159
Delta Hedging	p. 161
Other Greeks	p. 161
Position Greeks	p. 163
Delta-Gamma Hedging	p. 164
Delta-Gamma-Vega Hedging	p. 165
Trading Options	p. 167
Bull Strategies	p. 167
Bear Strategies	p. 168
Other Spread Strategies	p. 169
Volatility Strategies	p. 170
Replication of P&L Profiles	p. 172
The Black-Scholes-Merton Model	p. 173
Assumptions	p. 174
Black-Scholes-Merton PDE	p. 175
Is the Underlying the Spot or the Futures Contract?	p. 176
Black-Scholes-Merton Pricing Formula	p. 178
Interpretation of the Black-Scholes-Merton Formula	p. 180
Implied Volatility	p. 183
Adjusting BSM Prices for Stochastic Volatility	p. 183
The Black-Scholes-Merton Greeks	p. 186
Delta	p. 187
Theta and Rho	p. 188
Gamma	p. 189
Vega, Vanna and Volga	p. 190
Static Hedges for Standard European Options	p. 193
Interest Rate Options	p. 194
Caplets and Floorlets	p. 195
Caps, Floors and their Implied Volatilities	p. 196
European Swaptions	p. 198
Short Rate Models	p. 199
LIBOR Model	p. 201
Case Study: Application of PCA to LIBOR Model Calibration	p. 203
Pricing Exotic Options	p. 207
Pay-offs to Exotic Options	p. 208
Exchange Options and Best/Worst of Two Asset Options	p. 209
Spread Options	p. 211
Currency Protected Options	p. 213
Power Options	p. 214
Chooser Options and Contingent Options	p. 214
Compound Options	p. 216
Capped Options and Ladder Options	p. 216
Look-Back and Look-Forward Options	p. 218
Barrier Options	p. 219
Asian Options	p. 221
Summary and Conclusions	p. 224
Volatility	p. 227
Introduction	p. 227
Implied Volatility	p. 231
'Backing Out' Implied Volatility from a Market Price	p. 231
Equity Index Volatility Skew	p. 233
Smiles and Skews in Other Markets	p. 236
Term Structures of Implied Volatilities	p. 238
Implied Volatility Surfaces	p. 239
Cap and Caplet Volatilities	p. 240
Swaption Volatilities	p. 242
Local Volatility	p. 243
Forward Volatility	p. 244
Dupire's Equation	p. 245
Parametric Models of Local Volatility	p. 248
Lognormal Mixture Diffusion	p. 249
Modelling the Dynamics of Implied Volatility	p. 255
Sticky Models	p. 255
Case Study I: Principal Component Analysis of Implied Volatilities	p. 257
Case Study II: Modelling the ATM Volatility-Index Relationship	p. 261
Case Study III: Modelling the Skew Sensitivities	p. 264
Applications of Implied Volatility Dynamics to Hedging Options	p. 265
Stochastic Volatility Models	p. 268
Stochastic Volatility PDE	p. 269
Properties of Stochastic Volatility	p. 271
Model Implied Volatility Surface	p. 275
Model Local Volatility Surface	p. 277
Heston Model	p. 278
GARCH Diffusions	p. 280
CEV and SABR Models	p. 285
Jumps in Prices and in Stochastic Volatility	p. 287
Scale Invariance and Hedging	p. 289
Scale Invariance and Change of Numeraire	p. 291
Definition of Scale Invariance	p. 291
Scale Invariance and Homogeneity	p. 292
Model Free Price Hedge Ratios	p. 294
Minimum Variance Hedging	p. 297
Minimum Variance Hedge Ratios in Specific Models	p. 299
Empirical Results	p. 300
Trading Volatility	p. 303
Variance Swaps and Volatility Swaps	p. 304
Trading Forward Volatility	p. 306
Variance Risk Premium	p. 307
Construction of a Volatility Index	p. 308
Effect of the Skew	p. 309
Term Structures of Volatility Indices	p. 309
Vix and Other Volatility Indices	p. 311
Volatility Index Futures	p. 312
Options on Volatility Indices	p. 314
Using Realized Volatility Forecasts to Trade Volatility	p. 315
Summary and Conclusion	p. 316
Portfolio Mapping	p. 321
Introduction	p. 321
Risk Factors and Risk Factor Sensitivities	p. 323
Interest Rate Sensitive Portfolios	p. 323
Equity Portfolios	p. 324
International Exposures	p. 327
Commodity Portfolios	p. 328
Options Portfolios	p. 328
Orthogonalization of Risk Factors	p. 330
Nominal versus Percentage Risk Factors and Sensitivities	p. 330
Cash Flow Mapping	p. 332
Present Value Invariant and Duration Invariant Maps	p. 332
PV01 Invariant Cash Flow Maps	p. 333
Volatility Invariant Maps	p. 334
Complex Cash Flow Maps	p. 336
Applications of Cash Flow Mapping to Market Risk Management	p. 337
Risk Management of Interest Rate Sensitive Portfolios	p. 337
Mapping Portfolios of Commodity Futures	p. 338
Mapping an Options Portfolio to Price Risk Factors	p. 340
Taylor Expansions	p. 341
Value Delta and Value Gamma	p. 342
Delta-Gamma Approximation: Single Underlying	p. 344
Effect of Gamma on Portfolio Risk	p. 346
Price Beta Mapping	p. 347
Delta-Gamma Approximation: Several Underlyings	p. 349
Including Time and Interest Rates Sensitivities	p. 351
Mapping Implied Volatility	p. 353
Vega Risk in Options Portfolios	p. 353
Second Order Approximations: Vanna and Volga	p. 354
Vega Bucketing	p. 355
Volatility Beta Mapping	p. 356
Case Study: Volatility Risk in FTSE 100 Options	p. 357
Estimating the Volatility Betas	p. 357
Model Risk of Volatility Mapping	p. 360
Mapping to Term Structures of Volatility Indices	p. 361
Using PCA with Volatility Betas	p. 361
Summary and Conclusions	p. 364
References	p. 367
Index	p. 377
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