Pricing Convertible Bonds

by Connolly, Kevin B.

• ISBN13: 9780471978725
• ISBN10: 0471978728
• Edition: 1st
• Format: Hardcover
• Copyright: 1998-10-15
• Publisher: WILEY

Summary

The Convertible Bonds (CB) market is growing all the time. To date, over one trillion dollars worth of CBs are in circulation. Corporations are finding this source of fund-raising more and more attractive. And for different reasons, the buyers are finding CBs increasingly attractive investment vehicles.There are few works on the subject of pricing convertible bonds. Most books discussing derivative products cover all details of pricing futures and options in minute detail. Convertible bonds and warrants are usually mentioned as an after thought in the latter chapters. This is the first book to address the very complex issue of pricing convertible bonds.Kevin Connolly, Researcher of complex volatility trading for Refco Overseas Ltd. and Lecturer at City University Business School and London Guildhall University, has put together an excellent treatment of pricing convertible bonds, delving into topics such as: Returns distributions and associated descriptive statistics Modeling the share price process The basic convertible bond model Introducing the complications Convertible bond sensitivities Using equity warrant models to price CBs Refix clauses Fund managers, hedge players/traders, undergraduates and postgraduates will find this book invaluable. Easy to understand software on Microsoft Excel spreadsheets is also supplied.

Author Biography

KEVIN B. CONNIOLLYin used to be Head of Quantitative Research at James Capel & Co. He then joined Cresvale International Asset Management as Director responsible for instituting scientific risk management for Cresvales principal Japanese warrants market-making section. He is currently undertaking research into complex volatility trading for Refco Overseas Ltd. He also lectures at City University Business School and London Guildhall University, UK. Kevin has already published a book in 1997, Buying and Selling Volatility.

Table of Contents

Preface	ix
1 Introduction	1	(19)
1.1 Bonds	1	(1)
1.2 Equity	2	(1)
1.3 Convertible bonds	3	(10)
1.4 Non-standard investment strategies	13	(7)
2 Using computer spreadsheets	20	(20)
2.1 Features of Excel used in CB modelling	20	(7)
2.2 Simulating random events	27	(8)
2.3 Backward induction -- a simple CB model	35	(1)
2.4 Using the data table feature to create tables and figures	36	(2)
2.5 Finding the implied volatility of a CB using the goal seek command	38	(2)
3 Returns distributions and associated descriptive statistics	40	(23)
3.1 Measures of return	40	(4)
3.2 Return distributions	44	(1)
3.3 Averages and expected returns	45	(2)
3.4 A measure of dispersion -- MAD, variance and standard deviation	47	(3)
3.5 The concept of a population, sample and sampling variation	50	(3)
3.6 Adding distributions	53	(3)
3.7 Adding the same distributions	56	(2)
3.8 From stock prices to returns	58	(3)
3.9 From stock prices to more appropriate returns	61	(2)
4 Modelling the share price process	63	(19)
4.1 The expected value and standard deviation of a Bernoulli trial	63	(1)
4.2 The simple additive model of stock price changes	64	(8)
4.3 The multiplicative Binomial model	72	(6)
4.4 A model with time dependence	78	(4)
5 The basic convertible bond model	82	(38)
5.1 A simple two-way bet -- the zero arbitrage approach	82	(8)
5.2 The one-period CB model	90	(9)
5.3 Introducing interest rate considerations	99	(2)
5.4 The two-period CB model	101	(5)
5.5 The three-period CB model	106	(2)
5.6 The general n-period CB model	108	(2)
5.7 The effects of volatility	110	(1)
5.8 The effects of interest rates	111	(1)
5.9 Introducing coupons	112	(4)
5.10 A final note on the value and meaning of the p and q parameters	116	(3)
5.11 Summary	119	(1)
5.12 Solutions to exercises in Figure 5.2	119	(1)
6 Introducing the complications	120	(33)
6.1 Introducing dividends	120	(5)
6.2 Introducing the issuer's call option	125	(4)
6.3 Introducing a bond put	129	(2)
6.4 Interest rate effects revisited	131	(8)
6.5 Non-domestic CBs and the foreign exchange complication	139	(14)
7 Convertible bond sensitivities	153	(20)
7.1 Calculation of CB sensitivities	153	(1)
7.2 The delta or hedge ratio -- sensitivity to the underlying share price	154	(5)
7.3 Theta -- time decay	159	(2)
7.4 Vega -- volatility sensitivity	161	(3)
7.5 Rho -- interest rate sensitivity	164	(2)
7.6 The effect of time on CB sensitivities -- second-order sensitivities	166	(3)
7.7 Contour diagrams	169	(2)
7.8 Concluding remarks on CB sensitivities	171	(2)
8 Using equity warrant models to price CBs	173	(39)
8.1 Equity warrants	173	(2)
8.2 Model for warrant prices	175	(16)
8.3 A common error in using the Black and Scholes model to value CBs	191	(1)
8.4 The dilution issue	192	(2)
8.5 Modelling investment trust warrants	194	(18)
9 Refix clauses	212	(14)
9.1 An example	212	(1)
9.2 CB price on the refix day	213	(1)
9.3 CB price prior to refix day	213	(2)
9.4 Modelling refix clauses -- two-stage binomial trees	215	(2)
9.5 A five-period refix model example	217	(1)
9.6 Increasing the number of periods	218	(1)
9.7 The effects of a refix clause on CB prices	219	(1)
9.8 How much is a refix clause worth?	220	(2)
9.9 Upside and downside refix clauses	222	(2)
9.10 The effects of refix clauses on CB price sensitivities	224	(1)
9.11 Multiple refix clauses	225	(1)
9.12 Refix clauses and dilution	225	(1)
Appendix: A guide to the software supplied on disk	226	(23)
Index	249