The Handbook of Convertible Bonds: Pricing, Strategies and Risk Management (The Wiley Finance Series 583)

This is a complete guide to the pricing and risk management of convertible bond portfolios. Convertible bonds can be complex because they have both equity and debt like features and new market entrants will usually find that they have either a knowledge of fixed income mathematics or of equity derivatives and therefore have no idea how to incorporate credit and equity together into their existing pricing tools. Part I of the book covers the impact that the 2008 credit crunch has had on the markets, it then shows how to build up a convertible bond and introduces the reader to the traditional convertible vocabulary of yield to put, premium, conversion ratio, delta, gamma, vega and parity. The market of stock borrowing and lending will also be covered in detail. Using an intuitive approach based on the Jensen inequality, the authors will also show the advantages of using a hybrid to add value - pre 2008, many investors labelled convertible bonds as 'investing with no downside', there are of course plenty of 2008 examples to prove that they were wrong. The authors then go onto give a complete explanation of the different features that can be embedded in convertible bond. Part II shows readers how to price convertibles. It covers the different parameters used in valuation models: credit spreads, volatility, interest rates and borrow fees and Maturity. Part III covers investment strategies for equity, fixed income and hedge fund investors and includes dynamic hedging and convertible arbitrage. Part IV explains the all important risk management part of the process in detail. This is a highly practical book, all products priced are real world examples and numerical examples are not limited to hypothetical convertibles. It is a must read for anyone wanting to safely get into this highly liquid, high return market. Content: Reading this Book xiii Preface xv Acknowledgements xvii PART I THE CONVERTIBLES MARKET 1 1 Terminology 3 1.1 The Payoff 3 1.2 Advantages of Convertibles 4 1.2.1 For the Issuer 5 1.2.2 For the Investor 8 1.3 Basic Terminology 13 1.4 Advanced Terminology 17 1.5 Legal Terminology 20 1.6 Analytics and Hedge Ratios 21 2 Convertible Bond Anatomy 25 2.1 Payoff to the Investor 25 2.2 Payoff Graph 26 2.2.1 Example 30 2.3 Boundary Conditions 31 2.3.1 Bond Floor 32 2.3.2 Parity 33 2.3.3 Investment Premium 33 2.3.4 Conversion Premium 34 2.4 Effect of the Call Protection 35 2.5 Announcement Effect 35 2.5.1 Dilution 41 2.5.2 Arbitrage Activity 41 3 Convertible and Hybrid Structures 43 3.1 Preferred Shares 43 3.2 Convertible Bond Option 45 3.3 Reverse Convertible 45 3.4 Perpetuals 46 3.5 Cross-Currency 46 3.6 Mandatory 48 3.6.1 PERCS 48 3.6.2 PEPS 48 3.7 Cashout Option 51 3.8 Exchangeable 51 3.9 Dividend Entitlement 52 4 Convertible Bonds Market 55 4.1 The Convertible Universe 55 4.1.1 Credit Rating 55 4.1.2 Convertible Type 56 4.1.3 Convertible Category 56 4.1.4 Maturity 57 4.1.5 Region 57 4.1.6 144A 57 4.2 The Prospectus 58 4.3 The Investors 58 4.3.1 Outright Investors 58 4.3.2 Convertible Bond Arbitrageurs 59 4.3.3 Example 60 4.3.4 Conclusions 62 4.4 Market Participants 62 4.4.1 Lead Manager 63 4.4.2 Trustee 63 4.4.3 Paying Agent 64 4.4.4 Market Makers 64 4.5 New Issuance 64 PART II PRICING 67 5 The Road to Convexity 69 5.1 Break-Even Analysis 69 5.1.1 Dollar Method 70 5.1.2 Equity Method 70 5.2 Discounted Yield Advantage 72 5.3 Convexity 74 5.4 Jensen's Inequality 75 5.5 Time Decay 77 5.6 Double-Signed Gamma 79 5.7 Colour 80 5.8 First Steps Using Convexity 81 5.8.1 A Fixed Income Investor 81 5.8.2 An Equity Investor 82 6 Basic Binomial Trees 85 6.1 Models 85 6.2 The Basic Ingredients 86 6.3 A Primer in Stochastic Calculus 91 6.3.1 Stochastic Equations 91 6.3.2 Ito's Lemma 92 6.3.3 Shares as Generalized Wiener Processes 93 6.3.4 Shares as a Log Process 93 6.3.5 Linking Both 94 6.4 Elementary Credit Model 95 6.4.1 Probabilities 95 6.4.2 Recovery Rate 98 6.4.3 Credit Triangle 98 6.5 Binomial Equity Models 99 6.5.1 Introduction 99 6.5.2 Binomial Tree 100 6.5.3 Unconditional Default Risk in the Binomial Tree 109 6.5.4 Adding Conditional Default Risk 116 6.5.5 Alternative Ways to Incorporate Credit Risk 120 6.6 Pricing Convertibles Using Binomial Trees 122 6.7 Credit Spread Modelling in Binomial Trees: A Practitioner's Approach 155 6.8 Conclusions 156 7 Multinomial Models 159 7.1 Convergence of the Binomial Model 159 7.1.1 Distribution Error 160 7.1.2 Non-linearity Error 160 7.2 Moments 161 7.3 Multinomial Models 164 7.4 Trinomial Model 166 7.4.1 Solving Moment-Matching Equations 166 7.4.2 Alternative Trinomial Models 167 7.5 Heptanomial Model 170 7.5.1 Solving Moment-Matching Equations 170 7.5.2 Calculation Time 171 7.6 Further Optimization 172 7.6.1 Smoothing 173 7.6.2 Adaptive Mesh Method 174 7.6.3 Truncation 175 7.6.4 Richardson Extrapolation 175 7.6.5 Bardhan-Derman-Kani-Ergener Correction 175 7.7 Other Refinements 179 7.7.1 Stock Borrowing 179 7.7.2 Cross-Currency 182 7.7.3 Discrete Dividends 184 7.7.4 Transaction Costs 196 7.7.5 Rational Issuers 199 7.7.6 Pricing Dilution 201 7.8 Resets in Multinomial Models 201 7.8.1 Convertible Bond Pricing: Conclusions 203 8 Ascots 207 8.1 Risk Components of a Convertible 207 8.2 Asset Swaps 208 8.2.1 Introduction 208 8.2.2 Credit Risk 211 8.2.3 Closing Out the Swap 212 8.3 Ascots 213 8.3.1 Making the Asset Swap Callable 213 8.3.2 Convertible Asset Swap Package 213 8.3.3 Ascot Features 215 8.3.4 Ascot Term Sheet 216 8.4 Advantages for the Credit Buyer 216 8.5 Advantages for the Ascot Buyer 217 8.5.1 Credit 217 8.5.2 Leverage 218 8.6 Pricing of Ascots 219 8.6.1 Intrinsic Model 219 8.6.2 Option Model 219 8.7 Ascot Greeks 222 8.7.1 Rho 222 8.7.2 Delta 223 8.7.3 Vega 225 8.8 CB Warrants 226 PART III RISK MANAGEMENT AND STRATEGIES 227 9 Measuring the Risk 229 9.1 Portfolio Risk 229 9.2 A Portfolio in Trouble 231 9.3 Risk Categories 238 9.3.1 Market Risk 238 9.3.2 Liquidity Risk 239 9.3.3 Takeover Risk 242 9.3.4 Example: Nokian Tyres 0% 2014 246 9.3.5 Example: Allergan Inc 1.5% 2026 247 9.3.6 Documentation Risk 248 9.3.7 Model Risk 248 9.3.8 Counterparty Risk 249 9.3.9 Operational Risk 249 9.3.10 Regulation Risk 250 9.3.11 Financing Risk 250 9.4 Coherent Risk Measures 251 9.5 Option Greeks 253 9.5.1 Introduction 253 9.5.2 Extended Tree Method 257 9.5.3 Delta 258 9.5.4 Gamma 260 9.5.5 Rho 261 9.5.6 Omicron 263 9.5.7 Vega 265 9.5.8 Volga 266 9.5.9 Epsilon 269 9.5.10 Theta 270 9.6 Fixed Income Measures 272 9.6.1 Duration (Modified) 272 9.6.2 Yields 273 9.7 Cross Greeks 275 9.7.1 Charm 278 9.7.2 Vanna 279 9.8 Speed and Colour 282 9.9 VaR and Beyond 283 9.9.1 VaR Approaches 284 9.9.2 VaR-Related Measures 289 9.9.3 VaR Caveats 291 9.10 Back Testing 292 9.11 Stress Testing 293 10 Dynamic Hedging 295 10.1 Hedge Instruments 295 10.2 Delta Hedging 297 10.2.1 Introduction 297 10.2.2 More than Only Delta 297 10.2.3 Delta Hedge: Neutral, Over- or Under-hedge 299 10.2.4 Delta Caveats 302 10.2.5 Delta and Volatility 302 10.3 Volatility 302 10.3.1 Estimating Historical Volatility 304 10.3.2 Volatility Cone 306 10.3.3 Volatility Surface 308 10.3.4 Term Structure of sigmaI 309 10.3.5 Volatility Smile of sigmaI 310 10.3.6 Volsurface Movements 310 10.3.7 At-the-Money Volatility 310 10.4 Gamma Trading 311 10.4.1 Rebalancing the Delta Hedge 312 10.4.2 Dynamic Hedging with Transaction Costs 314 10.4.3 Hedging at What Volatility? 317 10.5 The Variance Swap 324 10.5.1 Introduction 324 10.5.2 Volatility Convexity 326 10.5.3 Spot and Forward Start 327 10.5.4 Mark to Market of the Variance Swap 327 10.5.5 Caveats 328 11 Monte Carlo Techniques for Convertibles 329 11.1 Adding More Realism 329 11.1.1 Introduction 329 11.1.2 Deterministic Volatility 330 11.1.3 Multifactor Models 330 11.2 Monte Carlo Method 334 11.2.1 Introduction 334 11.2.2 Generating Random Paths 336 11.2.3 Errors 338 11.2.4 Variance Reduction 338 11.3 American Monte Carlo 340 11.3.1 Introduction 340 11.3.2 Longstaff and Schwartz Model 343 11.3.3 Example 346 References 363 Index 369 The Handbook of Convertible Bonds 3 Contents 9 Reading this Book 15 Preface 17 Acknowledgements 19 PART I THE CONVERTIBLES MARKET 21 1 Terminology 23 1.1 The Payoff 23 1.2 Advantages of Convertibles 24 1.2.1 For the Issuer 25 1.2.2 For the Investor 28 1.3 Basic Terminology 33 1.4 Advanced Terminology 37 1.5 Legal Terminology 40 1.6 Analytics and Hedge Ratios 41 2 Convertible Bond Anatomy 45 2.1 Payoff to the Investor 45 2.2 Payoff Graph 46 2.2.1 Example 50 2.3 Boundary Conditions 51 2.3.1 Bond Floor 52 2.3.2 Parity 53 2.3.3 Investment Premium 53 2.3.4 Conversion Premium 54 2.4 Effect of the Call Protection 55 2.5 Announcement Effect 55 2.5.1 Dilution 61 2.5.2 Arbitrage Activity 61 3 Convertible and Hybrid Structures 63 3.1 Preferred Shares 63 3.2 Convertible Bond Option 65 3.3 Reverse Convertible 65 3.4 Perpetuals 66 3.5 Cross-Currency 66 3.6 Mandatory 68 3.6.1 PERCS 68 3.6.2 PEPS 68 3.7 Cashout Option 71 3.8 Exchangeable 71 3.9 Dividend Entitlement 72 4 Convertible Bonds Market 75 4.1 The Convertible Universe 75 4.1.1 Credit Rating 75 4.1.2 Convertible Type 76 4.1.3 Convertible Category 76 4.1.4 Maturity 77 4.1.5 Region 77 4.1.6 144A 77 4.2 The Prospectus 78 4.3 The Investors 78 4.3.1 Outright Investors 78 4.3.2 Convertible Bond Arbitrageurs 79 4.3.3 Example 80 4.3.4 Conclusions 82 4.4 Market Participants 82 4.4.1 Lead Manager 83 4.4.2 Trustee 83 4.4.3 Paying Agent 84 4.4.4 Market Makers 84 4.5 New Issuance 84 PART II PRICING 87 5 The Road to Convexity 89 5.1 Break-Even Analysis 89 5.1.1 Dollar Method 90 5.1.2 Equity Method 90 5.2 Discounted Yield Advantage 92 5.3 Convexity 94 5.4 Jensen’s Inequality 95 5.5 Time Decay 97 5.6 Double-Signed Gamma 99 5.7 Colour 100 5.8 First Steps Using Convexity 101 5.8.1 A Fixed Income Investor 101 5.8.2 An Equity Investor 102 6 Basic Binomial Trees 105 6.1 Models 105 6.2 The Basic Ingredients 106 6.3 A Primer in Stochastic Calculus 111 6.3.1 Stochastic Equations 111 6.3.2 It ̄o’s Lemma 112 6.3.3 Shares as Generalized Wiener Processes 113 6.3.4 Shares as a Log Process 113 6.3.5 Linking Both 114 6.4 Elementary Credit Model 115 6.4.1 Probabilities 115 6.4.2 Recovery Rate 118 6.4.3 Credit Triangle 118 6.5 Binomial Equity Models 119 6.5.1 Introduction 119 6.5.2 Binomial Tree 120 6.5.3 Unconditional Default Risk in the Binomial Tree 129 6.5.4 Adding Conditional Default Risk 136 6.5.5 Alternative Ways to Incorporate Credit Risk 140 6.6 Pricing Convertibles Using Binomial Trees 142 6.7 Credit Spread Modelling in Binomial Trees: A Practitioner’s Approach 175 6.8 Conclusions 176 7 Multinomial Models 179 7.1 Convergence of the Binomial Model 179 7.1.1 Distribution Error 180 7.1.2 Non-linearity Error 180 7.2 Moments 181 7.3 Multinomial Models 184 7.4 Trinomial Model 186 7.4.1 Solving Moment-Matching Equations 186 7.4.2 Alternative Trinomial Models 187 7.5 Heptanomial Model 190 7.5.1 Solving Moment-Matching Equations 190 7.5.2 Calculation Time 191 7.6 Further Optimization 192 7.6.1 Smoothing 193 7.6.2 Adaptive Mesh Method 194 7.6.3 Truncation 195 7.6.4 Richardson Extrapolation 195 7.6.5 Bardhan–Derman–Kani–Ergener Correction 195 7.7 Other Refinements 199 7.7.1 Stock Borrowing 199 7.7.2 Cross-Currency 202 7.7.3 Discrete Dividends 204 7.7.4 Transaction Costs 216 7.7.5 Rational Issuers 219 7.7.6 Pricing Dilution 221 7.8 Resets in Multinomial Models 221 7.8.1 Convertible Bond Pricing: Conclusions 223 8 Ascots 227 8.1 Risk Components of a Convertible 227 8.2 Asset Swaps 228 8.2.1 Introduction 228 8.2.2 Credit Risk 231 8.2.3 Closing Out the Swap 232 8.3 Ascots 233 8.3.1 Making the Asset Swap Callable 233 8.3.2 Convertible Asset Swap Package 233 8.3.3 Ascot Features 235 8.3.4 Ascot Term Sheet 236 8.4 Advantages for the Credit Buyer 236 8.5 Advantages for the Ascot Buyer 237 8.5.1 Credit 237 8.5.2 Leverage 238 8.6 Pricing of Ascots 239 8.6.1 Intrinsic Model 239 8.6.2 Option Model 239 8.7 Ascot Greeks 242 8.7.1 Rho 242 8.7.2 Delta 243 8.8 CB Warrants 245 PART III RISK MANAGEMENT AND STRATEGIES 247 9 Measuring the Risk 249 9.1 Portfolio Risk 249 9.2 A Portfolio in Trouble 251 9.3 Risk Categories 258 9.3.1 Market Risk 258 9.3.2 Liquidity Risk 259 9.3.3 Takeover Risk 262 9.3.4 Example: Nokian Tyres 0% 2014 266 9.3.5 Example: Allergan Inc 1.5% 2026 267 9.3.6 Documentation Risk 268 9.3.7 Model Risk 268 9.3.8 Counterparty Risk 269 9.3.9 Operational Risk 269 9.3.10 Regulation Risk 270 9.3.11 Financing Risk 270 9.4 Coherent Risk Measures 271 9.5 Option Greeks 273 9.5.1 Introduction 273 9.5.2 Extended Tree Method 277 9.5.3 Delta 278 9.5.4 Gamma 280 9.5.5 Rho 281 9.5.6 Omicron 283 9.5.7 Vega 285 9.5.8 Volga 286 9.5.9 Epsilon 289 9.5.10 Theta 290 9.6 Fixed Income Measures 292 9.6.1 Duration (Modified) 292 9.6.2 Yields 293 9.7 Cross Greeks 295 9.7.1 Charm 298 9.7.2 Vanna 299 9.8 Speed and Colour 302 9.9 VaR and Beyond 303 9.9.1 VaR Approaches 304 9.9.2 VaR-Related Measures 309 9.9.3 VaR Caveats 311 9.10 Back Testing 312 9.11 Stress Testing 313 10 Dynamic Hedging 315 10.1 Hedge Instruments 315 10.2 Delta Hedging 317 10.2.1 Introduction 317 10.2.2 More than Only Delta 317 10.2.3 Delta Hedge: Neutral, Over- or Under-hedge 319 10.2.4 Delta Caveats 322 10.2.5 Delta and Volatility 322 10.3 Volatility 322 10.3.1 Estimating Historical Volatility 324 10.3.2 Volatility Cone 326 10.3.3 Volatility Surface 328 10.3.4 Term Structure of σI 329 10.3.5 Volatility Smile of σI 330 10.3.6 Volsurface Movements 330 10.3.7 At-the-Money Volatility 330 10.4 Gamma Trading 331 10.4.1 Rebalancing the Delta Hedge 332 10.4.2 Dynamic Hedging with Transaction Costs 334 10.4.3 Hedging at What Volatility? 337 10.5 The Variance Swap 344 10.5.1 Introduction 344 10.5.2 Volatility Convexity 346 10.5.3 Spot and Forward Start 347 10.5.4 Mark to Market of the Variance Swap 347 10.5.5 Caveats 348 11 Monte Carlo Techniques for Convertibles 349 11.1 Adding More Realism 349 11.1.1 Introduction 349 11.1.2 Deterministic Volatility 350 11.1.3 Multifactor Models 350 11.2 Monte Carlo Method 354 11.2.1 Introduction 354 11.2.2 Generating Random Paths 356 11.2.3 Errors 358 11.2.4 Variance Reduction 358 11.3 American Monte Carlo 360 11.3.1 Introduction 360 11.3.2 Longstaff and Schwartz Model 363 11.3.3 Example 366 References 383 Index 389

having Both Equity And Debt Like Features, Convertible Bonds Are Highly Complex, Challenging New Market Entrants To Incorporate Credit And Equity Together Into Their Existing Pricing Tools.

the Handbook Of Convertible Bonds Is A Comprehensive Guide To The Pricing And Risk Management Of This Highly Profitable Asset Class In A Post Credit Crunch Setting.

part I Introduces The Convertibles Market, Covering The Impact That The 2008 Credit Crunch Has Had On The Markets. It Shows How To Build Up A Convertible Bond And Introduces The Reader To The Traditional Convertible Vocabulary Of Yield To Put, Premium, Conversion Ratio, Delta, Gamma, Vega And Parity. The Market Of Stock Borrowing And Lending Is Also Covered In Detail. Using An Intuitive Approach Based On The Jensen Inequality, The Authors Also Show The Advantages Of Using A Hybrid To Add Value. The Authors Then Go On To Give The Advantages Of Using A Hybrid To Add Value. The Authors Then Go On To Give A Complete Explanation Of The Different Features That Can Be Embedded In Convertible Bonds. part Ii Shows Readers How To Price Convertibles, Covering The Different Parameters Used In Valuation Models: Credit Spreads, Volatility, Interest Rates Ad Borrow Fees And Maturity. part Iii Concludes The Book By Covering The All Important Risk Management Part Of The Process In Detail.

this Is A Highly Piratical Book, All Products Priced Are Real World Examples And Numerical Examples Are Not Limited To Hypothetical Convertibles. It Is A Must Read For Anyone Wanting To Safely Get Into This Market.