The Handbook of Hybrid Securities For other titles in the Wiley Finance series please see www.wiley.com/finance The Handbook of Hybrid Securities Convertible Bonds, CoCo Bonds, and Bail-In Jan De Spiegeleer Wim Schoutens Cynthia Van Hulle This edition first published 2014 © 2014 Jan De Spiegeleer, Wim Schoutens and Cynthia Van Hulle Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher Wiley publishes in a 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disclaim any implied warranties of merchantability or fitness for a particular purpose It is sold on the understanding that the publisher is not engaged in rendering professional services and neither the publisher nor the author shall be liable for damages arising herefrom If professional advice or other expert assistance is required, the services of a competent professional should be sought Library of Congress Cataloging-in-Publication Data Spiegeleer, Jan de The handbook of hybrid securities : convertible bonds, coco bonds, and bail-in / Jan De Spiegeleer, Wim Schoutens, Cynthia Van Hulle pages cm—(The Wiley finance series) Includes bibliographical references and index ISBN 978-1-118-44999-8 (hardback) Convertible securities—Handbooks, manuals, etc Convertible bonds—Handbooks, manuals, etc I Schoutens, Wim II Van Hulle, Cynthia, III Title HG4652.S67 2014 332.63′ 2044—dc23 2013046701 A catalogue record for this book is available from the British Library ISBN 978-1-118-44999-8 (hardback) ISBN 978-1-118-45002-4 (ebk) ISBN 978-1-118-45000-0 (ebk) ISBN 978-1-118-86265-0 (obk) Cover image: Shutterstock.com Set in 10/12pt Times by Aptara, Inc., New Delhi, India Printed in Great Britain by CPI Group (UK) Ltd, Croydon, CR0 4YY To Klaartje, Charlotte, Pieter-Jan and Willem Jan To Ethel, Jente and Maitzanne Wim To my mother Cynthia Contents Reading this Book xv Acknowledgments xvii Hybrid Assets 1.1 Introduction 1.2 Hybrid Capital 1.3 Preferreds 1.4 Convertible Bonds 1.5 Contingent Convertibles 1.6 Other Types of Hybrid Debt 1.6.1 Hybrid Bank Capital 1.6.2 Hybrid Corporate Capital 1.6.3 Toggle Bonds 1.7 Regulation 1.7.1 Making Failures Less Likely 1.7.2 Making Failures Less Disruptive 1.8 Bail-In Capital 1.9 Risk and Rating 1.9.1 Risk 1.9.2 Rating 1.10 Conclusion 1 7 13 14 15 15 15 16 17 17 18 18 19 19 22 22 22 23 25 27 27 33 Convertible Bonds 2.1 Introduction 2.2 Anatomy of a Convertible Bond 2.2.1 Final Payoff 2.2.2 Price Graph 2.2.3 Quotation of a Convertible Bond 2.2.4 Bond Floor (𝐵𝐹 ) 2.2.5 Parity 2.2.6 Convexity 2.2.7 Optional Conversion viii Contents 2.2.8 Forced Conversion 2.2.9 Mandatory Conversion Convertible Bond Arbitrage 2.3.1 Components of Risk 2.3.2 Delta 2.3.3 Delta Hedging 2.3.4 Different Notions of Delta 2.3.5 Greeks Standard Features 2.4.1 Issuer Call 2.4.2 Put 2.4.3 Coupons 2.4.4 Dividends Additional Features 2.5.1 Dividend Protection 2.5.2 Take-Over Protection 2.5.3 Refixes Other Convertible Bond Types 2.6.1 Exchangeables 2.6.2 Synthetic Convertibles 2.6.3 Cross-Currency Convertibles 2.6.4 Reverse Convertibles 2.6.5 Convertible Preferreds 2.6.6 Make-Whole 2.6.7 Contingent Conversion 2.6.8 Convertible Bond Option Convertible Bond Terminology 2.7.1 144A 2.7.2 Fixed-Income Metrics Convertible Bond Market 2.8.1 Market Participants 2.8.2 Investors Conclusion 35 35 37 37 42 45 45 46 47 47 50 53 56 58 58 59 60 62 62 63 64 66 67 67 67 68 68 68 68 73 73 74 76 Contingent Convertibles (CoCos) 3.1 Introduction 3.2 Definition 3.3 Anatomy 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Common Equity Tier capital CoCos 94, 101–6, 111, 316–17 concepts 93–104, 111, 131, 132, 316–17 leverage ratios 99–106 liquidity requirements 99–106 phased implementation 97, 101–2 risk-weighted assets 95–106 too-big-to-fail banks 95–6 bear markets, convertible bonds 20–1 Bermudan options 203–4, 352–3 Bernoulli experiments 235 betas 9–10 bid–offer spreads 74, 180–1, 246–8, 368–9 binary down-and-in options (BDIs) 309–16, 322 binary down-and-out options (BDOs) 318–21 binomial trees 145, 148, 160, 177–9, 186–204 Black model 365 black-box pricing models 153–7 Black–Scholes pricing model 33, 68, 144, 148, 152, 159, 165, 167, 180–6, 200, 217, 227, 241–2, 265, 267–8, 269–70, 274–5, 281–3, 284–8, 292–5, 297–9, 304–46, 347 see also closed-form solutions; geometric Brownian motion; partial differential equations assumptions 180–2, 275, 322 CEV model 269–70, 274–5, 281–3, 284–8, 292–5, 297–9 definition 182–3, 227 jump diffusion model mix-ups 227, 326–9 blended yield (BY) 70 bond basis, CDSs 262–3 bond ceilings 89, 109 bond floor calculations 6–7, 23, 30–3, 48–50, 62, 71, 89, 242, 289–95 bonds 1–18, 19–76, 77–8, 84, 113–26, 127–37, 145, 184–6, 241–2, 243–65, 295, 302–46, 347 see also convertible ; corporate ; government terminology 68–73 382 Index bonuses, banks 107, 136–7 borrowing fees 180–1, 275 Bradford & Bingley 130 break even calculations, convertible bonds 142–3 Brownian motion 33, 144–5, 159, 164–7, 169–71, 176, 177–9, 180–6, 193–204, 206–10, 212–27, 229–42, 245–6, 264–5, 267–99, 330, 334–9, 348, 365–71 see also geometric ; Ito processes; martingales; Wiener process buffer convertible capital securities (BCCS) see contingent convertibles calibration of models 144–5, 240–2, 250–1, 257–9, 268, 271–4, 295–9, 325–9, 348 call cushions, convertible bonds 49–50 call notice periods, convertible bonds 48–50 call option enhanced reverse convertibles (COERCs) 106–7 call protection periods, convertible bonds 48–50, 119–21, 191–204 call triggers, soft issuer calls 47–50, 55–6, 293–5, 348–9 callable bonds 9–13, 121, 123–6, 141–3 calls 7, 9–10, 13–14, 22–3, 35, 47–50, 63–6, 70, 106–7, 119–26, 140–3, 152–7, 160, 183–6, 199–204, 224–7, 240–2, 268–70, 274–7, 295–9, 311–16, 327–9, 335–9, 348–71 capital conservation buffers (CCBs), Basel III 94–106 Capital Requirements Regulation (CRRI) 132 cash compensation, toggle bonds 14–15 cash delta 45 CDSs see credit default swaps central banks 15–16 CEV see constant elasticity of variance model change of control puts, convertible bonds 59–60 ‘cheap equity’, corporate hybrids 13–14 cheapness concepts, models 147–9 chi-squared function 276 Cholesky factorization 230–4, 236–40 clean prices 23–5 closed-form solutions 28–9, 46, 144–5, 160–1, 180–6, 252–6, 257–60, 265, 267–8, 277, 305–7, 322–3, 335 see also Black–Scholes pricing model closing price differences, theoretical prices 3–4 CoCoCos 86–7, 329–33 CoCos see contingent convertibles coefficient of determination (R-squared) 38–40, 325–9 collateralized debt obligations (CDOs) 92–3, 144–5 Common Equity Tier capital (CET1) 8, 81–2, 84, 86–7, 94–107, 212, 302–3, 316–17 cones, volatilities 4–5 confidence intervals 72–3, 171, 336–9 constant elasticity of variance model (CEV) 169, 176, 187–8, 192–204, 214, 267–99, 330–3, 347 analytical solution valuations 274–7 Beckers parameter estimation 271–4 Black–Scholes pricing model 269–70, 274–5, 281–3, 284–8, 292–5, 297–9 calibration of CEV 268, 271–4, 295–9 definition 268–70 historical parameter estimates 270–4 jump-to-default extended CEV process 283–6 mandatory conversions 268–9, 286–8 Monte Carlo simulations 283 Randal parameter estimation 273–4 refix/reset features of convertibles 268–9, 288–95 trinomial trees 277–83, 284–6, 292–5 constrained regressions 363–71 contagion risk 15, 16, 20–1, 108, 174, 234–5 contingent conversion feature, convertible bonds 67, 86–9 contingent convertibles (CoCos) 1–3, 7–8, 15–16, 77–111, 128, 131–3, 137, 144, 147, 149–52, 155–7, 176, 180, 186, 227–8, 240–2, 244, 263, 265, 268–99, 301–46, 347, 371 alternative structures 106–7 anatomy 79–87, 301–2, 318 balance sheets 106–7 Basel III 94, 101–6, 111, 316–17 CEV model 268–99, 330–3 characteristics 81–2, 149 conclusions 110–11 convertible bonds 67, 86–9 convexity 88–9, 109–10, 315–16, 330–3, 339–41 critique 107–11, 322 definition 2–3, 7, 8, 77–87, 128, 301–2 high and low-trigger CoCos 104–6, 302–7, 338 historical background 7, 77–8, 131–3 host instruments 77, 78, 79, 86–7, 329–33 indices 111 loss-absorption mechanisms 77, 78, 79–83, 104–6, 212, 301–46 prices 78, 109–11, 144, 147, 149–52, 155–7, 176, 180, 186, 227–8, 244, 263, 268–99, 301–46, 347 regulations 77–87, 89–106, 111, 131–3, 303–7, 316–17 risk 7, 15, 77–8, 84–111, 144, 147, 149–52, 155–7, 176, 301–46 sensitivity analysis 155–7 statistics 2–3, stochastic credit 333–9 trigger events 77, 78, 79, 83–111, 131, 149–50, 155–7, 212, 301–46 trinomial trees 321–3, 341–6 two-factor models 333–9 continuation values 35, 201–4, 222–7, 350–71 conversion ratios 5–6, 19–76, 79–111, 155, 180, 185–6, 191–204, 286–99, 302–7, 329–33, 350–71 Index conversion values 6–7, 22–3, 47–52, 60–8, 79–111, 185–6, 222–7, 286–99, 302–7, 343–6, 352–71 convertible bond options (Ascots) 68 convertible bonds 1–7, 8, 19–76, 78, 86–9, 123–4, 140, 142–4, 147–57, 160, 180–204, 211–12, 215–27, 241–6, 263–5, 268–99, 305–7, 329–33, 347–8 see also contingent ; corporate hybrids additional features 58–62, 67 anatomy 22–37 arbitrage 37–46, 61–2, 74–5 bond floor calculations 6–7, 23, 30–3, 48–50, 62, 71, 89, 242, 289–95 break even calculations 142–3 calls 22–3, 47–50, 63–6, 70, 106–7, 119–26, 140–3, 183–6, 224–7, 295–9, 348–71 CEV model 268–99 characteristics 6, 24–5, 30, 37, 42, 48, 52, 56, 58–9, 61, 62–5, 67, 123–4, 142, 245, 285, 306 cheapness concepts 147–9 convexity 27–33, 36–7, 39, 40–6, 62, 88–9, 109–10, 122–6, 181–6, 242, 286–95, 315–16, 330–3, 339–41, 369–71 coupon features 53–6 definition 5–6, 8, 19–37, 62–8, 78, 87–9 dividend features 56–9 double-signed gamma 30–3, 286–8 efficient frontiers 21 final payoffs 22–3, 36–7, 66–7, 206–10, 222–7, 356–71 forced conversions 35, 55–6, 86–9, 139–40, 149–50, 224–7, 245–6, 268–9, 286–8, 320–1, 330–3 historical background 19–21 investors 74–6, 114–15, 329–33 issuer calls 47–50, 113–14, 119–26, 223–7, 348–9 jump diffusion 221–7, 263, 284–6, 292–5, 347–8 make-whole feature 67 mandatory conversions 35–7, 55–6, 86–9, 139–40, 149–50, 224–7, 245–6, 268–9, 286–8, 320–1, 330–3, 347 markets 73–6, 147–9 optional aspects 5–6, 33–5, 86–9, 329–33, 348–71 optional conversions 5–6, 33–5, 86–9, 222–7, 245–6, 293–5, 329–33, 348–71 participants 73–6 price graphs 22–3, 27–8, 31, 51–2 prices 6–7, 18, 19–21, 22–5, 37–46, 47–62, 74–6, 140, 142–3, 144, 147–57, 160, 180–204, 215–27, 241–2, 243–6, 263–5, 268–99, 347–71 puts 22–3, 26–7, 48–52, 59–60, 66–7, 69–70, 89, 119–26, 154, 160, 183–6, 191–204, 223–7, 293–9, 311–16, 322, 348–9 quoted prices 23–5 refix/reset features 7, 60–2, 109–11, 154, 191–2, 204, 223–7, 268–9, 288–95, 348–9 returns 6–7, 18, 19–21, 74–5, 114–26, 243–6 risk 19–21, 30–3, 37–46, 53, 61–2, 72–3, 114–26, 140–57, 180–6, 211–12, 215–27 383 standard features 47–62 statistics 2–3, 5–6, 19–37 take-overs 19, 22, 59–60 terminology 19, 22–37, 68–73, 76 types 2–3, 5–6, 7, 8, 19–37, 62–8 convertible preferreds 67 convexity 27–33, 36–7, 39, 40–6, 62, 88–9, 109–10, 122–6, 181–6, 242, 286–95, 315–16, 330–3, 339–41, 369–71 see also interest rate ; negative gamma; positive gamma Cooke ratio 91 copulas 144–5, 236–40 see also correlation corporate bonds 1–18, 19, 84, 113–26, 145, 184–6, 243–6, 259–65, 295, 302–7, 312–16, 347 corporate hybrids 13–14, 113–26, 140–3, 243–4, 317–18, 371 definition 13–14, 113 structures 115–21 correlation 9–10, 139–40, 227–40, 334–9, 348–71 see also Cholesky factorization; copulas; Pearson ; Spearman correlation risk, hybrid securities 227–8 counter-cyclical buffers, Basel III 94–106 counting process 172–6 see also Poisson coupon deferrals 1, 8–11, 13–14, 78, 81, 86–7, 113–26, 317–21, 341–6, 347 coupon features, convertible bonds 53–6 coupon pushers 13, 113, 118 coupons 1, 3–6, 8–11, 13–14, 22–76, 77–111, 113–26, 140–57, 173–6, 184–6, 204, 208–10, 252–65, 301–46, 347, 348 covariance 229–40 Cox process (doubly stochastic Poisson process) 175–6, 247–8, 263–5 Cox–Ingersoll–Ross interest rate model (CIR) 167, 176 credit 1–2, 11–12, 30–3, 46, 75, 104–6, 111, 114–15, 123–6, 139–57, 166–7, 214, 227, 229–30, 235, 240–1, 243–65, 302–7, 323–9, 333–9 credit crisis see financial crisis from 2007 credit default swaps (CDSs) 1–2, 11–12, 75, 111, 114–15, 144–5, 150–1, 166, 214, 229–30, 235, 240–1, 243–4, 248–65, 271, 295–6, 325–9, 334–9, 347 bond basis 262–3 case studies 257–9 curves 243–4, 250–1 definition 75, 248–50 market conventions 256–7 options 265 premium/credit legs 251–9, 263 prices 251–9, 263, 295–6, 347 rule of thumb 255–6, 259–60 statistics 1–2, 11–12, 250–1 uses 214, 248–50, 271, 295–6, 325–9, 334–9 384 Index credit derivatives 1–2, 11–12, 139–40, 214, 229–30, 235, 248–65, 301–46 credit elasticity 324–9, 341–6 credit events 248–65, 268–99, 302–7 credit rating agencies 1, 9, 11, 13–15, 17–18, 77, 92–3, 108, 115, 118–19, 121, 126, 268–70, 301 see also Standard & Poor’s credit ratings 1, 9, 13–15, 17–18, 77, 92–3, 108, 115, 118–19, 121, 126, 268–70, 301 credit risk 63, 68, 74, 75, 91–106, 243–65, 268–99, 323–9, 352–71 credit spreads 30–3, 46, 104–6, 123–6, 139–57, 166–7, 227, 243–65, 295, 302–7, 325–9, 347–71 definition 243–4, 259–60, 261 working methods 244–6, 259–63 credit trees 255–6, 259 credit triangles 259–63, 302–7 credit valuation adjustments (CVAs) 95–6 Crisis Management Directive (CMD) 132–3, 136 cross-currency convertibles 64–6, 227–8 cross-Greeks 151, 369–71 cumulative deferrals 13–14, 116–17, 126 cumulative distribution functions 159–64, 207–10 cumulative dividend rights, preferreds (preference shares) 4–5, 173–4 cumulative normal distributions 72 currencies 64–6, 227–8, 366–7 currency risk 65–6 current yield (CY) 3–5, 68, 70, 142–3 day count conventions 24, 249–50 death spiral risk 61–2, 109–11, 339–41 debt 1–18, 268–70 see also bonds; credit ; hybrid securities; loans; subordinated debt-for-equity swaps 106–7 debt–to–equity ratios 106–7, 268–70 default events 2–11, 16, 63, 68, 75, 114–16, 133–7, 144–5, 172–6, 208–10, 214–21, 234–40, 246–65, 268–99, 301–7, 334–9, 342–6, 347–8, 357–71 default intensities 246–8, 250–6, 261–5, 267–99, 302–7, 323–9, 333–9, 341–6, 347, 348, 352–71 deferral risk 10–11, 14, 122, 319–21 delta 29–30, 40–6, 61–2, 65–6, 72–3, 152–3, 178–9, 181–6, 190–204, 245–6, 290–5, 313–16, 326–9, 332–3, 339–46 delta-hedging 29–30, 45, 61–2, 181–6, 245–6, 326–9, 339–41 deposit guarantee schemes (DGSs), bail-out methods 16 derivatives 1–2, 33, 68, 72, 139–40, 143–4, 146–57, 159, 160, 177–9, 180–204, 206–10, 244–6, 268–99, 301–46 see also credit ; equity ; forwards; options; swaps Dickey–Fuller test 264 diffusion 33, 148, 165–6, 192–204, 212–27, 281–6, 349–52 digital options see binary dilution 60–2, 77–111 dirty prices 23–5, 57–8, 68–9, 306 discount factors 141, 146–57, 173–6, 179, 222–7, 243–65, 312–46, 351–71 dividend features, convertible bonds 56–9 dividend pass through feature, convertible bonds 58–9 dividend protection, convertible bonds 58–9, 180, 191–204, 348–9 dividend pushers 13, 113, 118 dividend stoppers 13, 82, 113, 118–26 dividend thresholds, convertible bonds 58–9 dividend yields 46, 142–3, 154–5, 179, 180–6, 193–210, 284–8, 297–9, 304–7, 322–3, 357–71 dividends 3–8, 13–14, 22–3, 35–7, 46, 56–9, 62–8, 104, 113, 142–3, 154–5, 173–6, 179, 180–6, 193–210, 275, 284–8, 297–9, 304–16, 322–3, 330, 357–71 documentation risk 53, 55–6 Dodd–Frank Act 15, 108, 111 dollar duration (DV01) 72, 126 dollar nuking/neutral pricing 42–3, 72 double-signed gamma, convertible bonds 30–3, 286–8 Dow Jones Euro Stoxx 50 index 295, 367 drift 144–5, 165–76, 213–27, 231–40, 264–5, 268–70, 324–9 dual-strike structures, convertible bonds 36–7 duration 68–73, 122–3, 126 early exercise 199–204, 206–7, 222, 223, 277, 297–9, 348–71 EBITDA 116 effective triggers 343–6 efficient frontiers, convertible bonds and government bonds 21 elasticity parameter, CEV model 267–99, 333 enhanced capital notes see contingent convertibles epsilon 46 equity 1–21, 37–46, 58–76, 77–111, 126, 128–37, 139–57, 159–76, 177–9, 180–210, 211–42, 243–6, 248–65, 267–99, 301–46, 347–71 credit links 323–9 interest rate correlations 365–71 returns 17–18, 20–1, 177–9, 193–210, 212–27 volatility comparisons 4–5, 37–46 equity derivatives 1–2, 33, 68, 144, 148, 152, 159, 160, 177–9, 253–6, 301, 307–46 equity desks at investment banks 1–2 European Banking Authority (EBA) 77–8, 94, 97–8 European Central Bank (ECB) 128–9, 133–4 European Commission 130, 132, 136 European Council 130, 132–3 European options 144, 152, 160, 165, 180–6, 199–204, 240–2, 265, 274–7, 327–9, 335–9, 365–71 Index exchangeable convertibles 62–3 exercise values, trinomial trees 201–4, 222–7 exotic options 1–2, 61–2, 180, 186, 295–9, 304–7, 309–16, 322, 343–6 see also barrier ; binary ; lookback expected values, trinomial trees 34–7 explicit finite difference methods 205 exponential distributions 162–3, 174–6, 207–10, 235–6 extension risk 11, 122–3 extreme events 170–1, 176, 211–12, 281–3 see also fat-tail risk factors, models 144–5, 149–52, 180–6, 206–10, 229–40 failures, banks 8–11, 15–17, 77–8, 89–90, 107–8, 127–8, 130–7 fat-tail risk 176, 211–12, 281–3 see also extreme events; kurtosis Federal Deposit Insurance Corporation (FDIC), US 16, 99–100 filtration, stochastic processes 145–6 final conversion events, convertible bonds 33–5 final payoffs, convertible bonds 22–3, 36–7, 66–7, 206–10, 222–7, 356–71 final redemption events, convertible bonds 33–5, 54–6, 104, 115, 331–3, 350–71 financial crisis from 2007 8–12, 15–16, 17–18, 19–21, 75, 89–90, 92–3, 95, 104–5, 107, 127–8, 130–3, 136, 174, 211–12 financial innovations, financial crisis from 2007 92–3 Financial Services Authority (FSA) 99, 130 Financial Services Compensation Scheme (FSCS) 16 Financial Stability Board (FSB) 15, 95, 130–2 Financial Stability Oversight Council (FSOC) 108, 111, 132 finite difference methods 46, 145, 148, 204–5, 335–6, 348 fixed conversion price, CoCos 79, 80–1 fixed-income desks at investment banks 1–2, 23–4 fixed-income metrics 68–73 flash crash on the US stock market on May 6th 2010 85 floating conversion price, CoCos 79, 80–1 floating rate notes (FRNs) 9–10, 11, 86, 104, 117–18, 119–26, 140–57 floored conversion price, CoCos 81 forced conversions 35, 55–6, 86–9, 139–40, 149–50, 224–7, 245–6, 268–9, 286–8, 320–1, 330–3 forwards 62–3, 309–16, 318–22 France 24–5, 56–8, 63–4, 90, 128, 243–4 fugit 73 full write-downs, CoCos 79, 82–3, 302–7 funding sources 2–3, 268–70 see also debt; equity gamma 28–33, 36–7, 62, 88–9, 109–10, 162–3, 181–6, 242, 286–95, 316, 330–3, 369–71 garbage in garbage out (GIGO) 54 385 Gaussian copulas 144–5, 236–40 Gaussian L´evy processes 164 Gaussian processes 164, 165–6 geometric Brownian motion (GBM) 33, 144–5, 165–7, 169–71, 176, 177–9, 180–6, 193–204, 206–10, 214–27, 230–42, 245–6, 264–5, 267–99, 330, 348–52, 365–71 see also Brownian Girsanov’s Theorem 147 global calibrations 296–9 going concern capital 8, 16–17, 77–111, 318 gone concern capital 8, 77–8, 97–9 government bonds 3–4, 11, 20–1, 84, 243–4 the Greeks 46, 68, 151–3, 155, 178–9, 181–6, 248–9, 313–16, 326, 332–3, 369–71 see also delta; epsilon; gamma; omicron; rho; sensitivity analysis; vega; volga haircuts 16–17, 79–111 see also write-downs Hang Seng 367 hard issuer calls 47–50 Heath–Jarrow–Morton model (HJM) 268 hedge funds 15–16, 74–5, 78, 108 hedging 15–16, 29–30, 45, 60, 61–2, 74, 109–10, 143–4, 152, 177–86, 245–6, 248–9, 262–5, 326–9, 339–41 Henkel 120–1, 122–5 Hermite polynomials 355–6 Heston model 144, 180, 267–8, 292, 295 heteroskedasticity 192–3 heuristic models 139–57, 255–6, 296–9 HFR Convertible Arbitrage Index 75 high beta corporate hybrids 113–14 high and low-trigger CoCos 104–6, 302–7, 338 HJM see Heath–Jarrow–Morton model homoskedasticity 192–3 host instruments, CoCos 77, 78, 79, 86–7, 329–33 Hull–White interest rate model 144, 364–71 hybrid corporate capital see corporate hybrids hybrid securities 1–18, 139–57, 204, 208–10, 214–65, 267–99, 347–71 see also bail-in ; contingent convertibles; convertible bonds; corporate ; hybrid Tier ; models; preferreds ; prices; toggle bonds balance sheets 2–3, 106–7, 127, 129, 301–2 CDS curves 250–1 CEV model 169, 176, 187–8, 192–204, 214, 267–99, 330–3 concepts 1–18, 139–57, 208–10, 214–27 correlation 9–10, 139–40, 227–40 credit ratings 18, 115, 121, 126 definition 1–2, 139–40 multi-factor models 39, 139–40, 144, 151–2, 206–10, 268, 323–9, 333–9, 347–8, 364–71 recovery rates 122, 215–27, 248, 249–50, 252–6, 285–6, 302–7, 352–71 returns 9–10, 17–18, 19–21 386 Index hybrid securities (Continued ) statistics 2–3, 18 types 1–2, 3–18 hybrid Tier instruments 8–11, 13, 18, 77, 104, 137, 212, 316–17 see also floating rate notes characteristics definition 8–10 hybrid Tier instruments 10–13, 18, 137, 316–17 characteristics 11 definition 10–11 implicit finite difference methods 205 implied default probabilities 257–9, 262–5 implied volatilities 66–7, 181–6, 227, 228, 270–1, 275, 284–8, 297–9, 305–16, 326–9 in-the-money options 152–3, 154–5, 245–6, 350–2, 356 Independent Commission on Banking (ICB) 15, 132 independent exponentially distributed variables 162–3, 174–6 indices 18, 19–21, 62, 75, 111, 366–7 infinite variation property of Brownian motion 164–5 innovative hybrid Tier instruments 7–10, 94 Institute of International Finance (IIF) 127–8 institutional investors 74 insurance companies 78, 108 intensity parameter of the Poisson process 172–6, 208–10, 213–27, 237–40, 246–8 interest rate coverage ratio 100–6, 116 interest rate models 144, 364–71 interest rate risk 75, 139–40, 268 interest rate swaps 75, 240–1 interest rates 3–5, 8–11, 14, 23–35, 39–46, 53–6, 75, 81–2, 111, 113, 119–26, 139–57, 166–76, 180–6, 193–210, 217–40, 244–6, 248–65, 268–99, 302–71 see also coupon ; rho internal risk models 95–7 International Swaps and Derivatives Association (ISDA) 1–2, 257 Internet bubble 20 investment banks 1–2, 6–7, 15–16, 23–4, 66–7, 73–5, 132, 134–6, 184–6, 250, 263 investment premium see premium to the bond floor investment value of the convertible 6–7 investors CoCos 108, 302–46 convertible bonds 74–6, 114–15, 329–33 corporate hybrids 114–15 Ireland, bail-in capital 17 ISDA see International Swaps and Derivatives Association issuer calls 47–50, 113–14, 119–26, 223–7, 348–9 Italy 17–18, 90, 128 Ito processes 165–71, 186–204, 267–8, 273–4, 278–83 see also Brownian motion; stochastic Ito’s lemma 166–9, 193–204, 267–8, 278–83, 324–9, 333–9 jump diffusion 148, 212–27, 263, 267–8, 284–6, 292–5, 326–9, 334–9, 341–6, 347–8, 349–52, 367–71 see also Brownian motion; Poisson process; skewness Black–Scholes pricing model mix-ups 227, 326–9 convertible bond prices 221–7, 263, 284–6, 292–5, 347–8 definition 212–13, 227 Monte Carlo simulations 214, 349–52, 367–71 jump-to-default extended CEV process (JDCEV) 283–6, 292–5 jumps 148, 172–6, 188–204, 212–27, 263, 267–8, 283–6, 326–9, 347, 349–52 see also default events; Poisson process junk bonds 14–15 ‘knocked in’ positions 301, 307–46 ‘knocked out’ positions 307–46 kurtosis 161–2, 212–27 see also fat-tail risk Laguerre polynomials 355–6 lattice models see tree-based methods law of small numbers 164 lead managers, convertible bond markets 73–4 Lehman Brothers 15, 16, 17, 21, 107–8, 127, 130, 134–6, 148–9, 174 Leland’s corrected volatility number 181 leptokurtosis 212 Levenberg–Marquardt model 296–7 leverage ratios 99–106, 116, 268–70 L´evy processes 164, 172–6, 181–6 Libor 81–2, 243–4 linear components of risk 37–40, 43, 149–51 liquidity coverage ratio 100–6, 116 liquidity requirements, Basel III 99–106 liquidity risk 95–7, 99–107, 149, 246–8, 262–5, 299 listed securities, market makers 74 ‘living wills’ in the event of bankruptcy 16 loans 2–3, 84, 91–106, 240–2, 268–70 local calibrations 296–9 local volatility models 292 log processes, Ito’s lemma 166–7 log returns 9, 21, 29, 171, 193–210, 211–27, 271–99, 366–71 lognormal density functions 32–3, 161–2, 170, 181–2, 265, 273–4, 281–3, 335–9, 365–71 ‘long gamma’ portfolios 29–30 long positions 49–50, 61–2, 65–6, 74–5, 119–26, 139–40, 177–9, 199–204, 252–6, 301–46 Longstaff and Schwartz (LS) Monte Carlo method 206, 351, 352–71 Index lookback options 180, 295–9 lookback periods 13 loss given default (LGD) 249–65 loss-absorbing instruments 1–3, 7, 8, 15, 16, 77–111, 127–37, 212, 301–46 see also bail-in capital; contingent convertibles low-trigger CoCos 104–6, 338 LS see Longstaff and Schwartz Monte Carlo method LTCM 66–7 Macaulay duration, definition 71 make-whole feature, convertible bonds 67 mandatory conversions 35–7, 55–6, 86–9, 139–40, 149–50, 224–7, 245–6, 268–9, 286–8, 320–1, 330–3, 347 mandatory coupon deferrals 13–14, 116–18, 124–6, 320–1 maps, model maps 146–8, 323–4, 347–8 mark-to-market losses 95–7 market conventions, CDSs 256–7 market makers 74, 143–4 market risk 17–18, 37–46, 75, 85, 92–106, 122–3, 139–40 market trigger events, CoCos 85, 108, 308–46 market value recovery post-default values 216–27 Markov property of Brownian motion 164, 170–1 martingales 145–6 mean reversion 167–9, 176, 264–5, 324–9, 365–71 Merton jump-diffusion model 213 Merton, Robert 159, 180–6, 213, 275 Merton structural model 240, 268–9, 301–2 minimum capital ratios 91–106, 108 see also Basel ; Cooke ; Tier minority interests models 19, 22–3, 28–9, 33, 37–46, 49–50, 53–6, 74–6, 95–106, 125–6, 139–57, 159–76, 177–210, 211–42, 267–99, 323–4, 347–71 see also Black–Scholes ; closed-form ; Heston ; Monte Carlo simulations; multi-factor ; one-factor ; risk-neutrality; sensitivity analysis; stochastic processes; trinomial trees; two-factor advanced issues 211–42 building methods 143–52 calibration of models 144–5, 240–2, 250–1, 257–9, 268–70, 271–4, 295–9, 325–9, 348 CEV 169, 176, 187–8, 192–204, 214, 267–99, 330–3, 347 cheapness concepts 147–9 concepts 39, 139–57, 159–76, 323–4 correlation 9–10, 139–40, 227–40, 334–9 factors 144–5, 149–52, 180–6, 206–10, 229–40 heuristic approaches 139–57, 255–6, 296–9 maps 146–8, 323–4, 347–8 software 152–3, 160–3, 205–10, 221–7, 230 structural (firm-value) models 151–2, 240–2, 268–70, 301–2, 347 modified duration 71–2 Monarch Financial Holding convertible preferred 67 387 money markets 177–9, 335–6 Monte Carlo simulations 28–9, 145, 148, 153–7, 205–10, 233–40, 283, 322, 335–9, 348–71 see also sensitivity analysis American options 206–7, 348–71 CEV model 283 correlation 233–40 definition 153–4, 205–6 jump diffusion 214, 349–52, 367–71 Longstaff and Schwartz Monte Carlo method 206, 351, 352–71 mortgage-backed securities 92 MSCI equity market index 18, 19–21 MSCI World Index 18, 19–21, 62 multi-factor models 39, 139–40, 144, 151–2, 206–10, 268, 323–9, 333–9, 347–8, 364–71 multi-variate trigger events, CoCos 85 negative gamma 30–3, 36–7, 62, 88–9, 109–10, 242, 286–95, 316, 330–3, 339–41 Nelder–Mead simplex algorithm 296–8 net stable funding ratio (NSFR), Basel III 100–6 no-arbitrage models 145, 148, 365–71 non-cumulative coupon deferrals 13, 116–17, 318–21 non-linear components of risk 39, 149–51, 153–7, 343–6 non-viable events, hybrid Tier instruments 10–11, 303 normal distributions 32–3, 72, 160–6, 170–1, 206–10, 211–12, 213–27, 229–40, 304–7, 337–9 numerical methods 46, 53–6, 144–5, 208–10, 224–7, 276–7, 279–83, 348–71 omicron 46 one-and-a-half factor models 144, 148, 323–9, 334–9, 341–6, 347–8 one-factor models 139–57, 180–6, 268–99, 347–8 see also models operational risk 92–106, 257, 326–9 option-adjusted spreads (OASs) 246–7 optional conversions 5–6, 33–5, 86–9, 222–7, 245–6, 293–5, 329–33, 348–71 optional coupon deferrals 13–14, 115–18, 124–6, 317–21 options 1–2, 9–10, 22–3, 26–7, 47–52, 63–73, 89, 106–7, 119–26, 144–7, 152–3, 160, 165–6, 180–204, 224–7, 240–2, 253–6, 265, 268–70, 290–9, 304–46, 348–71 see also American ; barrier ; Bermudan ; binary ; call ; European ; exotic ; put ordinary least squares (OLS) 37–46, 150–1, 272, 325, 351–71 out-of-the-money options 183–6, 227, 228, 299, 322–3, 327–9 over-the-counter transactions (OTC) 74, 95–7, 248–9 388 Index par recovery plus accrued post-default values 216–27 par recovery post-default values 216–27 parametric VaR 72–3 see also Value at Risk parity 23, 27, 35, 47–50, 59–60, 63, 155, 222–8, 329, 353–71 partial differential equations (PDEs) 160, 182–6 see also Black–Scholes pricing model partial write-downs, CoCos 79, 82–3 participants, convertible bonds 73–6 path-dependent securities 205–10, 335–9, 365–71 paying agents, convertible bond markets 74 payment in kind bonds (PIKs) 15 Pearson linear correlation coefficient 228–40 pension funds 17, 173–4 PEPS/PRIDE/DECS mandatory convertible bonds 35–7 permanence factors, corporate hybrids 13–14, 113–14 perpetual cash flows 3–4, 9–10, 13–14, 104–6, 116–17, 122, 140–57, 173–6, 245–6 Poisson distributions 163–4 Poisson process 172–6, 208–10, 213–27, 237–40, 246–8, 263–5, 334–9 see also counting ; Cox ; jumps portfolios 29–30, 45, 53–6, 72–3, 139–57, 171, 177–9, 180–6, 227–40 positive gamma 28–33, 36–7, 88–9, 181–6, 286–95, 316, 330–3 post-default values 215–27 pre-default process 215–27, 326–9, 342–6, 364–71 preferreds (preference shares) 1, 2–5, 9–10, 18, 67, 134–6, 173–6, 215–16, 234–5 characteristics 3–4, 67 definition 3–4 prices 3–5, 18 risk 3–4, 173–6, 234–5 statistics 2–5, 18 premium to the bond floor, definition 27 premium to parity, definition 27, 143 premium/credit legs, CDSs 251–9, 263 present value recovery post-default values 216–27 price graphs, convertible bonds 22–3, 27–8, 31, 51–2 prices 3–7, 9–12, 17–21, 22–5, 37–46, 47–62, 74–6, 78, 104–6, 109–11, 139–57, 160, 176, 177–227, 241–2, 251–9, 261–5, 268–99, 301–46, 347–71 see also models; returns Black–Scholes pricing model 33, 68, 144, 148, 152, 159, 165, 167, 180–6, 200, 217, 227, 241–2, 265, 267–8, 269–70, 274–5, 281–3, 284–8, 292–5, 297–9, 304–46, 347 bonds 3–4, 9–10, 20–1, 37–46, 47–62, 241–2, 261–5 CDSs 251–9, 263, 295–6, 347 CEV model 169, 176, 187–8, 192–204, 214, 267–99, 330–3, 347 CoCoCos 86–7, 329–33 CoCos 78, 109–11, 144, 147, 149–52, 155–7, 176, 180, 186, 227–8, 244, 263, 268–99, 301–46, 347 concepts 301–46 convertible bonds 6–7, 18, 19–21, 22–5, 37–46, 47–62, 74–6, 140, 142–3, 144, 147–57, 160, 180–204, 215–27, 241–2, 243–6, 263–5, 268–99, 347–71 corporate hybrids 140–3, 243–4 coupons 3–5, 184–6, 204, 208–10, 252–65, 306–7, 309–16 derivatives 33, 68, 144, 148, 152, 159, 160, 177–9, 180–204, 206–10, 244–6, 268–99, 301–46 dividends 3–5, 56–8, 142–3 equity 17–18, 20–1, 37–46, 58–62, 109–11, 139–57, 159–76, 177–9, 180–210, 211–40, 243–6, 248–65, 267–99, 330–3, 341–6, 347–71 government bonds 3–4, 20–1 hybrid Tier instruments 9–10, 18 hybrid Tier instruments 11–12, 18 perpetual cash flows 3–4, 9–10, 104–6, 140–57, 173–6, 245–6 preferreds (preference shares) 3–5, 18 senior bonds 9–10 theoretical/closing price differences 3–4 private equity funds 15–16 probabilities of default 214–21, 234–5, 250–65, 267–8, 283–6, 302–7, 342–6, 352–71 probability density functions 32–3, 159–64 put–call parity, convertible bonds 22–3 puts 7, 22–3, 26–7, 48–52, 59–60, 66–7, 69–70, 89, 119–26, 147, 154, 160, 183–6, 191–204, 223–7, 274–7, 293–9, 311–16, 322, 348–71 quoted prices, convertible bonds 23–5 Radon–Nikodyn derivative 147 Randal, John 273–4 random numbers 153–7, 166, 206–10, 236–40 random walks 211–12, 227, 349–52 ratchet clauses, take-overs 22, 59–60 recapitalizations 127–37 recombining trinomial trees 193 recovery rates 122, 215–27, 248, 249–50, 252–6, 259–65, 285–6, 302–7, 352–71 reduced-form model types 267–8, 302–7 references 373–80 refix/reset features 7, 60–2, 109–11, 121, 154, 191–2, 204, 223–7, 268–9, 288–95, 348–9 regression methods 37–46, 150–1, 229–40, 264–5, 272–4, 325–9, 351, 352–71 regulations 2–3, 7–13, 15–16, 77–111, 127–37, 288–9, 303–7, 311–17, 330–3, 339–41 see also bail-in capital; Basel ; Financial Stability Board; Tier regulatory/non-viability trigger events, CoCos 84, 86–7, 108–9, 303–7, 311–16, 330–3, 339–41 Renewable Energy convertible bonds 30–3, 211–13 Index replacement capital covenants (RCCs) 118–20, 121, 126 resolution funds (RFs), bail-out methods 16, 130–3 resolution regimes 16, 129–37 returns 3–5, 6–7, 9–10, 17–18, 19–21, 29, 74–5, 114–26, 136–7, 171, 177–9, 193–210, 211–27, 234–40, 243–6, 271–99 see also prices convertible bonds 6–7, 18, 19–21, 74–5, 114–26, 243–6 corporate hybrids 114–26, 243–4 equity 17–18, 20–1, 177–9, 193–210, 212–27 hybrid Tier instruments 9–10, 18 hybrid Tier instruments 11–12, 18 log returns 9, 21, 29, 171, 193–210, 211–27, 271–99, 366–71 risk–return profiles 93, 122, 136 statistics 20–1, 75 reverse convertibles 66–7, 89, 106–7, 180, 182–6, 301, 347 rho 39–41, 46, 369–71 see also interest rates risk 3–4, 7, 10–11, 15, 17–18, 19–21, 37–46, 53, 61–2, 72–3, 75, 77–8, 84–111, 114–26, 139–57, 176, 177–210, 211–28, 243–65, 268–99, 347–71 see also contagion ; credit ; currency ; death spiral ; deferral ; extension ; interest rate ; jump ; market ; operational ; volatilities CoCos 7, 15, 77–8, 84–111, 144, 147, 149–52, 155–7, 176, 301–46 components 37–46, 227–8 convertible bonds 19–21, 30–3, 37–46, 53, 61–2, 72–3, 114–26, 140–57, 180–6, 211–12, 215–27 corporate hybrids 114–15, 122–6 fat-tail risk 176, 211–12, 281–3 linear components 37–40, 43, 149–51 preferreds (preference shares) 3–4, 173–6, 234–5 risk-free rates 4, 25–6, 74–5, 177–9, 243–8, 262–3, 302–7, 309, 311, 312–16, 336–9 risk-neutrality 35, 146, 177–210, 216–27, 244–6, 267–99, 324–9, 335–9, 348 risk–return profiles 93, 122, 136 risk-weighted assets 8, 91–106, 132–3 roll-back procedures, trinomial trees 200–4, 222–7, 293–5, 336–9, 345–6, 356 rule of thumb 255–6, 259–60, 302–7 safe haven corporate hybrids 113–14 scaling property of Brownian motion 164–5 semi-closed-form formula, CEV model 275–6 senior bonds 9–10, 18, 98–106, 113–14, 121–2, 127, 133–7, 215–16, 240–2, 257, 347 senior debt 2–3, 9–10, 13, 18, 98–106, 113–14, 121–2, 127–37, 215–16, 240–2, 257, 347 sensitivity analysis 37–46, 68, 72–3, 89, 152–7, 205–10, 248–9, 314–16, 321, 369–71 see also Greeks; models; Monte Carlo simulations 389 September 2001 terrorist attacks 20 settlement dates, convertible bonds 24 shifting property of Brownian motion 164–5 short positions 45, 60, 119–26, 177–9, 245–6, 252–6, 310–46 SIFIs see systemically important financial institutions skewness 161–2, 212–27, 270, 284–6, 327–9 snapshot reset features, convertible bonds 60–2 soft issuer calls 47–50, 55–6, 293–5, 348–9 software, models 152–3, 160–3, 205–10, 221–7, 230 solvency trigger events, CoCos 85, 108 sovereign debt meltdown from 2011 17–18, 21, 97 Spearman rank correlation coefficient 228–9 specified triggers, effective triggers 343–6 Squam Lake Working Group on Financial Regulation 85 square-root processes, Ito’s lemma 167–9, 187–8, 268 staggered write-downs, CoCos 79, 82–3 Standard & Poor’s 1, 9, 14, 18, 92, 115, 121, 366 standard deviations 29, 123–6, 155–7, 171, 211–14, 273–4 standard features, convertible bonds 47–62 step-up clauses 9–11, 13–14, 104, 113, 121, 122–6 stochastic calculus 146, 160–76 stochastic credit 263–5, 333–9, 351–71 stochastic differential equations (SDEs) 146, 165–71, 193–204, 213–27, 267–99, 323–9, 364–71 stochastic interest rates 148, 151–2, 263–5, 364–71 stochastic processes 29, 139–40, 144–57, 159–76, 186–204, 213–27, 229–42, 246–8, 263–5, 267–99, 301–2, 323–9, 333–9, 341–6, 347–71 see also Brownian motion; Ito ; martingales; Poisson stochastic volatilities 33, 144–5, 148, 152–7, 180, 267–8, 295, 369–71 structural (firm-value) models 151–2, 240–2, 268–70, 301–2, 347 structured products 1–2, 14, 15–16, 77–8, 301–2 subordinated debt 1, 2–3, 8, 10–14, 17–18, 99, 113–26, 128–37, 215–16, 257 see also corporate hybrids; Tier capital subordination risk 122 subprime crisis 92–3 see also financial crisis from 2007 survival probabilities 172–6, 216–27, 235–40, 247–8, 258–65, 302–7, 352–71 swaps 1–2, 11–12, 75, 81, 106–7, 111, 114–15, 118, 119–26, 240–1, 243–4, 248–65 see also credit default ; interest rate synthetic convertibles 63–4 systemically important financial institutions (SIFIs) 95–6, 97–106, 127–8, 131–3 T-bill recovery 216 take-overs 19, 22, 59–60 taxes 8, 111, 113, 329 390 Index taxpayers, bail-outs 15–17, 77–8, 127–9, 134 Taylor series expansion 29, 368–71 term structure of interest rates 365–71 terminology, convertible bonds 19, 22–37, 68–73, 76 Tier bonds Tier capital 7–13, 18, 77, 78, 81–2, 84, 86–7, 94–106, 131, 137, 212, 303–4, 308–9, 316–17 see also Additional ; Common Equity ; hybrid Tier bonds 1, 10–13 Tier capital 8, 10–13, 18, 84, 94–106, 137, 316–17 Tier capital 94 time horizons 46 time slices 189–204, 218–27, 279–83, 293–5, 341–6, 356, 358–64 time-homogeneous Poisson process 174–6, 208–10, 235–6, 247–8 toggle bonds 14–15 too-big-to-fail banks, Basel III 95–6, 131–3 toxic mortgages 99–100 transaction costs 178–9, 180–1, 275 transformation matrices 231–40 transition probabilities, trinomial trees 189–204, 218–27, 279–83, 342–6 transparency issues, CoCos 108–11 tree-based methods 34–7, 143–4, 145, 147, 148, 160, 177–9, 186–204, 215–27, 245–6, 255–6, 259, 277–83, 292–6, 321–3, 335–9, 341–6, 348, 362 see also binomial ; finite difference ; trinomial trigger events 47–50, 55–6, 77, 78, 79, 83–111, 131, 149–50, 155–7, 212, 234–5, 293–5, 301–46, 348–9 trinomial pyramids 336–9 trinomial trees 34–7, 143–4, 145, 147, 148, 160, 186–204, 215–27, 245–6, 252–6, 259–60, 277–83, 284–6, 292–5, 321–3, 335–9, 341–6, 348, 362 see also binomial American options 199–204, 222, 223, 277 Bermudan options 203–4 CEV model 277–83, 284–6, 292–5 CoCos 321–3, 341–6 European options 199–200 jumps 215–27 roll-back procedures 200–4, 222–7, 293–5, 336–9, 345–6, 356 trustees, convertible bond markets 73–4 two linear components of risk 39–40, 43 two non-linear components of risk 40–2 two-factor models 139–40, 144, 151–2, 206–10, 323–9, 333–9, 348, 364–71 see also models; multi-factor unconstrained regressions 363–71 underlying prices 144–57, 177–210, 267–99, 309–46, 347–71 see also equity Value at Risk (VaR) 72–3, 95 variance 38–9, 152–7, 160–76, 181–6, 191–204, 229–40, 264–5, 267–99, 330–3, 341–6 see also constant elasticity ; standard deviations variance gamma process 181–6, 292 Vasicek interest rate model 364–5 vega 46, 315–16, 328–9 Vickers report 15, 132 volatilities 4–5, 9–10, 20–1, 29–33, 36–46, 59–60, 66, 75, 123–6, 139–57, 169–76, 177–9, 180–6, 193–210, 211–12, 213–27, 228–42, 243, 267–99, 304–46, 347–71 see also betas; implied ; risk; standard deviations; stochastic ; vega volatility risk 75 volatility skews 322–3, 327–9 volatility smiles 307, 322–3 volatility surfaces 275–99 Volcker rule section of the Dodd–Frank Act 15–16 volga 315–16 voting rights 3, 113–14 warrants, synthetic convertibles 63–4 Wiener process 164–5, 172, 212–27, 229–30 see also Brownian motion window reset features, convertible bonds 60–2 write-downs 2–3, 7, 16–17, 77–111, 127–37, 301–46 yield advantage 73, 142–3 yield to call (YTC) 70, 123–6, 140–3 yield to maturity (YTM) 68–70, 123–6, 139–41, 243–4 yield to put (YTP) 69 yield to worst (YTW) 70, 123–6 yields 3–5, 46, 68–73, 86–7, 114–26, 136–57, 179, 180–6, 193–210, 237–40, 284–8, 297–9, 304–7, 322–3, 329–33, 357–71 Z-(zero volatility) spreads 243–6, 261, 262–3 zero-coupon bonds 155–7, 182–6, 259–63, 292–5, 308–9, 318–21, 365–71 Index compiled by Terry Halliday [...]... return of a variable 𝑋 between two different dates 𝑡0 and 𝑡1 is given by log(𝑋𝑡1 ) − log(𝑋𝑡0 ) with 𝑡 0 < 𝑡1 6 The beta (𝛽) of a bond, stock, or portfolio is a number describing the volatility of this asset in relation to the volatility of a reference asset Beta measures the sensitivity of the returns of the asset with respect to changes in the price of the reference asset 10 The Handbook of Hybrid Securities. .. also often called the investment value of the convertible High prices of the underlying share lead to high conversion probabilities and the value of the convertible is then close to parity (𝑃𝑎 ) Under such circumstances, the value of a convertible is definitively more a share than a bond: 𝑃𝑡 ≈ 𝑃𝑎 = 𝐶 𝑟 𝑆𝑡 𝑁 (1.4) The parity or conversion value of a convertible represents the value of the amount of underlying... between the cone of the shares and the volatility cone of a corporate bond For the 1-month time horizon, the 90th percentile of the realized volatility is 54.33% for shares, 26.82% for bonds, and 40.08% for preferred shares This illustrates the higher risk of the preferred compared with a standard corporate bond from the same issuer With the help of the volatility cone, one can look under the hood of this... Date: April 25, 2012 the issuer This is a deferral risk There is another type of risk that will be explained in this book: extension risk This is the risk that the company will not call back the bond on the first call date Because of this, the life of the bond is extended at least till the next call date (if any) This would push the repayment of the redemption amount further into the future A Tier 2... coupon, the payment of which can be skipped at the discretion of the management of the company (optional deferral) A mandatory deferral corresponds to a case where a breach of a financial ratio would trigger the non-payment of the coupon The deferrals on the coupon payments can be cumulative or non-cumulative In the first case, the issuer has to deal with the coupon payments that were deferred in the past... – the day before its earnings announcement When the share price of Bear Stearns lost another 50% after this announcement, the Federal Reserve Bank of New 16 The Handbook of Hybrid Securities York stepped in Their actions led to the take over of the ailing investment bank by JP Morgan Chase On March 17, 2008 JP Morgan Chase had offered to acquire Bear Stearns at a price of $2 per share, a fraction of. .. Only 6 months later, the market turned out to be less able to deal with the failure of a big international player The bankruptcy of Lehman Brothers sent shock waves throughout the financial system The aftermath of the default of Lehman Brothers extended beyond the United States In fact, it was the administration process in Europe which proved to be most difficult The US part of the Lehman business had... might not be paid Such an event does not push the issuing bank into default, however Studying the price returns of both bonds of Table 1.2 in the second half of 2011 reveals the equity nature of Tier 1 debt There is no direct relationship between the Tier 1 bond and the underlying shares according to the prospectus Nevertheless, the perpetual nature of the bond and its deep subordination make it sensitive... this result, both the 90th and the 10th percentiles for each of these rolling windows are connected on a graph The volatility cone for ALCOA for the period 2003–2013 can be found in Figure 1.3 A volatility cone is an interesting graphical snapshot view of the historical volatility of an asset From the sample volatility cone of ALCOA, we learn that the cone and therefore the risk of the preferred share... financial regulation, but it nevertheless covers the big overhauls that reshaped the financial landscape xvi Reading this Book A handbook can never be of any value to a practitioner if there is no mention at all of what the regulatory implications of each of the different instruments are The quantitative part of this book is very pragmatic The first steps into the landscape of hybrid instruments will take