The Oxford Guide to Financial Modeling
Table of Contents
PART 1. DERIVATIVES VALUATION 1
1. Introduction: Discounted Cash Flow Method 2
1.1 Examples of Financial Issues 2
1.2 Financial Models 5
1.3 Basics of Modeling: Present Value and Measures of Risk 10
1.4 Summary 15
2. Equity Market: the Capital Asset Pricing Model 18
2.1 Real and Financial Sectors 19
2.2 Stocks and Stock Markets 20
2.3 Perfect Capital Market 25
2.4 Efficient Capital Market Hypothesis 27
2.5 Diversification 29
2.6 Capital Asset Pricing Model (CAPM) 34
2.7 Beta – the Systematic Risk 37
2.8 The Stock Model – Dividend Discount Model 40
2.9 An Application of the Capital Asset Pricing Model in Investment Services 42
2.10 Empirical Tests of Capital Asset Pricing Model 42
2.11 Summary 44
Appendix A: Expectations and Standard Deviations
Appendix B: A Summary of the CAPM
3. Bond Markets: the Bond Model 51
3.1 Bond Mathematics 52
3.2 Bonds and Bond Markets 54
3.3 Swap Markets 57
3.4 Economics of the Yield Curve 58
3.5 The Bond Model 62
3.6 Forward Prices and Forward Rates 66
3.7 Bond Analysis 72
3.8 Applications of the Bond Analytics 84
3.9 Law of One Price: an Arbitrage Trade and Fair Value Analysis 86
3.10 Summary 87
Appendix A Taylor Expansion
Appendix B The Derivation of Macaulay Duration and Convexity
Appendix C Duration & Convexity in measuring price sensitivity
4. Equity Options: the Black-Scholes Model 97
4.1 A Description of an Option 98
4.2 Institutional Framework 99
4.3 Put-Call Parity 100
4.4 The Main Insight of the Black-Scholes Model 103
4.5 Valuation Methods 111
4.6 Relationships of Risk Neutral and Market Binomial Lattices 117
4.7 Option Behavior and the Sensitivity Analysis 119
4.8 Extensions of the Black-Scholes Model 123
4.9 Option Pricing Procedure and the Analytic Framework 125
4.10 Applications of Option Models 126
4.11 Accounting for Employee Stock Options 129
4.12 Intuitive Explanations of the Behavior of an Equity Option 131
4.13 Summary 132
Appendix A The Derivation of the Black-Scholes Continuous Time Model using Different Numeraire
Appendix B The Relationship Between the Time Decay and the Gamma of a Delta Neutral Portfolio
Appendix C Pathwise Valuation
Appendix D Derivation of Discrete Time Parameters
Appendix E Monte Carlo Simulation and Finite Difference Methods
5. Interest Rate Derivatives: Interest Rate Models 148
5.1 Interest Rate Movements: Historical Experiences 148
5.2 The Three Factor Yield Curve Movement Model 155
5.3 Equilibrium Models 158
5.4 Arbitrage Free Models 163
5.5 A Comparison of Models 188
5.6 Generalizations of Interest Rate Models 190
5.7 Summary 197
Appendix A Yield Curve Movement Represented by the Principal Components
Appendix B Derivations of Ho-Lee, the Extended Ho-Lee and the Ho-Lee 2- Factor Models
6. Implied Volatility Surface: Calibrating the Models 207
6.1 Implied Volatility Surface and Benchmark Securities 207
6.2 Price Quotes of Benchmark Securities 210
6.3 Valuation of Interest Rate Derivatives Using Market Benchmark Prices 219
6.4 Calibration of the Black, Derman and Toy Models 222
6.5 Calibration of the Ho-Lee Models 223
6.6 Calibration of Longstaff, Santa-Clara and Schwartz “string” Model 225
6.7 Calibration of the Brace-Gatarek-Musiela/Jamshidian Model (the LIBOR Market Model) 231
6.8 Comparing the Black Model and the Interest Rate Models 234
6.9 Applications of Interest Rate Models 240
6.10 Key Rate Duration and Dynamic Hedging 243
6.11 Path-wise Valuation and a Decomposition of an Option 248
6.12 Intuitive Explanation of the Bond Option Valuation 250
6.13 Lecture on Convexity 251
6.14 Summary 252
7. Exotic Options: Bellman’s Optimization, Filtration Model and n-Factor Model 256
7.1 Option with Alternative Payoffs at Expiration 257
7.2 Option with Boundary Conditions 260
7.3 Options with the Early Exercise Feature (American) and the Bellman Optimization 263
7.4 Compound Options 269
7.5 Options with Lookback Features (Asian) and the Filtration Model 272
7.6 Chooser Options 277
7.7 Multiple Risk Sources 282
7.8 Constant Maturity Swap 285
7.9 Interest Rate Spread Option 287
7.10 Options on Forward/Futures Contracts 290
7.11 Commodity Options 292
7.12 An Overview of the Valuation Framework 295
7.13 Summary 297
Appendix A Optimal Early Exercise Using Simulations
Appendix B N-Factor Lattice Model
Appendix C A Numerical Example of Dynamic Programming
PART 2. CORPORATE LIABILITIES 307
8. Investment Grade Corporate Bonds: Option Adjusted Spreads 308
8.1 Describing a Corporate Bond 309
8.2 Valuation of a Bond 314
8.3 Numerical Examples 325
8.4 Liquidity (Marketability) Spread 333
8.5 Credit Scoring Approaches 335
8.6 Bond Aanlysis 336
8.7 Numerical Example-Valuing a Eurobond Issue 339
8.8 Applications of Bond Analytics 342
8.9 Explaining the Concept of the arbitrage-free condition in a solemn occasion
344
8.10 Summary……………………………………………………………… 345
Appendix Callable Bond and Sinking Fund Bond Pricing
9. High Yield Corporate Bonds: the Structural Models 354
9.1 An Exapmple of a High Yield Bond 355
9.2 Institutional Framework of Bankruptcy and Bankruptcy Proceedings 358
9.3 The Fisher Model 362
9.4 An Actuarial Model 363
9.5 Historical Experience and Esimation of the Parameters of Default Models 364
9.6 The Reduced Form Models 368
9.7 The Structural Model 370
9.8 Valuation of a Debt Package Using a Compound Option Model 374
9.9 Empirical Evidence 379
9.10 A Review of the High Yield Bond Models 380
9.11 Analysis of the McleodUSA Bond 382
9.12 Analysis of Credit Risk 383
9.13 Summary 386
10. Convertibles, MBS/CMO, and Other Bonds: the Behavioral Models 392
10.1 Convertible Bonds 393
10.2 Mortgage-Backed Securities (Passthrough Certificates) 403
10.3 Collateralized Mortgage Obligations (CMO) 411
10.4 Other Bonds 416
10.5 Credit Derivatives 419
10.6 Managing a CMO Portfolio……………..………………………………422
10.7 Summary 428
11. Financial Institutions’ Liabilities: Required Option Adjusted Spread 431
11.1 Balance Sheet Analysis-Book Value 432
11.2 Fair Values 434
11.3 Liability Modeling 441
11.4 Bank Liabilities 443
11.5 Property and Casualty Insurance 447
11.6 Life Insurance Products 453
11.7 Pension Liabilities………………………………………………………474
11.8 Applications of the Financial Models to Liability Management 477
11.9 “Not If, But When” 478
11.10 Summary 479
PART 3. CORPORATE FINANCE 483
12. Valuation of a Firm: the Business Model 484
12.1 Descriptions of a Firm 485
12.2 A Review of Traditional Firm Valuation Methodologies 489
12.3 Corporate Financial Decisions and Firm Value Maximization 492
12.4 Miller-Modigliani Theories 494
12.5 Free Cash Flow Discount Model 503
12.6 Business Model 505
12.7 Implications of the Valuation Model 517
12.8 Analyses of the Business Model 518
12.9 From the Senior Management Perspective 519
12.10 Summary 520
Appendix A The Miller-Modigliani Propositions
Appendix B The Miller Model
13. Strategic Value of a Firm: Real Options 530
13.1 Characteristics of a Growth Company – an Example of Real Options 531
13.2 Salient Features of Real Options 532
13.3 Examples of Real Options in Capital Budgeting 536
13.4 Exmaples of Businesses with Embedded Options 540
13.5 Strategic Value of a Firm 543
13.6 Analysis of the Real Option Value 545
13.7 A Business Model with Embedded Options: Starbucks Coffee Japan 547
13.8 A Business Model Approach and the Free Cash-Flow Discounting Approach - A Comparison 551
13.9 Empirical Implications of the Business Model 551
13.10 Implications of the Business Model 556
13.11 Empirical Research on Real Option 560
13.12 Summary……………………………………………………………….561
Appendix The Business Model
14. Optimal Corporate Financial Decisions: Corporate Model 575
14.1 Corporate Financial Planning – the DFA Approach 576
14.2 Extensions of the MM Theory 580
14.3 Empirical Evidence on the MM Theory and the Extensions of MM Theory 583
14.4 The Corporate Model 587
14.5 Specifications of the Corporate Model 590
14.6 A Comparison with Previous Research…………………………………597
14.7 New Perspectives in Viewing Firms as Contingent Claims 598
14.8 Principles in Risk Management…………………………………………601
14.9 What is Financial Modeling to Senior Management?………………..…602
14.10 Summary 604
Appendix The Firm Model
15. Risk Management 614
15.1 Risk Measurement-Value at Risk(VaR) 615
15.2 Market Risk 617
15.3 Delta Normal Methodology 618
15.4 Historical Simulation Methodology 626
15.5 Monte Carlo Simulation Methodology 627
15.6 Extreme Value Theory 630
15.7 Credit Risk 632
15.8 Risk Reporting 640
15.9 Risk Monitoring 642
15.10 Risk Management 643
15.11 Boardroom with a view- the Coffin Story 647
15.12 Summary 649
Appendix A Selected Financial Losses
Appendix B Lessons learnt from the Historical Financial Losses
16. Financial Institutions: Applications of Financial Models 661
16.1 An Overview of the Financial Sector 662
16.2 Organization and the Business Model of a Financial Institution 666
16.3 Financial Disclosures on Valuation 669
16.4 Risk Management 672
16.5 Capital Allocation and Risk Adjusted Performance Measures 673
16.6 Financial Modeling of a Financial Institution 676
16.7 Applications: Asset and Liability Management 692
16.8 Regulatory Issues 695
16.9 Summary 701
Appendix A What Actions have Commercial Banks taken?
Appendix B Capital Requirements and Risk Based Capital
17. Structured Finance: Foreign Exchange Models 709
17.1 Background 709
17.2 Economics of the Structure 710
17.3 Deal Structure 711
17.4 Pricing 715
17.5 Simulation 719
17.6 VaR Calculation 721
17.7 Remarks 722
17.8 Concluding Remarks on Financial Modeling…………………………...723
Appendix A Total Return Swap Terms and Conditions As of January 29, 1997
Appendix B Indonesian Rupiah Linked Note Final Terms and Conditions Sheet
Appendix C The Put-Call Parity
18. Concluding Thoughts 728
18.1 Conceptual Developments of Financial Models 728
18.2 Overview of Valuation Models 731
18.3 Applications of the Financial Models 732
18.4 Financial Modeling as a Process………………………………………..736
18.5 Looking into the Future 738
18.6 The World of Contingent Claims………………………………………..741
19. Epilogue: Market Model and Binomial Lattices 743
19.1 Building a Market Model in a Binomial Lattice 741
19.2 A General Approach to Valuation 759
19.3 Comparision of the Option Derivation between Discrete-time and Continuous-time 778
Appendix A Continuous-time Versions of the Ho and Lee Models
Appendix B Summary of continuous time interest rate model
Appendix C Recombining Lattice
Notation 750
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