Table of contents for Mathematical modeling and methods of option pricing / Lishang Jiang ; translated by Canguo Li.


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1. Risk Management and Financial Derivatives                  1
1.1 Risk and Risk Management . . . . . . . . . . . . . .  .  1
1.2 Forward Contracts and Futures . . . . . . . . . . . . . ...  2
1.3  Options  .. . . . .......     . . .  . ...........    3
1.4 Option Pricing ...... . . . . . . .  .   .  .  .  .  .  .....  5
1.5 Types of Traders ...... . . . . . . .  .    .  .  .  .  .....  6
2. Arbitrage-Free Principle                                   9
2.1 Financial Market and Arbitrage-Free Principle . . . . . . .  9
2.2 European Option Pricing and Call-Put Parity . . . . . ...  13
2.3 American Option Pricing and Early Exercise . . . . . ...  15
2.4 Dependence of Option Pricing on the Strike Price .  . . . . .  19
3. Binomial Tree Methods -   Discrete Models of Option Pricing  25
3.1 An Example ....................        ... ... .   . . 25
3.2 One-Period and Two-State Model . . . . . . . . . . .....  26
3.3 Binomial Tree Method of European Option Pricing (I)
-   Non-Dividend-Paying . . . . . . . . . . . . . . . ....  32
3.4 Binomial Tree Method of European Options (II)
-     Dividend-Paying ............. .......           39
3.5 Binomial Tree Method of American Option Pricing . . . . .  42
3.6 Call-Put Symmetry ..... . . . . . . .  .  .   . . . .  .  48
4. Brownian Motion and It6 Formula                           55
4.1 Random Walk and Brownian Motion .............          55
4.2 Continuous Models of Asset Price Movement . . . . . ...  58
4.3 Quadratic Variation Theorem . . . . . . . . . . . . .....  61
4.4 Ito Integral ....... . . . . . . . . . . . . . . .....  64
4.5  It6  Formula  .................        . .....     .  66
5. European Option Pricing-  Black-Scholes Formula             73
5.1  History  ........   .  .  .........     ......     .  73
5.2 Black-Scholes Equation  . . . . . . . .  .  .  .  .....  .  74
5.3 Black-Scholes Formula . . . . . . . .  . .  .  .   . . . ..79
5.4 Generalized Black-Scholes Model (I) -- Dividend-Paying
Options  .............        ...  ..   ....  .......  82
5.5 Generalized Black-Scholes Model (II) -- Binary Options
and Compound Options . . . . . . . .  .   .  .   . . . ..88
5.6 Numerical Methods (I) -  Finite Difference Method . . .  93
5.7 Numerical Methods (II) -- Binomial Tree Method and Fi-
nite Difference Method . . . . . . . .  .  .  .   . . . ..100
5.8 Properties of European Option Price . . . . . . . . . ....  104
5.9 Risk Management . ...................... ..           107
6. American Option Pricing and Optimal Exercise Strategy      113
6.1 Perpetual American Option . . . . . . . .  .  .  .  .  .   .  113
6.2 Models of American Options . . . . . . .   .  .  .  .  .   .  124
6.3 Decomposition of American Options . . . . . . . . . ....  127
6.4 Properties of American Option Price . . . . . . . . . ....  134
6.5 Optimal Exercise Boundary . . . . . . . . . . . . . ....  146
6.6 Numerical Method (I)-  Finite Difference Method  . . . . 165
6.7 Numerical Methods(II)-  Line Method . . . . . . . . ...  178
6.8 Other Types of American Options . . . . . . . . . . .. .  189
7. Multi-Asset Option Pricing                                201
7.1 Stochastic Models of Multi-Assets Pricing . . . . . . . ...  201
7.2 Black-Scholes Equation  . . . . . . . . .  .  .  .   .  . ..203
7.3 Black-Scholes Formula . . . . . . .  .  .  .  .   . . . ..204
7.4 Rainbow Options ... . . . . . . .  .     . . . . .  . . 210
7.5 Basket Options ...... . . . . . . . .  . . . . . .....  216
7.6 Quanto Options . . . . . . . . . .......... .......   218
7.7 American Multi-Asset Options . . . . . . . . . . . ....  222
8. Path-Dependent Options (I)
--   Weakly Path-Dependent Options                      247
8.1  Barrier Options  . ..................       .   .... . .. 247
8.2 Time-Dependent Barrier Options . . . . . . . . . . . ....  255
8.3  Reset Options . .................. ..     .... .  .. 260
8.4 Modified Barrier Options ..... . . . . . . .  . . . . .....  263
9. Path-Dependent Options (II)
--   Strongly Path-Dependent Options                     275
9.1 Asian Options. .................. . . . . ....      275
9.2 Model and Simplification  . . . . . . . .  .  .  .  .  .  .   .  277
9.3 Valuation Formula for European-Style Geometric Average
Asian  Option  ..........       ......  ........  .  284
9.4 Call-Put Parities for Asian Options . . . . . . . . . . ....  288
9.5 Lookback Option . .................. ...... ..292
9.6 Numerical Methods ................... . .... .      301
10. Implied Volatility                                      311
10.1 Preliminaries .... .  ..................... ..     311
10.2 Dupire Method . ........................ ..        313
10.3 Optimal Control Method ..... . . . . . .  .  .  .  ......  . 315
10.4 Numerical Method .. ....... . . .  .     .  .  .  .. . .  320



Library of Congress subject headings for this publication: Options (Finance) Prices Mathematical models