Equity derivatives corporate and institutional applications

EQUIT Y DERIVATIVES CORPORATE AND INSTITUTIONAL APPLICATIONS NEIL C SCHOFIELD www.allitebooks.com Equity Derivatives www.allitebooks.com Neil C Schofield Equity Derivatives Corporate and Institutional Applications www.allitebooks.com Neil C Schofield Verwood, Dorset, United Kingdom ISBN 978-0-230-39106-2    ISBN 978-0-230-39107-9 (eBook) DOI 10.1057/978-0-230-39107-9 Library of Congress Control Number: 2016958283 © The Editor(s) (if applicable) and The Author(s) 2017 The author(s) has/have asserted their right(s) to be identified as the author(s) of this work in accordance with the Copyright, Designs and Patents Act 1988 This work is subject to copyright All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed The use of general descriptive names, registered names, trademarks, service marks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations Cover image © dowell / Getty Printed on acid-free paper This Palgrave Macmillan imprint is published by Springer Nature The registered company is Macmillan Publishers Ltd The registered company address is: The Campus, Crinan Street, London, N1 9XW, United Kingdom www.allitebooks.com Acknowledgements Like the vast majority of authors, I have been able to benefit from the insights of many people while writing this book First and foremost, I must thank my friend and fellow trainer, David Oakes of Dauphin Financial Training On more occasions than he cares to remember David has kindly answered my queries in his normal cheerful manner If you ever have a question on finance, I can assure you that David will know the answer! I must also thank Yolanda Clatworthy who spent a significant amount of time reviewing chapter three Her insights have added enormous value to the chapter Stuart Urquhart arranged for me to have access to Barclays Live and the quality of the data and screenshots has added significant value to the text Over the years that I have known Stuart he has been a great supporter of all my writing and training activities often when the benefit to himself is marginal A true gentleman Many thanks to Doug Christensen who gave permission for the Barclays Live data to be used Aaron Brask and Frans DeWeert both critiqued the original text proposal and made a number of useful pointers as to how the scope could be improved Although I had to drop some of the suggestions due to time and space constraints, their contributions were significant and gladly received Also thanks to Matt Deakin of Morgan Stanley who helped clarify some equity swap settlement conventions Troy Bowler was an invaluable sounding board in relation to a number of topics Thanks also go to the many participants who have attended my classroom sessions over the years The immediacy of the feedback that participants provide is invaluable in helping me deepen my understanding of a topic v www.allitebooks.com vi Acknowledgements Finally, a word of thanks to my family who have always been supportive of everything that I have done A special word of thanks to Nicki who never complains even when I work late “V” Although many people helped to shape the book any mistakes are entirely my responsibility I would always be interested to hear any comments about the text and so please feel free to contact me at neil.schofield@fmarketstraining.com or via my website www.fmarketstraining.com PS Alan and Roger—once again, two slices of white toast and a cuppa for me! Contents   Equity Derivatives: The Fundamentals1   Corporate Actions35   Equity Valuation45   Valuation of Equity Derivatives73   Risk Management of Vanilla Equity Options105   Volatility and Correlation139   Barrier and Binary Options203   Correlation-Dependent Exotic Options247   Equity Forwards and Futures271 10 Equity Swaps287 11 Investor Applications of Equity Options315 vii viii Contents 12 Structured Equity Products347 13 Traded Dividends385 14 Trading Volatility417 15 Trading Correlation461 Bibliography479 Index 481 List of Figures Fig 1.1 Movements of securities and collateral: non-cash securities lending trade 13 Fig 1.2 Movements of securities and collateral: cash securities lending trade 14 Fig 1.3 Example of an equity swap 20 Fig 1.4 Profit and loss profiles for the four main option building blocks 22 Fig 1.5 Example of expiry payoffs for reverse knock in and out options 24 Fig 1.6 At expiry payoffs for digital calls and puts 25 Fig 1.7 Overview of equity market interrelationship 32 Fig 2.1 Techniques applied to equity derivative positions dependent on the type of takeover activity 38 Fig 3.1 The asset conversion cycle 49 Fig 4.1 Structuring and hedging a single name price return swap 82 Fig 4.2 Diagrammatic representation of possible arbitrage between the equity, money and equity swaps markets 84 Fig 4.3 Diagrammatic representation of possible arbitrage between the securities lending market and the equity swaps market 85 Fig 4.4 ATM expiry pay off of a call option overlaid with a stylized normal distribution of underlying prices 92 Fig 4.5 ITM call option with a strike of $50 where the underlying price has increased to $51 93 Fig 4.6 Increase in implied volatility for ATM call option 93 Fig 4.7 The impact of time on the value of an ATM call option 95 Fig 4.8 Relationship between option premium and the underlying price for a call option prior to expiry 97 Fig 5.1 Relationship between an option’s premium and the underlying asset price for a long call option prior to expiry 106 Fig 5.2 Delta for a range of underlying prices far from expiry for a long-dated, long call option position 106 ix x  List of Figures Fig 5.3 Fig 5.4 Fig 5.5 Fig 5.6 Fig 5.7 Fig 5.8 Fig 5.9 Fig 5.10 Fig 5.11 Fig 5.12 Fig 5.13 Fig 5.14 Fig 5.15 Fig 5.16 Fig 5.17 Fig 5.18 Fig 5.19 Fig 5.20 Fig 6.1 Fig 6.2 Fig 6.3 Fig 6.4 Fig 6.5 Fig 6.6 Delta for a range of underlying prices close to expiry for a long call option position 107 Equity call option priced under different implied volatility assumptions109 Positive gamma exposure for a long call position 112 Expiry profile of delta-neutral short volatility position 114 Initial and expiry payoffs for delta-neutral short position 115 Impact on profit or loss for a 5 % fall in implied volatility on the delta-­neutral short volatility position 115 Sources of profitability for a delta-neutral short volatility trade 118 Theta for a 1-year option over a range of spot prices 121 The theta profile of a 1-month option for a range of spot prices 122 Pre- and expiry payoff values for an option, which displays positive theta for ITM values of the underlying price 123 Vega for a range of spot prices and at two different maturities 127 FX smile for 1-month options on EURUSD at two different points in time 130 Volatility against strike for 3-month options S&P 500 equity index 131 Implied volatility against maturity for a 100 % strike option (i.e ATM spot) S&P 500 equity index 132 Volatility surface for S&P 500 as of 25th March 2016 133 Volgamma profile of a long call option for different maturities for a range of spot prices Strike price = $15.15 135 Vega and vanna exposures for 3-month call option for a range of spot prices Option is struck ATM forward 136 Vanna profile of a long call and put option for different maturities and different degrees of ‘moneyness’ 137 A stylized normal distribution 140 Upper panel: Movement of Hang Seng (left hand side) and S&P 500 index (right hand side) from March 2013 to March 2016 Lower panel: 30-day rolling correlation coefficient over same period 145 The term structure of single-stock and index volatility indicating the different sources of participant demand and supply 146 Level of the S&P 500 and 3-month implied volatility for a 50 delta option March 2006–March 2016 151 Implied volatility for 3-month 50 delta index option versus 3-month historical index volatility (upper panel) Implied volatility minus realized volatility (lower panel) March 2006–March 2016 152 Average single-stock implied volatility versus average single-stock realized volatility (upper panel) Implied volatility minus realized volatility (lower panel) March 2006–March 2016 153 472  Equity Derivatives 15.4.5.3  Choice of Instruments A dispersion trade can be constructed by buying (or selling) volatility on the index against selling (or buying) volatility on the index constituents These trades are summarized in Table 15.2 Because of transaction costs traders will tend to favour indices with fewer constituents (e.g EURO STOXX 50) but may choose to express the view by trading the volatility of a larger index such as the S&P 500 against a representative basket of constituents (e.g the top 50 shares) There are a number of different instruments that the trader could use to express a view on dispersion: • Vanilla options—this is typically done using straddles or strangles To sell correlation the trader would sell straddles/strangles on the index and buy straddles/strangles on the index constituents with their trade size based on their index weight One of the benefits of using straddles/strangles is that they tend to be quoted with a higher level of implied volatility than variance swaps This is because variance swaps tend to be more expensive to hedge, which has to be reflected in their price Although options are typically very liquid the implementation of this strategy would require the position to be delta-hedged on an ongoing basis • Variance swaps—to short correlation using variance swaps the investor would sell index variance and buy single-stock variance Typically, the notional of the single-stock trades are based on the constituents’ weight within the index and their payouts would probably be capped Variance swaps are usually hedged with a static portfolio of puts and calls struck along a continuum Risk (2011) points out that before the financial crash traders would hedge using a limited number of strikes around the level of spot However, upon the collapse of Lehman Brothers this hedge liquidity dried up with dealers losing “billions” • Volatility swaps—for the buyer of correlation, these have the advantage of having lower losses than variance swaps if volatility on single name stocks increases significantly • Correlation swaps—these were considered in Sect 15.4.2 and consist of a single payoff between a pre-agreed strike and realized correlation The most Table 15.2 Components of a dispersion trade Index Constituents Sell correlation Buy correlation Sell volatility Buy volatility Buy volatility Sell volatility 15  Trading Correlation  473 common convention is for the names to have equal weights Although this offers a ‘pure’ exposure to correlation the instrument is relatively illiquid This lack of liquidity and the difficulty in hedging this type of instrument has meant that the strikes for these instruments are lower than those achieved when trading correlation using variance swaps (Granger et al 2005) 15.4.5.4  Dispersion Trade Weighting Techniques If a variance swap is set up with equal vega notionals the position will still have an exposure to volatility Suppose that an investor decides to execute the following short correlation trade: • Sell index variance swap with a vega notional of $20,000 at a strike of 15 • Buy single-stock variance swaps with a total vega notional of $20,000 at a strike of 25 Based on the correlation proxy equation, these two components suggest an implied correlation of 36 % Suppose that average single-stock volatility increases by 1 % but correlation remains unchanged Using the correlation proxy measure this means that index volatility will be 15.6 %.3 So a 1 % increase in single-stock volatility will cause index volatility to increase by 0.6 % Since the investor has executed a short correlation position the profit on the single-stock variance swap position will be greater than the loss on the index position, that is, the short correlation trade with equal vega notionals is vega positive To avoid this directional exposure to volatility the notionals would need to be adjusted to ensure that the trade is initially vega neutral The vega exposure of a variance swap measures how the position’s profit and loss will change if implied volatility were to move by 1 % point from its initial strike So vega neutrality requires that the notional amounts be set at such a level that a 1 % change in volatility for the index and its constituents will not generate any profit or loss This concept is also sometimes referred to as the ‘crossed vega’.4 To illustrate how a vega neutral trade is set up, consider the following hypothetical transaction referencing the EURO STOXX 50 Table 15.3  SQRT (0.36) × 26 % = 15.6 %  Crossed vega is the amount of vega traded on both single stock and indexes So $10 m of crossed vega at a portfolio level means that $10 m of vega on the single stocks is matched with $10 m vega on the index (Risk 2011) 474  Equity Derivatives Table 15.3  Term sheet for hypothetical dispersion trade Buyer Seller Maturity Volatility units (EUR per point) Variance units Volatility strike Index variance swap leg Single-stock variance swap legs Bank Hedge fund 1 year 126,229 3607 17.50 % Hedge fund Bank 1 year Various, totalling 100,000 Various Various Table 15.4  Structuring a variance swap dispersion trade on the EURO STOXX 50 Equity Index weight Volatility units (€ per point) Variance units Volatility strike Weighted strike ABN AMRO Aegon Ahold 2.20 % 0.90 % 0.60 % 2200 900 600 51 16 10 21.47 27.94 29.33 0.47 0.25 0.18 Telecom Italia Total Unilever Totals 1.60 % 1600 38 21.02 0.34 6.80 % 1.80 % 100 % 6800 1800 100,000 178 46 19.15 19.36 1.30 0.35 22.09 The index variance swap leg consists of a single swap on the underlying index, whereas the single-stock leg is made up of 50 individual variance swaps each with a different notional amount, partial details of which are shown in Table 15.4 Notional amounts on the single-stock positions are determined as follows: • The investor decides the total desired volatility exposure for the constituents (e.g €100,000) • The volatility units for each constituent are the product of this total desired exposure and the constituent weight within the index For ABN AMRO the volatility units are 100,000 ì 2.2% = 2200 The variance units for each constituent are equal to the volatility units divided by (2 × strike) For ABN AMRO this would be €2200/(2 × 21.47) = 51 The final stage is to determine the notional on the index trade to ensure vega neutrality This is achieved by weighting the total desired volatility ­exposure for the single-stock leg by the ratio of the implied volatilities of each leg of the trade For the index position the implied volatility used for this calculation is the variance swap strike, which in this case is 17.50 % For the single-­stock position, the implied volatility is calculated as the sum of the weighted strikes: 15  Trading Correlation  475 • The observed volatility strike is multiplied by the constituent’s weight in the index For ABN AMRO on Table 15.4, it is 0.47, that is, 21.47 ì 2.2% These individual values are then summed (e.g 22.09) Index Notional = Single stock notional × ∑ = 100, 000 × Weighted strike of constituents Volatility strike of index 22.09 17.50 = 126, 229 The payoff on all of the swaps follows the normal variance swap conventions illustrated in Sect 14.6.1 There are two other points worthy of mention with respect to dispersion trading: • ‘Market disruption events’ will impact the payoff of a variance swap as it will influence the calculation of the realized volatility Typical examples of market disruption would be as follows: –– Early closing of the market, for example, due to technological problems –– Suspension of trading in a share –– Insufficient liquidity or trading volumes –– Conditions that impact an entity’s ability to hedge an exposure • Some trades also allow for the closing value of the share to be adjusted by the amount of a gross cash dividend when it is paid on an observation date 15.4.5.5  Dispersion Options A dispersion option can be linked to the performance of a bespoke basket of assets such as equity indices Consider the following hypothetical termsheet: Notional amount: Maturity: Underlying indices: Strike rate: Option payoff: $1 m 1 year S&P 500, EURO STOXX 50, Nikkei 225 0.05 as a decimal or 5 % 476  Equity Derivatives  n Si  MAX  ∑ ti − Basket average − Strike,   n i =1 S    Where : Basket average = n Sti ∑ n i =1 S0i Sti = Final level of index ’i ’ S0i = Initial level of index ’i ’ To illustrate how the option might pay off consider the following example: The steps to calculate the option payoff are: • The performance of each index was calculated over the option’s maturity (fourth column of Table 15.5) • These individual performances were then averaged to determine the ‘basket average’ (bottom figure of column four of Table 15.5) • The absolute value of each index performance was then calculated with respect to the ‘basket average’ (5th column of Table 15.5) • These absolute values were then averaged (bottom of 5th column of Table 15.5) and compared to the strike rate to determine the option’s payoff The payoff of the option is therefore: $1, 000, 000 × MAX ( 0.08 − 0.05,0 ) = $30, 000 To get a sense of how the option’s payoff will vary consider Table 15.6, which takes the same initial values but a different set of final values, which are more dispersed Table 15.5  Calculation of dispersion option payoff Index Initial level S&P 500 EUROSTOXX 50 Nikkei 225 2000 3000 16,000 Final level Performance Absolute value of difference 1800 3150 17,600 Basket average = 0.9 1.05 1.10 1.02 0.9−1.02 = 0.12 1.05−1.02 = 0.03 1.10−1.02 = 0.08 0.08 15  Trading Correlation  477 Table 15.6  Calculation of option payoff in a ‘high’ dispersion scenario Index Initial level S&P 500 EUROSTOXX 50 Nikkei 225 2000 3000 16,000 Final level Performance Absolute value of difference 1600 3200 19,200 Basket average = 0.8 1.07 1.20 1.02 0.8−1.02 = 0.22 1.07−1.02 = 0.05 1.20−1.02 = 0.18 0.15 In Table 15.6 although the ‘basket average’ is about the same as the first example,5 the dispersion of values is greater The payoff of the option is therefore: $1, 000, 000 × MAX ( 0.15 − 0.05,0 ) = $100, 000 So the key features of the dispersion option as shown here are as follows: • The payoff will increase if realized correlation between the components falls (i.e if dispersion increases) • If implied volatilities are high this increases the possibility that the future realized performance will be more dispersed 15.5 Summary Chapter looked at the characteristics and calculation of correlation and covariance Chapter analysed the mechanics of a number of correlation-­ dependent structures such as basket options This chapter argued that correlation risk was a consequence of the investment banking business model The main focus of this chapter was the different ways in which correlation and covariance could be hedged and traded The products considered were as follows: • • • • • Correlation swaps Basket calls versus a basket of calls Covariance swaps Dispersion trading using variance swaps Dispersion options  The results are not strictly speaking the exactly same as the average has been rounded to two decimal places Bibliography Allen, P., Einchcomb, S., & Granger, N (2006) Variance swaps JP Morgan research Bank for International Settlements (BIS) (2013) – Triennial Central Bank survey Barclays Capital (2007) Investing in dividend yield Barclays Bank research Barclays Capital (2010) Dividend swaps and futures Barclays Bank research Barclays Capital (2016) Equity Gilt Study Barclays Bank research Barclays Capital (2011) Index dividend options primer Barclays Bank research Barclays Capital (2012) GAAP matter 2012 Barclays Bank research Bennett, C., & Gil, M (2012) Volatility trading Santander Blake, D (1990) Financial Market Analysis McGraw Hill BNP Paribas (2007) Corridor variance swaps BNP Paribas research BNP Paribas (2005) Volatility investing handbook BNP Paribas research Bossu, S., Strasser, E., & Guichard, R (2005) Just what you need to know about variance swaps JP Morgan research Bouzoubaa, M., & Osseiran, A (2010) Exotic options and hybrids Wiley Brask, A (2004) Variance swap primer Barclays Capital Research Brask, A (2005) Forward variance swap primer Barclays Capital Research Brask, A., Baror, E., Deb, A., & Tang, M (2007) Relative value vehicles and drivers Barclays Capital Citigroup (2008) A jargon-busting guide to volatility surfaces and changes in implied volatility Equity derivatives research Combescot, P (2013) Recent changes in equity financing Presentation to the Society of Actuaries De Weert, F (2006) An introduction to options trading Wiley De Weert, F (2008) Exotic option trading Wiley Deb, A., & Brask, A (2009) Demystifying volatility skew Barclays Capital Demeterfi, K., Derman, E., Kamal, M., & Zou, J (1999) More than you ever wanted to know about volatility swaps Goldman Sachs research © The Author(s) 2017 N Schofield, Equity Derivatives, DOI 10.1057/978-0-230-39107-9 479 480 Bibliography Derman, E (1992) Outperformance options Goldman Sachs Galitz, L (2013) Handbook of financial engineering third edition FT publishing Gray, G., Cusatis, P.J., & Woolridge, J.R (2004) Streetsmart guide to valuing a stock Second edition, McGraw Hill Granger, N., & Allen, P (2005) Correlation vehicles 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(2000) Assessing a fair level for implied volatility Goldman Sachs Risk Magazine (2011) Dispersion tactics Structured products, January Risk Magazine (2013) Inventory pressures August Risk Magazine (2015a) Autocallable issuance upsets Euro Stoxx volatility market August Risk Magazine (2015b) Korean crunch: how HSCEI fall hammered exotics desks November Risk Magazine (2015a) Autocallable issuance upsets Euro Stoxx volatility market August Risk Magazine (2016a) Dealers fear death of dividend risk premia strategy Risk Magazine (2016b) Sliding HSCIE threatens fresh autocallable losses Schofield, N.C (2008) Commodity derivatives Wiley Finance Series Schofield, N.C., & Bowler, T (2011) Trading, the fixed income, inflation and credit markets: a relative value guide Wiley Finance Series Simmons, M (2002) Securities Operations Wiley Finance Series Tompkins, R (1994) Options explained2 Palgrave Macmillan UBS (1999) Options: the fundamentals UBS Vasan, P (1998) Foreign exchange options Credit Suisse First Boston Vause (2005) Guide to analysing companies The Economist Viebig, Poddig, & Varmaz (2008) Equity valuation: models from leading investment banks Wiley Finance Series Watsham, T.J., & Parramore, K (1997) Quantitative methods in finance Thomson Index A adjustment ratio, 36, 37, 39, 42 American, 20, 40, 101, 103, 143, 235–8, 241, 242, 246 amortisation, 71 asset conversion cycle, 49, 58 assets, 2, 27–9, 46–8, 51, 55, 58, 59, 64–6, 80, 90, 143, 144, 149, 150, 202, 247, 248, 250–2, 254, 257–63, 276, 285, 291, 292, 340–3, 345, 346, 355, 360, 367, 368, 405, 463, 466, 468, 469, 475 at-the-money, 21 autocallable, 296, 359–63, 369, 371, 373–7, 386, 390 B the balance sheet, 2, 40, 42, 46–9, 51, 52, 69, 80, 292 barrier options, 23, 102, 203, 204, 206–8, 213, 225, 226, 234, 235, 237, 246, 321, 352, 357, 361, 425, 426 basket option, 33, 247–9, 251, 367, 368, 463, 466–8 bear spread, 330, 420 best of options, 20, 253–7, 269, 290, 291, 464 beta, 62, 271, 276–8 binary option, 24, 203–6, 370 Black Scholes Merton (BSM), 90, 95, 111, 113, 114, 124, 127–9, 139, 156, 161, 251, 350, 397, 401, 418 bonus issues, 12, 35, 36 BSM See Black Scholes Merton (BSM) bull spread, 329, 404, 419 C calendar spread, 281, 424 call option, 20, 22, 23, 37, 91–3, 95–7, 101, 102, 105–12, 122–7, 133, 135–7, 157, 159, 161, 162, 204–22, 225, 227, 229–35, 238, 241, 243–5, 248, 256–8, 259, 264–8, 270, 296, 319–22, 326–30, 332, 335–9, 341, 343, Note: Page numbers followed by ‘n’ denote notes © The Author(s) 2017 N Schofield, Equity Derivatives, DOI 10.1057/978-0-230-39107-9 481 482  Index 344, 347, 349–54, 365, 366, 368–70, 386, 397, 424–6, 438, 459, 466 call spread, 307, 328–33, 339, 369–71, 404 Capital Asset Pricing Model (CAPM), 57, 61, 277 capital structure, 2, 65, 68, 71, 415 cash and carry arbitrage, 73, 76, 103 cash flow statement, 47, 52, 53 cash-settled, 16, 17, 23, 247, 305, 338, 387, 401 collar, 162, 168, 308, 319–22, 325, 419, 420 collateral, 11, 13–15, 17, 89, 292, 299–301, 303, 307 comparable analysis, 45, 54, 64, 72 composite option, 264–9 conditional variance swap, 452–4, 457 contracts for difference, 287, 308 convertible bond, 12, 32, 66, 146, 223n5, 293 convertible bond arbitrage, 12 corporate actions, 12, 35–43, 312, 389 correlation, 19, 33, 138, 143–202, 247–70, 275, 341, 346, 348, 353, 367, 368, 374, 380, 387, 414, 461–77 correlation coefficient, 143, 144, 201, 461 correlation proxy, 148, 461, 473 correlation skew, 185 correlation swap, 19, 464–5, 472, 477 correlation vega, 252 corridor variance swap, 454–7 cost of carry, 74, 81, 100, 101, 138 covariance, 139, 143–5, 199, 201, 461, 468–70, 477 covariance swap, 468, 470, 477 covered call, 337–9 cum-entitlement, 36, 37 cumulative preference shares, D delta, 80, 105–20, 136, 138, 148, 159–61, 164, 174, 181–3, 189, 193, 210–11, 213, 216–19, 221–9, 231, 235, 238–9, 241–3, 256, 257, 279, 296, 311, 312, 327, 331–7, 340–4, 354, 359, 366, 371, 373, 377, 415, 416, 418, 419, 434, 466 delta bleed, 109 delta cash, 119, 120, 311 delta equivalent value, 107, 311, 442n7 delta one, 80, 231 depreciation, 51, 52, 58, 59, 71, 264–7, 294, 304, 309 digital options, 361, 363, 369, 377, 425 discount factor, 54, 86, 87 dispersion, 29, 33, 92, 139, 149, 199, 253, 348, 414, 458, 471–7 dispersion options, 475, 477 dividend discount model, 54–7 dividend futures, 271, 374, 386, 387, 390, 398–401, 403–8, 411, 414 dividend options, 399–401, 404 dividend per share, 5, 69, 390, 398 dividends, 2, 5, 12–13, 19, 20, 33, 39, 42, 48, 52–7, 61, 66, 69, 77, 79, 81–3, 85, 86, 88, 122, 124, 147n4, 272, 274, 275, 284, 288, 293, 294, 298, 302–11, 323, 343, 354, 373, 381, 385–416 dividend swaps, 19, 348, 387, 390, 391, 394–6, 389, 407, 413 dividend yields, 68, 69, 74, 76–9, 81, 87, 91, 95, 100–3, 105, 108, 123–6, 138, 248, 251n1, 257, 258, 263, 264, 266, 269, 271–3, 274, 279, 284, 306, 322, 327, 341, 349, 352, 354, 355, 358, 373, 397, 402, 411–13, 466  Index     dollar value of an 01, 88 Dow Jones Industrial Average, 3, 272 down and in, 24, 204–6, 209–12, 223–30, 357, 359, 362, 363, 365, 366, 369, 371, 372, 374, 377, 380, 386 down and out, 24, 204, 205, 213–15, 223, 225, 230–3, 321, 365, 366 E earnings per share, 6, 66–7 effective date, 85, 279 enterprise value, 64, 70, 71 equity index, 3, 4, 6, 31, 81, 131, 132, 143, 158, 187, 283, 287, 290, 299n6, 385, 387, 403, 429, 442, 463, 474 equity repo, 10–16, 74, 76–9, 83–6, 100, 102, 271–4, 195, 279, 284–9, 313, 373, 381, 396, 402, 411 equity swaps, 19, 83–5, 88, 90, 103, 287–313, 386 EURIBOR, 79, 293, 299–301 European, 21, 23, 91, 95, 101, 105, 122–4, 203, 205–7, 209, 211, 215, 220, 227–30, 234–7, 241–6, 256, 316, 350, 359, 373, 401, 408, 429, 430, 459 EURO STOXX, 50, 79, 281, 316, 375–80, 387, 388, 390, 399, 407, 448–51, 464, 465, 469, 470, 472–5 Exchange Delivery Settlement Price (EDSP), 19, 275 exchange for physical (EFP), 283, 411 exchange option, 260, 261 exchange traded fund, 29, 283, 295 ex-entitlement, 36, 37, 40 exercise price, 21, 36, 430 exotic option, 23, 79, 203, 279, 296 483 F fair value, 29, 38, 45, 55, 56, 77, 79, 80, 82, 87, 90, 95, 139, 190, 191, 196, 274, 275, 280, 289, 291, 317n1, 337, 356, 398, 402, 405–6, 413, 415, 436, 463 Fed Fund rate, 299 floor, 45, 290, 322, 323, 325, 326 forward transaction, 16, 20, 305, 324 forward variance swap, 451, 452 forward yields, 86 free cash flow, 57–60, 70 free float, 3, 388, 389, 398 FTSE, 3, 5, 17, 18, 76, 85, 100, 199–202, 247, 271, 274, 279–81, 288, 290, 291, 405 futures transaction, 16 G gamma, 41, 110–13, 117–21, 133, 148, 161, 181, 193, 210, 211, 213, 214, 217, 219, 220, 228, 229, 231, 232, 235, 239, 242, 243, 311, 312, 418, 431, 438–44, 457, 458 gamma cash, 119–21 gamma swap, 457, 458 Gordon growth model, 55 the Greeks, 105, 213, 256n3 H headline vega, 175, 177 hedge, 11, 12, 18, 29, 31, 32, 45, 74, 75, 79–83, 88, 90, 99–101, 103, 108, 109, 115, 116, 118, 136, 147, 148, 161, 181–2, 193, 222–6, 246–8, 276, 278, 279, 283–5, 289, 291–2, 302, 304, 307, 308, 310–12, 359, 370, 371, 376, 377, 380, 386, 387, 484  Index 395, 413, 417, 429, 433, 438, 439, 448, 458, 460, 463, 464, 467, 469, 472, 474, 475 hedge fund, 12, 18, 29, 32, 464, 469, 474 I implied equity repo rate, 284, 285, 295, 373 implied volatility, 91, 93–6, 98, 99, 108–11, 113, 114, 117, 118, 121, 122, 126–30, 132, 133, 135, 136, 138, 141, 143, 147–8, 147, 161–3, 166, 167, 171–88, 191, 197–9, 202, 207, 211, 213, 215–17, 223, 230, 234, 245, 246, 252, 253, 316–18, 320, 322, 327, 331–4, 341–4, 346, 349, 354, 358–71, 374, 375, 385, 397–403, 417–19, 424–9, 434, 435, 437, 441, 444, 460, 461, 472–4 the income statement, 47, 50–2, 58 index arbitrage, 12, 271, 274, 285, 415, 463 index dividend amount, 388, 389 index dividend point, 387–9, 410 index divisor, 4, 389, 393, 398 index futures, 12, 17, 18, 73, 78, 80, 83, 90, 271, 273, 276, 279–81, 316, 373, 377, 387, 390, 412–14, 463 index multiplier, 18, 276, 280, 414 initial margin, 18, 19, 292, 300, 310 in-the-money, 21 intrinsic value, 95, 96, 98, 99, 101, 121, 123–5, 215, 217, 221 investment trust, 29 K knock ins, 23, 225 knock outs, 23, 225 L leverage, 18, 29, 65, 80, 310, 331, 332 liabilities, 2, 26–8, 46–8, 54, 58, 348 LIBOR, 20, 74–6, 78, 79, 82–100, 103, 264, 274, 284, 287–90, 292, 294–304, 307, 309–11, 355, 386, 396, 411–13 lognormal distribution, 141, 161 M margin ratios, 66 market capitalisation, 64 mean reversion, 162, 190, 195, 460 merger, 5, 12, 37 merger arbitrage, 12 monetization, 307–8 Monte Carlo simulation, 347 mutual fund, 26–9, 32 N net carry, 74, 92, 101, 108, 271, 279, 402, 424 net debt, 60, 64, 71 no arbitrage, 73, 76–8, 83, 84, 121, 142, 234, 297, 305, 306, 373, 396, 428, 451, 463 normal distributions, 140 notional, 85, 87, 102, 108, 206, 223, 234, 254, 259, 263, 288–90, 298, 302, 311, 329, 331, 334, 336–9, 342, 344–6, 362, 364, 371, 381, 391, 393, 394, 409–14, 431–4, 442–3, 451–3, 459, 464, 467, 468, 470, 472–5 no touch, 25, 236, 237, 425, 426 novation, 395 O operating profit, 50–2, 58, 59, 66 option ratios, 331  Index     options, 20–4, 33, 39–41, 73, 90, 91, 94–6, 98–103, 105–41, 139, 146, 147, 157, 158, 160, 161, 166–8, 172, 175, 181, 191–5, 203–70, 191, 280, 290, 296, 315–46, 252, 351, 361–9, 376–81, 386, 387, 397, 399, 404, 419, 426–31, 438–42, 450, 467, 468, 472, 475, 477 options on realized variance, 459, 460 ordinary shares, 2, 39, 41, 48 out-of-the money, 21 outperformance option, 257–60, 291, 346 overnight index swap, 62, 89–90 P pairs trading, 11, 313 pairwise correlation, 148, 471 participation rate, 348–54, 367, 381–3 payer, 288, 290, 391, 393–5, 454 pension funds, 11, 27–8, 32 P/E to growth (PEG) ratio, 69–70 physically-settled, 16, 17, 22, 356 preferred shares, premium, 20, 21, 23, 29, 45, 62, 63, 91, 92, 94–102, 105–7, 109–10, 113, 116, 119, 121, 122, 126, 127, 135, 150, 157, 162, 168, 185, 193, 194, 206–9, 215, 216, 219, 225, 227, 231, 233–4, 236–8, 241, 250–3, 256–8, 262, 263, 316–32, 334–40, 342–4, 350, 351, 354, 356, 357, 359, 362, 371, 374, 379, 381, 397, 401, 415, 422–4, 430, 438, 444, 459, 466–8 prepaid forward, 305, 306 price / book value, 69–70 price-earnings, 7, 67, 68 price return, 5, 19, 81, 82, 85, 287, 305, 307, 358 485 prime broker, 18 psi, 125, 126, 138 pull to realized, 398 put-call parity, 102–3, 157 put option, 21, 22, 33, 91, 96, 99–102, 107, 110, 125–6, 137, 157, 162, 223–5, 237–54, 296, 316–19, 321, 323, 326, 329, 340, 341, 344, 355, 356, 359, 361–3, 365, 366, 369, 371, 372, 374, 375, 377, 386, 404, 425, 426, 459, 460 put spread, 318, 330 Q quanto option, 264–7, 269, 270 R realized correlation, 117, 391, 398 realized volatility, 113, 117, 118, 142, 152–5, 187, 190, 193–5, 334, 335, 366, 418, 429, 431–4, 438, 440–6, 452–9, 470, 475 receiver, 288, 391 regression analysis, 177 relative value, 385, 404–16, 451, 471 repurchase agreement, 14 required return on equity, 55 return of capital, 40 return on equity, 55, 65 reverse convertible, 33, 223n5, 355–9 reverse stock splits, 35, 36 rho, 125, 126, 138, 355, 359 rights issues, 9, 35–7, 41 risk premium, 62, 150, 444 risk reversal, 343–6, 376, 377, 420, 421 roll down, 446 rolling futures, 408 486  Index S sales, general and administrative expenses, 49 share price dilution, 8–10 short selling, 11, 108, 123, 344 skew, 129, 156–68, 172, 175, 185, 341, 343–5, 376, 402, 404, 419–21, 426, 436, 460 smile, 129, 130, 157, 159, 423 S&P 500, 17, 72, 129, 131–4, 145, 151, 155, 158, 163–4, 169–74, 175–80, 183–202, 276, 279–83, 290, 291, 295, 348, 349, 364, 367, 405, 426, 428–30, 432, 437, 439, 446–8, 463, 472, 475–7 special dividends, 12, 39, 388n1 specialness, 15 spin-off, 40 spot price, 16, 17, 30, 74, 75, 77, 78, 81, 91, 92, 94–6, 99, 100, 103, 105, 107, 109, 111, 114, 129, 133, 135, 136, 138, 141, 156, 158, 161, 182, 203–11, 213, 215–21, 223, 396, 401, 411, 418, 425, 426, 438, 440, 451 spread option, 260 standard deviation, 92, 94, 128, 140, 141, 199, 200, 202, 417, 432n3 statement of changes in shareholders’ equity, 47 sticky strike, 180, 181 stock lending, 10–16, 275 stock splits, 35, 36, 41, 312 straddle, 333–5, 337, 363, 422, 423, 460 strangle, 335–7, 422, 423 strike pinning, 180–2 strike rate, 21, 37, 39, 102, 110, 212, 236, 267, 341, 350, 354, 475, 476 T terminal value, 60, 61 term structure, 129, 146, 168–75, 185, 188, 189, 195, 196, 281, 282, 295–7, 299, 313, 369, 376, 386, 390, 399, 403, 406, 408, 409, 418, 422–4, 429, 446, 448, 460 theoretical ex-rights price, theta, 118, 119, 121–5, 138, 211–14, 217, 218, 220, 221, 229, 231–3, 235, 239, 240, 244, 257, 258, 263, 272, 335, 438, 441 time value, 95, 96, 99, 101, 121, 124, 125, 127, 216 total return, 5–7, 19, 31, 78, 80–3, 88, 90, 288, 290, 293, 295–7, 300, 302, 303, 305, 307, 374, 396, 397 total return swaps, 80, 88, 302, 374 Treasury stock, 2, 48 U unit trust, 11, 26, 28, 29, 32 up and in, 24, 204, 216–18, 225, 351, 352 up and out, 24, 204, 217, 219–20, 225, 235, 238, 351, 352, 361–3 V vanna, 136–8, 374, 376 variance, 139–40, 144, 164, 199–201, 251, 431–8, 443–6, 451–4, 459, 469, 472, 474 variance swaps, 1, 19, 164, 199, 382, 431, 433, 434, 438, 441, 442, 444, 446, 448, 451–2, 457, 465, 468–4, 477 variation margin, 18 vega, 117–19, 126–8, 133, 135–8, 148, 175–8, 193, 211, 221, 229, 230, 233, 240, 244, 245, 252, 257, 327, 331, 332, 354, 359, 366, 371, 372, 374–6, 417, 418, 429, 431–6, 444, 445, 451, 453, 454, 459, 467, 473, 474  Index     vega notional, 431–4, 442, 451, 455, 459, 473 the VIX®, 429 volatility, 105, 128, 131, 133, 134, 138–202, 208, 263, 335, 342, 343, 363, 402, 405, 417–60, 462, 469, 472, 474 volatility cone, 193, 196 volatility matrix, 129, 134 volatility regimes, 180–2 volatility surface, 129, 133, 156, 172, 180, 196, 418 volatility swap, 431–6, 460, 472 volatility units, 431–3, 442, 459, 474 volgamma, 133–5, 138 Volume-Weighted Average Price (VWAP), 7–8 487 W weighted average cost of capital, 60–3 weighted vega, 175, 177 whippy spot, 180, 182 withholding tax, 80–1, 86, 271–3, 276, 284, 293 working capital, 49, 58, 59, 70 worst of options, 256 Y yield enhancement, 33, 256, 296, 315, 337–40, 376, 404, 462 Z zero coupon yields, 86 zero premium strategies, 185 .. .Equity Derivatives www.allitebooks.com Neil C Schofield Equity Derivatives Corporate and Institutional Applications www.allitebooks.com Neil C Schofield... Contents   Equity Derivatives: The Fundamentals1   Corporate Actions35   Equity Valuation45   Valuation of Equity Derivatives 73   Risk Management of Vanilla Equity Options105   Volatility and Correlation139... Correlation139   Barrier and Binary Options203   Correlation-Dependent Exotic Options247   Equity Forwards and Futures271 10 Equity Swaps287 11 Investor Applications of Equity Options315 vii