实用金融期权估值导论(英文影印版)

.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　29
4　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 walkthrough　83
9　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　risk neutrality　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
13.6　notes and references　127
13.7　program of chapter 13 and walkthrough　128
14　implied volatility　131
14.1　motivation　131
14.2　implied volatility　131
14.3　option value as a function of volatility　131
14.4　bisection and newton　133
14.5　implied volatility with real data　135
14.6　notes and references　137
14.7　program of chapter 14 and walkthrough　137
15　monte carlo method　141
15.1　motivation　141
15.2　monte carlo　141
15.3　monte carlo for option valuation　144
15.4　monte carlo for greeks　145
15.5　notes and references　148
15.6　program of chapter 15 and walkthrough　149
16　binomial method　151
16.1　motivation　151
16.2　method　151
16.3　deriving the parameters　153
16.4　binomial method in practice　154
16.5　notes and references　156
16.6　program of chapter 16 and walkthrough　159
17　cash-or-nothing options　163
17.1　motivation　163
17.2　cash-or-nothing options　163
17.3　black-scholes for cash-or-nothing options　164
17.4　delta behaviour　166
17.5　risk neutrality for cash-or-nothing options　167
17.6　notes and references　168
17.7　program of chapter 17 and walkthrough　170
18　american options　173
18.1　motivation　173
18.2　american call and put　173
18.3　black-scholes for american options　174
18.4　binomial method for an american put　176
18.5　optimal exercise boundary　177
18.6　monte carlo for an american put　180
18.7　notes and references　182
18.8　program of chapter 18 and walkthrough　183
19　exotic options　187
19.1　motivation　187
19.2　barrier options　187
19.3　lookback options　191
19.4　asian options　192
19.5　bermudan and shout options　193
19.6　monte carlo and binomial for exotics　194
19.7　notes and references　196
19.8　program of chapter 19 and walkthrough　199
20　historical volatility　203
20.1　motivation　203
20.2　monte carlo-type estimates　203
20.3　accuracy of the sample variance estimate　204
20.4　maximum likelihood estimate　206
20.5　other volatility estimates　207
20.6　example with real data　208
20.7　notes and references　209
20.8　program of chapter 20 and walkthrough　210
21　monte carlo part ii: variance reduction by antithetic variates　215
21.1　motivation　215
21.2　the big picture　215
21.3　dependence　216
21.4　antithetic variates: uniform example　217
21.5　analysis of the uniform case　219
21.6　normal case　221
21.7　multivariate case　222
21.8　antithetic variates in option valuation　222
21.9　notes and references　225
21.10　program of chapter 21 and walkthrough　225
22　monte carlo part iii: variance reduction by control variates　229
22.1　motivation　229
22.2　control variates　229
22.3　control variates in option valuation　231
22.4　notes and references　232
22.5　program of chapter 22 and walkthrough　234
23　finite difference methods　237
23.1　motivation　237
23.2　finite difference operators　237
23.3　heat equation　238
23.4　discretization　239
23.5　ftcs and btcs　240
23.6　local accuracy　246
23.7　von neumann stability and convergence　247
23.8　crank-nicolson　249
23.9　notes and references　251
23.10　program of chapter 23 and walkthrough　252
24　finite difference methods for the black-scholes pde　257
24.1　motivation　257
24.2　ftcs, btcs and crank-nicolson for black-scholes　257
24.3　down-and-out call example　260
24.4　binomial method as finite differences　261
24.5　notes and references　262
24.6　program of chapter 24 and walkthrough　265
references　267
index ...　271