An Introduction to Options Trading

Preface xiii Acknowledgements xv Introduction xvii 1 OPTIONS 1 1.1 Examples 3 1.2 American versus European options 7 1.3 Terminology 8 1.4 Early exercise of American options 13 1.5 Payoffs 15 1.6 Put call parity 16 2 THE BLACK SCHOLES FORMULA 21 2.1 Volatility and the Black Scholes formula 28 2.2 Interest rate and the Black Scholes formula 29 2.3 Pricing American options 31 3 DIVIDENDS AND THEIR EFFECT ON OPTIONS 33 3.1 Forwards 34 3.2 Pricing of stock options including dividends 35 3.3 Pricing options in terms of the forward 36 3.4 Dividend risk for options 38 3.5 Synthetics 39 4 IMPLIED VOLATILITY 41 4.1 Example 44 4.2 Strategy and implied volatility 45 5 DELTA 47 5.1 Delta-hedging 52 5.2 The most dividend-sensitive options 57 5.3 Exercise-ready American calls on dividend paying stocks 57 6 THREE OTHER GREEKS 61 6.1 Gamma 62 6.2 Theta 65 6.3 Vega 69 7 THE PROFIT OF OPTION TRADERS 73 7.1 Dynamic hedging of a long call option 74 7.1.1 Hedging dynamically every $1 75 7.1.2 Hedging dynamically every $2 76 7.2 Dynamic hedging of a short call option 77 7.2.1 Hedging dynamically every $1 78 7.2.2 Hedging dynamically every $2 79 7.3 Profit formula for dynamic hedging 80 7.3.1 Long call option 81 7.3.2 Short call option 83 7.4 The relationship between dynamic hedging and 86 7.5 The relationship between dynamic hedging and when the interest rate is strictly positive 88 7.6 Conclusion 91 8 OPTION GREEKS IN PRACTICE 93 8.1 Interaction between gamma and vega 94 8.2 The importance of the direction of the underlying share to the option Greeks 97 8.3 Pin risk for short-dated options 98 8.4 The riskiest options to go short 99 9 SKEW 101 9.1 What is skew? 102 9.2 Reasons for skew 103 9.3 Reasons for higher volatilities in falling markets 104 10 SEVERAL OPTION STRATEGIES 105 10.1 Call spread 106 10.2 Put spread 107 10.3 Collar 109 10.4 Straddle 111 10.5 Strangle 112 11 DIFFERENT OPTION STRATEGIES AND WHY INVESTORS EXECUTE THEM 117 11.1 The portfolio manager s approach to options 118 11.2 Options and corporates with cross-holdings 119 11.3 Options in the event of a takeover 120 11.4 Risk reversals for insurance companies 122 11.5 Pre-paid forwards 123 11.6 Employee incentive schemes 126 11.7 Share buy-backs 126 12 TWO EXOTIC OPTIONS 129 12.1 The quanto option 130 12.2 The composite option 135 13 REPO 137 13.1 A repo example 138 13.2 Repo in case of a takeover 139 13.3 Repo and its effect on options 140 13.4 Takeover in cash and its effect on the forward 141 Appendices A PROBABILITY THAT AN OPTION EXPIRES IN THE MONEY 143 B VARIANCE OF A COMPOSITE OPTION 145 Bibliography 149 Index 151