Title Details

After his academic career he started working as trader for Barclays Capital in London. In this role he gained experience in trading many different derivative products on European and American equities. After two and half years in London, he moved to New York to start trading derivatives on both Latin American as well as US underlyings. Frans de Weert lives in New York city.

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 Θ 86

7.5 The relationship between dynamic hedging and Θ 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