영문목차
Preface=xvii
Ⅰ. THE SETTING:MARKETS, MODELS, INTEREST RATES, UTILITY MAXIMIZATION, RISK=1
1. Financial Markets=3
1.1. Bonds=3
1.1.1. Types of Bonds=5
1.1.2. Reasons for Trading Bonds=5
1.1.3. Risk of Trading Bonds=6
1.2. Stocks=7
1.2.1. How Are Stocks Different from Bonds?=8
1.2.2. Going Long or Short=9
1.3. Derivatives=9
1.3.1. Futures and Forwards=10
1.3.2. Marking to Market=11
1.3.3. Reasons for Trading Futures=12
1.3.4. Options=13
1.3.5. Calls and Puts=13
1.3.6. Option Prices=15
1.3.7. Reasons for Trading Options=16
1.3.8. Swaps=17
1.3.9. Mortgage-Backed Securities;Callable Bonds=19
1.4. Organization of Financial Markets=20
1.4.1. Exchanges=20
1.4.2. Market Indexes=21
1.5. Margins=22
1.5.1. Trades That Involve Margin Requirements=23
1.6. Transaction Costs=24
Summary=25
Problems=26
Further Readings=29
2. Interest Rates=31
2.1. Computation of Interest Rates=31
2.1.1. Simple versus Compound Interest;Annualized Rates=32
2.1.2. Continuous Interest=34
2.2. Present Value=35
2.2.1. Present and Future Values of Cash Flows=36
2.2.2. Bond Yield=39
2.2.3. Price-Yield Curves=39
2.3. Term Structure of Interest Rates and Forward Rates=41
2.3.1. Yield Curve=41
2.3.2. Calculating Spot Rates;Rates Arbitrage=43
2.3.3. Forward Rates=45
2.3.4. Term-Structure Theories=47
Summary=48
Problems=49
Further Readings=51
3. Models of Securities Prices in Financial Markets=53
3.1. Single-Period Models=54
3.1.1. Asset Dynamics=54
3.1.2. Portfolio and Wealth Processes=55
3.1.3. Arrow-Debreu Securities=57
3.2. Multiperiod Models=58
3.2.1. General Model Specifications=58
3.2.2. Cox-Ross-Rubinstein Binomial Model=60
3.3. Continuous-Time Models=62
3.3.1. Simple Facts about the Merton-Black-Scholes Model=62
3.3.2. Brownian Motion Process=63
3.3.3. Diffusion Processes, Stochastic Integrals=66
3.3.4. Technical Properties of Stochastic Integrals=67
3.3.5. ItSmall o, circumflex accent's Rule=69
3.3.6. Merton-Black-Scholes Model=74
3.3.7. Wealth Process and Portfolio Process=78
3.4. Modeling Interest Rates=79
3.4.1. Discrete-Time Models=79
3.4.2. Continuous-Time Models=80
3.5. Nominal Rates and Real Rates=81
3.5.1. Discrete-Time Models=81
3.5.2. Continuous-Time Models=83
3.6. Arbitrage and Market Completeness=83
3.6.1. Notion of Arbitrage=84
3.6.2. Arbitrage in Discrete-Time Models=85
3.6.3. Arbitrage in Continuous-Time Models=86
3.6.4. Notion of Complete Markets=87
3.6.5. Complete Markets in Discrete-Time Models=88
3.6.6. Complete Markets in Continuous-Time Models=92
3.7. Appendix=94
3.7.1. More Details for the Proof of ItSmall o, circumflex accent's Rule=94
3.7.2. Multidimensional ItSmall o, circumflex accent's Rule=97
Summary=97
Problems=98
Further Readings=101
4. Optimal Consumption/Portfolio Strategies=103
4.1. Preference Relations and Utility Functions=103
4.1.1. Consumption=104
4.1.2. Preferences=105
4.1.3. Concept of Utility Functions=107
4.1.4. Marginal Utility, Risk Aversion, and Certainty Equivalent=108
4.1.5. Utility Functions in Multiperiod Discrete-Time Models=112
4.1.6. Utility Functions in Continuous-Time Models=112
4.2. Discrete-Time Utility Maximization=113
4.2.1. Single Period=114
4.2.2. Multiperiod Utility Maximization:Dynamic Programming=116
4.2.3. Optimal Portfolios in the Merton-Black-Scholes Model=121
4.2.4. Utility from Consumption=122
4.3. Utility Maximization in Continuous Time=122
4.3.1. Hamilton-Jacobi-Bellman PDE=122
4.4. Duality/Martingale Approach to Utility Maximization=128
4.4.1. Martingale Approach in Single-Period Binomial Model=128
4.4.2. Martingale Approach in Multiperiod Binomial Model=130
4.4.3. Duality/Martingale Approach in Continuous Time=133
4.5. Transaction Costs=138
4.6. Incomplete and Asymmetric Information=139
4.6.1. Single Period=139
4.6.2. Incomplete Information in Continuous Time=140
4.6.3. Power Utility and Normally Distributed Drift=142
4.7. Appendix:Proof of Dynamic Programming Principle=145
Summary=146
Problems=147
Further Readings=150
5. Risk=153
5.1. Risk versus Return:Mean-Variance Analysis=153
5.1.1. Mean and Variance of a Portfolio=154
5.1.2. Mean-Variance Efficient Frontier=157
5.1.3. Computing the Optimal Mean-Variance Portfolio=160
5.1.4. Computing the Optimal Mutual Fund=163
5.1.5. Mean-Variance Optimization in Continuous Time=164
5.2. VaR:Value at Risk=167
5.2.1. Definition of VaR=167
5.2.2. Computing VaR=168
5.2.3. VaR of a Portfolio of Assets=170
5.2.4. Alternatives to VaR=171
5.2.5. The Story of Long-Term Capital Management=171
Summary=172
Problems=172
Further Readings=175
Ⅱ. PRICING AND HEDGING OF DERIVATIVE SECURITIES=177
6. Arbitrage and Risk-Neutral Pricing=179
6.1. Arbitrage Relationships for Call and Put Options;Put-Call Parity=179
6.2. Arbitrage Pricing of Forwards and Futures=184
6.2.1. Forward Prices=184
6.2.2. Futures Prices=186
6.2.3. Futures on Commodities=187
6.3. Risk-Neutral Pricing=188
6.3.1. Martingale Measures;Cox-Ross-Rubinstein(CRR) Model=188
6.3.2. State Prices in Single-Period Models=192
6.3.3. No Arbitrage and Risk-Neutral Probabilities=193
6.3.4. Pricing by No Arbitrage=194
6.3.5. Pricing by Risk-Neutral Expected Values=196
6.3.6. Martingale Measure for the Merton-Black-Scholes Model=197
6.3.7. Computing Expectations by the Feynman-Kac PDE=201
6.3.8. Risk-Neutral Pricing in Continuous Time=202
6.3.9. Futures and Forwards Revisited=203
6.4. Appendix=206
6.4.1. No Arbitrage Implies Existence of a Risk-Neutral Probability=206
6.4.2. Completeness and Unique EMM=207
6.4.3. Another Proof of Theorem 6.4=210
6.4.4. Proof of Bayes' Rule=211
Summary=211
Problems=213
Further Readings=215
7. Option Pricing=217
7.1. Option Pricing in the Binomial Model=217
7.1.1. Backward Induction and Expectation Formula=217
7.1.2. Black-Scholes Formula as a Limit of the Binomial Model Formula=220
7.2. Option Pricing in the Merton-Black-Scholes Model=222
7.2.1. Black-Scholes Formula as Expected Value=222
7.2.2. Black-Scholes Equation=222
7.2.3. Black-Scholes Formula for the Call Option=225
7.2.4. Implied Volatility=227
7.3. Pricing American Options=228
7.3.1. Stopping Times and American Options=229
7.3.2. Binomial Trees and American Options=231
7.3.3. PDEs and American Options=233
7.4. Options on Dividend-Paying Securities=235
7.4.1. Binomial Model=236
7.4.2. Merton-Black-Scholes Model=238
7.5. Other Types of Options=240
7.5.1. Currency Options=240
7.5.2. Futures Options=242
7.5.3. Exotic Options=243
7.6. Pricing in the Presence of Several Random Variables=247
7.6.1. Options on Two Risky Assets=248
7.6.2. Quantos=252
7.6.3. Stochastic Volatility with Complete Markets=255
7.6.4. Stochastic Volatility with Incomplete Markets;Market Price of Risk=256
7.6.5. Utility Pricing in Incomplete Markets=257
7.7. Merton's Jump-Diffusion Model=260
7.8. Estimation of Variance and ARCH/GARCH Models=262
7.9. Appendix:Derivation of the Black-Scholes Formula=265
Summary=267
Problems=268
Further Readings=273
8. Fixed-Income Market Models and Derivatives=275
8.1. Discrete-Time Interest-Rate Modeling=275
8.1.1. Binomial Tree for the Interest Rate=276
8.1.2. Black-Derman-Toy Model=279
8.1.3. Ho-Lee Model=281
8.2. Interest-Rate Models in Continuous Time=286
8.2.1. One-Factor Short-Rate Models=287
8.2.2. Bond Pricing in Affine Models=289
8.2.3. HJM Forward-Rate Models=291
8.2.4. Change of Numeraire=295
8.2.5. Option Pricing with Random Interest Rate=296
8.2.6. BGM Market Model=299
8.3. Swaps, Caps, and Floors=301
8.3.1. Interest-Rate Swaps and Swaptions=301
8.3.2. Caplets, Caps, and Floors=305
8.4. Credit/Default Risk=306
Summary=308
Problems=309
Further Readings=312
9. Hedging=313
9.1. Hedging with Futures=313
9.1.1. Perfect Hedge=313
9.1.2. Cross-Hedging;Basis Risk=314
9.1.3. Rolling the Hedge Forward=316
9.1.4. Quantity Uncertainty=317
9.2. Portfolios of Options as Trading Strategies=317
9.2.1. Covered Calls and Protective Puts=318
9.2.2. Bull Spreads and Bear Spreads=318
9.2.3. Butterfly Spreads=319
9.2.4. Straddles and Strangles=321
9.3. Hedging Options Positions;Delta Hedging=322
9.3.1. Delta Hedging in Discrete-Time Models=323
9.3.2. Delta-Neutral Strategies=325
9.3.3. Deltas of Calls and Puts=327
9.3.4. Example:Hedging a Call Option=327
9.3.5. Other Greeks=330
9.3.6. Stochastic Volatility and Interest Rate=332
9.3.7. Formulas for Greeks=333
9.3.8. Portfolio Insurance=333
9.4. Perfect Hedging in a Multivariable Continuous-Time Model=334
9.5. Hedging in Incomplete Markets=335
Summary=336
Problems=337
Further Readings=340
10. Bond Hedging=341
10.1. Duration=341
10.1.1. Definition and Interpretation=341
10.1.2. Duration and Change in Yield=345
10.1.3. Duration of a Portfolio of Bonds=346
10.2. Immunization=347
10.2.1. Matching Durations=347
10.2.2. Duration and Immunization in Continuous Time=350
10.3. Convexity=351
Summary=352
Problems=352
Further Readings=353
11. Numerical Methods=355
11.1. Binomial Tree Methods=355
11.1.1. Computations in the Cox-Ross-Rubinstein Model=355
11.1.2. Computing Option Sensitivities=358
11.1.3. Extensions of the Tree Method=359
11.2. Monte Carlo Simulation=361
11.2.1. Monte Carlo Basics=362
11.2.2. Generating Random Numbers=363
11.2.3. Variance Reduction Techniques=364
11.2.4. Simulation in a Continuous-Time Multivariable Model=367
11.2.5. Computation of Hedging Portfolios by Finite Differences=370
11.2.6. Retrieval of Volatility Method for Hedging and Utility Maximization=371
11.3. Numerical Solutions of PDEs;Finite-Difference Methods=373
11.3.1. Implicit Finite-Difference Method=374
11.3.2. Explicit Finite-Difference Method=376
Summary=377
Problems=378
Further Readings=380
Ⅲ. EQUILIBRIUM MODELS=381
12. Equilibrium Fundamentals=383
12.1. Concept of Equilibrium=383
12.1.1. Definition and Single-Period Case=383
12.1.2. A Two-Period Example=387
12.1.3. Continuous-Time Equilibrium=389
12.2. Single-Agent and Multiagent Equilibrium=389
12.2.1. Representative Agent=389
12.2.2. Single-Period Aggregation=389
12.3. Pure Exchange Equilibrium=391
12.3.1. Basic Idea and Single-Period Case=392
12.3.2. Multiperiod Discrete-Time Model=394
12.3.3. Continuous-Time Pure Exchange Equilibrium=395
12.4. Existence of Equilibrium=398
12.4.1. Equilibrium Existence in Discrete Time=399
12.4.2. Equilibrium Existence in Continuous Time=400
12.4.3. Determining Market Parameters in Equilibrium=403
Summary=406
Problems=406
Further Readings=407
13. CAPM=409
13.1. Basic CAPM=409
13.1.1. CAPM Equilibrium Argument=409
13.1.2. Capital Market Line=411
13.1.3. CAPM formula=412
13.2. Economic Interpretations=413
13.2.1. Securities Market Line=413
13.2.2. Systematic and Nonsystematic Risk=414
13.2.3. Asset Pricing Implications:Performance Evaluation=416
13.2.4. Pricing Formulas=418
13.2.5. Empirical Tests=419
13.3. Alternative Derivation of the CAPM=420
13.4. Continuous-Time, Intertemporal CAPM=423
13.5. Consumption CAPM=427
Summary=430
Problems=430
Further Readings=432
14. Multifactor Models=433
14.1. Discrete-Time Multifactor Models=433
14.2. Arbitrage Pricing Theory(APT)=436
14.3. Multifactor Models in Continuous Time=438
14.3.1. Model Parameters and Variables=438
14.3.2. Value Function and Optimal Portfolio=439
14.3.3. Separation Theorem=441
14.3.4. Intertemporal Multifactor CAPM=442
Summary=445
Problems=445
Further Readings=445
15. Other Pure Exchange Equilibria=447
15.1. Term-Structure Equilibria=447
15.1.1. Equilibrium Term Structure in Discrete Time=447
15.1.2. Equilibrium Term Structure in Continuous Time;CIR Model=449
15.2. Informational Equilibria=451
15.2.1. Discrete-Time Models with Incomplete Information=451
15.2.2. Continuous-Time Models with Incomplete Information=454
15.3. Equilibrium with Heterogeneous Agents=457
15.3.1. Discrete-Time Equilibrium with Heterogeneous Agents=458
15.3.2. Continuous-Time Equilibrium with Heterogeneous Agents=459
15.4. International Equilibrium;Equilibrium with Two Prices=461
15.4.1. Discrete-Time International Equilibrium=462
15.4.2. Continuous-Time International Equilibrium=463
Summary=466
Problems=466
Further Readings=467
16. Appendix:Probability Theory Essentials=469
16.1. Discrete Random Variables=469
16.1.1. Expectation and Variance=469
16.2. Continuous Random Variables=470
16.2.1. Expectation and Variance=470
16.3. Several Random Variables=471
16.3.1. Independence=471
16.3.2. Correlation and Covariance=472
16.4. Normal Random Variables=472
16.5. Properties of Conditional Expectations=474
16.6. Martingale Definition=476
16.7. Random Walk and Brownian Motion=476
References=479
Index=487