Arbitrage Theory in Continuous Time

✍ Scribed by Tomas Björk

• Publisher: Oxford University Press, USA
• Year: 1999
• Tongue: English
• Leaves: 324
• Edition: 0
• Category: Library

✦ Synopsis

Combining sound mathematical principles with the necessary economic focus, Arbitrage Theory in Continuous Time is specifically designed for graduate students, and includes solved examples for every new technique presented, numerous exercises, and recommended reading lists for each chapter.

✦ Table of Contents

0198775180......Page 1
Contents......Page 9
1.1 Problem Formulation......Page 14
2.1.1 Model Description......Page 19
2.1.2 Portfolios and Arbitrage......Page 20
2.1.3 Contingent Claims......Page 23
2.1.4 Risk Neutral Valuation......Page 25
2.2.1 Portfolios and Arbitrage......Page 28
2.2.2 Contingent Claims......Page 31
2.4 Notes......Page 39
3.1 Introduction......Page 40
3.2 Information......Page 42
3.3 Stochastic Integrals......Page 43
3.4 Martingales......Page 46
3.5 Stochastic Calculus and the Itö Formula......Page 48
3.6 Examples......Page 53
3.7 The Multidimensional Itö Formula......Page 56
3.8 Correlated Wiener Processes......Page 58
3.9 Exercises......Page 62
3.10 Notes......Page 64
4.1 Stochastic Differential Equations......Page 65
4.2 Geometric Brownian Motion......Page 66
4.3 The Linear SDE......Page 69
4.4 The Infinitesimal Operator......Page 70
4.5 Partial Differential Equations......Page 71
4.6 The Kolmogorov Equations......Page 75
4.7 Exercises......Page 77
4.8 Notes......Page 81
5.1 Introduction......Page 82
5.2 Self-financing Portfolios......Page 85
5.3 Dividends......Page 87
5.4 Exercises......Page 88
6.1 Introduction......Page 89
6.2 Contingent Claims and Arbitrage......Page 90
6.3 The Black-Scholes Equation......Page 95
6.4 Risk Neutral Valuation......Page 98
6.5 The Black-Scholes Formula......Page 100
6.6.1 Forward Contracts......Page 103
6.6.2 Futures Contracts and the Black Formula......Page 104
6.7 Volatility......Page 105
6.7.1 Historic Volatility......Page 106
6.8 American options......Page 107
6.9 Exercises......Page 109
6.10 Notes......Page 111
7.1 Introduction......Page 112
7.2 Completeness in the Black-Scholes Model......Page 113
7.3 Completeness--Absence of Arbitrage......Page 118
7.4 Exercises......Page 119
7.5 Notes......Page 120
8.1 ParityRelations......Page 121
8.2 The Greeks......Page 123
8.3 Delta and Gamma Hedging......Page 126
8.4 Exercises......Page 130
9.1 Introduction......Page 132
9.2 Pricing......Page 134
9.3 Risk Neutral Valuation......Page 139
9.4 Reducing the State Space......Page 140
9.5 Hedging......Page 144
9.6 Exercises......Page 147
10.2 A Scalar Nonpriced Underlying Asset......Page 148
10.3 The Multidimensional Case......Page 157
10.4 A Stochastic Rate of Interest......Page 161
10.5 Summing Up......Page 162
10.6 Exercises......Page 165
11.1.1 Price Dynamics and Dividend Structure......Page 167
11.1.2 Pricing Contingent Claims......Page 168
11.2.1 Continuous Dividend Yield......Page 173
11.2.2 The General Case......Page 176
11.3 Exercises......Page 178
12.1 Pure Currency Contracts......Page 180
12.2 Domestic and Foreign Equity Markets......Page 183
12.3 Domestic and Foreign Market Prices of Risk......Page 188
12.4 Exercises......Page 193
12.5 Notes......Page 194
13.1 Mathematical Background......Page 195
13.2 Out Contracts......Page 196
13.2.1 Down-and-out Contracts......Page 197
13.2.2 Up-and-out Contracts......Page 200
13.2.3 Examples......Page 201
13.3 In Contracts......Page 205
13.4 Ladders......Page 207
13.5 Lookbacks......Page 208
13.7 Notes......Page 210
14.1 An Example......Page 211
14.2 The Formal Problem......Page 212
14.3 The Hamilton-Jacobi-Bellman Equation......Page 215
14.4 Handling the HJB Equation......Page 222
14.5 The Linear Regulator......Page 223
14.6.1 A Generalization......Page 226
14.6.2 Optimal Consumption......Page 227
14.7.1 The Case with No Risk Free Asset......Page 230
14.7.2 The Case with a Risk Free Asset......Page 234
14.8 Exercises......Page 236
14.9 Notes......Page 240
15.1 Zero Coupon Bonds......Page 241
15.2.1 Definitions......Page 242
15.2.2 Relations between df(t, T), dp(t, T) and dr(t)......Page 244
15.2.3 An Alternative View of the Money Account......Page 247
15.3 Coupon Bonds, Swaps and Yields......Page 248
15.3.2 Floating Rate Bonds......Page 249
15.3.3 Interest Rate Swaps......Page 251
15.3.4 Yield and Duration......Page 252
15.4 Exercises......Page 253
15.5 Notes......Page 254
16.1 Generalities......Page 255
16.2 The Term Structure Equation......Page 258
16.3 Exercises......Page 263
16.4 Notes......Page 264
17.1 Q-dynamics......Page 265
17.2 Inversion of the Yield Curve......Page 266
17.3.1 Definition and Existence......Page 268
17.3.2 A Probabilistic Discussion......Page 270
17.4.1 The Vasiček Model......Page 272
17.4.2 The Ho-Lee Model......Page 273
17.4.4 The Hull-White Model......Page 274
17.5 Exercises......Page 277
17.6 Notes......Page 278
18.1 The Heath-Jarrow-Morton Framework......Page 279
18.2 Martingale Modeling......Page 281
18.3 The Musiela Parameterization......Page 283
18.4 Exercises......Page 284
18.5 Notes......Page 286
19.1 Introduction......Page 287
19.2 The Normalized Economy......Page 289
19.3 Pricing......Page 294
19.4.1 Using the T-bond as Numeraire......Page 298
19.4.2 An Expectation Hypothesis......Page 299
19.5 A General Option Pricing Formula......Page 301
19.6 The Hull-White Model......Page 304
19.7 The General Gaussian Model......Page 306
19.8 Caps and Floors......Page 307
19.9 Exercises......Page 308
19.10 Notes......Page 309
20.1 Forward Contracts......Page 310
20.2 Futures Contracts......Page 312
20.4 Notes......Page 315
References......Page 316
D......Page 321
I......Page 322
O......Page 323
Y......Page 324