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目录结构如下：
Part I Fundamentals
1 Introduction 3
2 Fundamental Risk Factors of Financial Markets 7
2.1 Interest rates 7
2.2 Market prices 21
2.3 An intuitive model for financial risk factors 22
2.4 Ito processes and stochastic analysis 32
3 Financial Instruments: A System of Derivatives and
Underlyings 48
3.1 Spot transactions 49
3.2 Forward transactions 56
3.3 Options 59
Part II Methods
4 Overview of the Assumptions 65
5 Present Value Methods, Yields, and Traditional Risk Measures 68
5.1 Present value and yield to maturity 68
5.2 Internal rate of return and net present value 70
5.3 Accrued interest, residual debt, and par rates 73
5.4 Traditional sensitivities of interest rate instruments 76
6 Arbitrage 84
6.1 Forward contracts 84
6.2 Options 89
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vi CONTENTS
7 The Black-Scholes Differential Equation 94
7.1 The Black-Scholes equation from arbitrage arguments 95
7.2 The Black-Scholes equation and the backward equation 101
7.3 The relationship to the heat equation 105
8 Integral Forms and Analytic Solutions in
the Black-ScholesWorld 109
8.1 Option prices as solutions of the heat equation 109
8.2 Option prices and transition probabilities 111
8.3 Compilation of Black-Scholes option prices for
different underlyings 114
9 Numerical Solutions Using Finite Differences 121
9.1 Discretizing the Black-Scholes equation 122
9.2 Difference schemes 129
9.3 Convergence criteria 151
9.4 Discrete dividends 156
9.5 Example 157
10 Binomial and Trinomial Trees 161
10.1 General trees 161
10.2 Recombinant trees 165
10.3 The relationship between random walk and binomial
parameters 173
10.4 The binomial model with infinitesimal steps 176
10.5 Trinomial trees 178
11 Monte Carlo Simulations 184
11.1 A simple example: The area of a disk 186
11.2 The general approach to Monte Carlo simulations 190
11.3 Monte Carlo simulation of risk factors 191
11.4 Pricing 197
12 Hedging 199
12.1 Replicating portfolios as synthetic derivatives 199
12.2 Hedging derivatives with spot transactions 200
12.3 Hedging derivatives with forward contracts 203
12.4 Hedge-ratios for arbitrary combinations of
financial instruments 209
12.5 “Greek” risk management with sensitivities 211
12.6 Computation of the greek risk variables 218
13 Martingales and Numeraires 224
13.1 The martingale property 224
13.2 The numeraire 226
13.3 Self-financing portfolio strategies 230
CONTENTS vii
13.4 Generalization to continuous time 233
13.5 The drift 243
13.6 The market price of risk 247
13.7 Tradable underlyings 248
13.8 Applications in the Black-Scholes world 249
14 Interest Rates and Term Structure Models 254
14.1 Instantaneous spot rates and
instantaneous forward rates 255
14.2 Important numeraire instruments 257
14.3 The special case of deterministic interest rates 261
14.4 Tradable and nontradable variables 263
14.5 Convexity adjustments 264
14.6 Arbitrage-free interest rate trees 272
14.7 Market rates vs. instantaneous rates 282
14.8 Explicit specification of short rate models 288
14.9 The example program TermStructureModels.xls 296
14.10 Monte Carlo on the tree 303
14.11 The drift in term structure models 304
14.12 Short rate models with discrete compounding 310
Part III Instruments
15 Spot Transactions on Interest Rates 315
15.1 Zero bonds 316
15.2 Floaters 317
15.3 Coupon bonds 319
15.4 Swaps 326
15.5 Annuity loans 331
16 Forward Transactions on Interest Rates 343
16.1 Forward rate agreements 343
16.2 Interest rate futures 344
16.3 Forward swaps 348
16.4 Forward bonds 353
17 Plain Vanilla Options 357
17.1 Options on spot and forward prices 358
17.2 Index options and index futures 361
17.3 Foreign exchange options and futures 362
17.4 Interest rate options 364
18 Exotic Options 378
18.1 Traditional and general definition of an option 378
18.2 Payoff profiles for selected exotics 378
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18.3 Black-Scholes for exotics 383
18.4 Numerical pricing methods for exotics 394
Part IV Risk
19 Fundamental Risk Concepts 407
19.1 Confidence, percentile, and risk 408
19.2 The value at risk of a single risk factor 411
19.3 Approximations in the distribution of risk factors 417
19.4 The covariance matrix 419
20 The Variance-Covariance Method 430
20.1 Portfolios vs. financial instruments 432
20.2 The delta-normal method 434
20.3 The delta-gamma method 439
21 Simulation Methods 462
21.1 Monte Carlo simulation 462
21.2 Historical simulation 465
21.3 Crash and stress testing:Worst case scenarios 467
22 Interest Rate Risk and Cash Flows 470
22.1 Cash flow structures of financial instruments 470
22.2 Interpolation and cash flow mapping 485
23 Example of a VaR Computation 491
23.1 The portfolio 491
23.2 Market data 492
23.3 Cash flow mapping 493
23.4 Calculation of risk 493
24 Backtesting: Checking the Applied Methods 496
24.1 Profit-loss computations 496
24.2 The traffic light approach of
the supervising authorities 497
Part V Portfolios
25 Classical Portfolio Management 507
25.1 From risk management to portfolio management 508
25.2 Portfolio optimization 517
26 Attributes and their Characteristic Portfolios 535
26.1 General properties of characteristic portfolios 536
26.2 The leverage 539
26.3 The excess return 540
CONTENTS ix
26.4 The optimal portfolio 544
26.5 The efficient frontier revisited 547
27 Active Management and Benchmarking 552
27.1 The capital asset pricing model 552
27.2 Benchmarking against an index 554
27.3 Benchmark and characteristic portfolios 559
27.4 Relations between Sharpe ratio and information ratio 567
Part VI Market Data
28 Interest Rate Term Structures 575
28.1 Bootstrapping 576
28.2 Interpolations 588
29 Volatility 590
29.1 Implied volatilities 590
29.2 Local volatility surfaces 592
29.3 Volatility transformations 599
30 Market Parameter from Historical Time Series 615
30.1 Historical yields, volatility, and correlation 615
30.2 Error estimates 617
30.3 Return and covariance estimates 627
31 Time Series Modeling 634
31.1 Stationary time series and autoregressive models 637
31.2 Calibration of time series models 648
32 Forecasting with Time Series Models 656
32.1 Forecasting with autoregressive models 657
32.2 Volatility forecasts with GARCH(p, q) processes 660
32.3 Volatility forecasts with GARCH(1,1) processes 665
32.4 Volatility forecasts with moving averages 668
33 Principal Component Analysis 671
33.1 The general procedure 671
33.2 Principal component analysis of the German term
structure 678
34 Pre-Treatment of Time Series and Assessment of Models 682
34.1 Pre-treatment of time series 682
34.2 Measuring the goodness of time series models 686
A Probability and Statistics 699
A.1 Probability, expectation, and variance 699
A.2 Multivariate distributions, covariance,
correlation, and beta 701
x CONTENTS
A.3 Moments and characteristic functions 705
A.4 A Collection of important distributions 710
A.5 Transformations between distributions 734
Bibliography 739
Index 745
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