List of illustrations page xiii
Preface xvii
1 Options 1
1.1 What are options? 1
1.2 Whydo we studyoptions? 2
1.3 How are options traded? 4
1.4 Typical option prices 6
1.5 Other financial derivatives 7
1.6 Notes and references 7
1.7 Program of Chapter 1 and walkthrough 8
2 Option valuation preliminaries 11
2.1 Motivation 11
2.2 Interest rates 11
2.3 Short selling 12
2.4 Arbitrage 13
2.5 Put–callparity 13
2.6 Upper and lower bounds on option values 14
2.7 Notes and references 16
2.8 Program of Chapter 2 and walkthrough 17
3 Random variables 21
3.1 Motivation 21
3.2 Random variables, probabilityand mean 21
3.3 Independence 23
3.4 Variance 24
3.5 Normal distribution 25
3.6 Central Limit Theorem 27
3.7 Notes and references 28
3.8 Program of Chapter 3 and walkthrough 294 Computer simulation 33
4.1 Motivation 33
4.2 Pseudo-random numbers 33
4.3 Statistical tests 34
4.4 Notes and references 40
4.5 Program of Chapter 4 and walkthrough 41
5 Asset price movement 45
5.1 Motivation 45
5.2 Efficient market hypothesis 45
5.3 Asset price data 46
5.4 Assumptions 48
5.5 Notes and references 49
5.6 Program of Chapter 5 and walkthrough 50
6 Asset price model: Part I 53
6.1 Motivation 53
6.2 Discrete asset model 53
6.3 Continuous asset model 55
6.4 Lognormal distribution 56
6.5 Features of the asset model 57
6.6 Notes and references 59
6.7 Program of Chapter 6 and walkthrough 60
7 Asset price model: Part II 63
7.1 Computing asset paths 63
7.2 Timescale invariance 66
7.3 Sum-of-square returns 68
7.4 Notes and references 69
7.5 Program of Chapter 7 and walkthrough 71
8 Black–Scholes PDE and formulas 73
8.1 Motivation 73
8.2 Sum-of-square increments for asset price 74
8.3 Hedging 76
8.4 Black–Scholes PDE 78
8.5 Black–Scholes formulas 80
8.6 Notes and references 82
8.7 Program of Chapter 8 and walkthrough9 More on hedging 87
9.1 Motivation 87
9.2 Discrete hedging 87
9.3 Delta at expiry 89
9.4 Large-scale test 92
9.5 Long-Term Capital Management 93
9.6 Notes 94
9.7 Program of Chapter 9 and walkthrough 96
10 The Greeks 99
10.1 Motivation 99
10.2 The Greeks 99
10.3 Interpreting the Greeks 101
10.4 Black–Scholes PDE solution 101
10.5 Notes and references 102
10.6 Program of Chapter 10 and walkthrough 104
11 More on the Black–Scholes formulas 105
11.1 Motivation 105
11.2 Where is μ? 105
11.3 Time dependency 106
11.4 The big picture 106
11.5 Change of variables 108
11.6 Notes and references 111
11.7 Program of Chapter 11 and walkthrough 111
12 Risk neutrality 115
12.1 Motivation 115
12.2 Expected payoff 115
12.3 Riskneutrality 116
12.4 Notes and references 118
12.5 Program of Chapter 12 and walkthrough 120
13 Solving a nonlinear equation 123
13.1 Motivation 123
13.2 General problem 123
13.3 Bisection 123
13.4 Newton 124
13.5 Further practical issues 127...............