Contents -- Acknowledgments -- Preface -- Foreword -- Part I. Option Pricing Theory and its Foundations -- Introduction -- References -- 1. Approximate Option Valuation for Arbitrary Stochastic Processes R. Jarrow and A. Rudd -- 1. Introduction -- 2. Approximating distribution -- 3. Approximate option valuation formula -- 4. Approximating option values with the Black-8cboles formula -- 5. N umerieal analysis of residual error -- 6. Conclusion -- Appendix 1: Proof of the generalized Edgeworth series expansion -- References -- 2. Arbitrage, Continuous Trading, and Margin Requirements D. Heath and R. Jarrow -- I. The Model -- II. Market Constraints on Trading Strategies -- III. Option Pricing under Margin Requirements -- IV. Conclusion -- Appendix -- REFERENCES -- 3. Ex-Dividend Stock Price Behavior and Arbitrage Opportunities D. Heath and R. Jarrow -- I. Introduction -- II. The Model -- III. Characterization of Arbitrage Opportunities at the Ex-Dividend Date -- IV. Escrowed Dividend Stock Processes -- V. Conclusion -- Appendix -- Proofs of Theorems 1 and 2 -- References -- 4. The Stop-Loss Start-Gain Paradox and Option Valuation: A New Decomposition into Intrinsic and Time Value P. Carr and R. Jarrow -- 1. The Black-Scholes Model, Terminology, and the Stop-Loss StartGain Strategy -- 2. Resolution of the Paradox -- 3. Valuation Results -- 4. Genera1izing the Stock-Price Process -- 5. Conclusions -- Appendix -- References -- 5. Alternative Characterizations of American Put Options P. Carr, R. Jarrow and R. Myneni -- 1. THE EARLY EXERCISE PREMIUM -- 2. REPRESENTING EUROPEAN PUTS IN TERMS OF A BOUNDARY -- 3. VARIOUS AMERICAN PUT REPRESENTATIONS -- 4. SUMMARY AND EXTENSIONS -- 5. APPENDIX -- REFERENCES -- 6. Market Manipulation, Bubbles, Corners, and Short Squeezes R. Jarrow -- I. Introduction -- II. The Model -- III. The Market Structure.

IV. Paper Wealth, Real Wealth, and Market Manipulation Trading Strategies -- V. The Existence of Market Manipulation Trading Strategies -- VI. Sufficient Conditions for the Nonexistence of Market Manipulation Trading Strategies -- VII. Infinite Trading Horizon Speculators -- VIII. Conclusion -- Appendix -- References -- 7. Derivative Security Markets, Market Manipulation, and Option Pricing Theory R. Jarrow -- Abstract -- I. Introduction -- II. The Model -- III. Market Manipulation Using the Derivative Security -- IV. Synchronous Markets -- V. A Theory for Option Pricing -- VI. Conclusion -- Appendix -- References -- 8. Liquidity Risk and Arbitrage Pricing Theory U. Oetin, R. Jarrow and P. Protter -- 1 Introduction -- 2 The model -- 2.1 Supply curve -- 2.2 Trading strategies -- 2.3 The marked-to-market value of a s.ft.s. and its liquidity cost -- 3 The extended first fundamental theorem -- 4 The extended second fundamental theorem -- 5 Example (extended Black-Scholes economy) -- 5.1 The economy -- 5.2 Call option valuation -- 6 Discontinuous supply curve evolutions -- 6.1 The supply curve and s.f.t.s. 's -- 6.2 The extended first fundamental theorem -- 6.3 The extended secondfundamental theorem -- 7 Conclusion -- Appendix -- A.I Proof of the first fundamental theorem -- A.2 Construction of the self-financing condition for a class of trading strategies -- A.3 Approximating stochastic integrals with continuous and of FV integrands -- A.4 A Numeraire invariance theorem -- References -- 9. Pricing Options in an Extended Black-Scholes Economy with Illiquidity: Theory and Empirical Evidence U. Oetin, R. Jarrow, P. Protter and M. Warachka -- 1. The Model -- 1.1 Trading strategies and liquidity costs -- 1.2 Fundamental theorems of asset pricing with illiquidity -- 2. An Extended Black Scholes Economy -- 2.1 Pricing a European call option.

2.2 Discrete hedging strategies -- 3. Supply Curve Estimation -- 3.1 Estimation procedure -- 3.2 Estimation results -- 3.3 Robustness tests -- 3.4 Stochastic liquidity -- 4. Optimal Discrete Option Hedging Strategies -- 4.1 Super-replication of options -- 4.2 Solution methodology -- 4.3 Implementation -- 5. Discrete Hedging Strategies for Comparison -- 6. Empirical Results -- 6.1 Non-optimal hedges -- 6.2 Summary of empirical results -- 7. Conclusion -- Appendix A: Liquidity Cost of Black Scholes Hedge -- Appendix B: Dynamic Programming Details -- B.1 Binomial implementation of dynamic program -- References -- Part II. Stochastic Interest Rates -- Introduction -- References -- 10. Liquidity Premiums and the Expectations Hypothesis R. Jarrow -- 1. Introduction -- 2. Quantifying the expectations hypothesis -- 3. Conclusion -- References -- 11. Forward Contracts and Futures Contracts R. Jarrow and G. Oldfield -- 1. Introduction -- 2. Values of forward and futures contracts -- 3. Forward prices and futures prices -- 4. Treasury bill futures contract: An example -- 5. Conclusion -- References -- 12. The Pricing of Commodity Options with Stochastic Interest Rates R. Jarrow -- I. INTRODUCTION -- II. THE ECONOMY -- III. THE ARBITRAGE PRICING METHODOLOGY -- IV. FOR WARD CONTRACTS -- V. FUTURES CONTRACTS -- VI. COMMODITY OPTIONS ON THE SPOT COMMODITY -- VII. COMMODITY OPTIONS ON FUTURES CONTRACTS -- VIII. SUMMARY -- APPENDIX -- NOTES -- REFERENCES -- 13. Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation D. Heath, R. Jarrow, and A. Morton -- 1. INTRODUCfION -- 2. TERMINOLOGY AND NOTATION -- 3. TERM STRUCTURE MOVEMENTS -- 4. ARBITRAGE FREE BOND PRICING AND TERM STRUCTURE MOVEMENTS -- 5. CONTINGENT CLAIM VALUATION -- 6. EXAMPLES -- 7. A CLASS OF STOCHASTIC DIFFERENTIAL EQUATIONS.

8. THE EQUILIBRIUM PRICING VERSUS THE ARBITRAGE PRICING METHODOLOGY -- 9. SUMMARY -- APPENDIX -- REFERENCES -- 14. Pricing Foreign Currency Options Under Stochastic Interest Rates K. Amin and R. Jarrow -- I. The economy -- II. Arbitrage free international economy -- III. Valuing European options on the spot exchange rate -- IV. Futures contracts, forward contracts and their options -- V. Valuation under a foreign trader based perspective -- VI. Conclusion -- Appendix A -- Appendix B -- Notes -- References -- 15. Pricing Options on Risky Assets in a Stochastic Interest Rate Economy K. Amin and R. Jarrow -- 1. INTRODUCTION -- 2. THE TERM STRUCTURE MODEL -- 3. THE EXPANDED RISKY ASSET ECONOMY -- 4. VALUING AMERICAN CONTINGENT CLAIMS -- 5. EXAMPLE: NONEXISTENCE OF OPTIMAL EXERCISE STRATEGIES -- 6. CONCLUSION -- REFERENCES -- 16. Pricing Treasury Inflation Protected Securities and Related Derivatives Using an HJM Model R. Jarrow and Y. Yildirim -- Abstract -- I. Introduction -- II. The Model -- III. Data Description -- A. Treasury Bond Price Data -- B. TIPS Prices -- C. CPI-U Data -- IV. Coupon Bond Stripping -- A. Stripping the Real Zero-Coupon Bond Prices -- B. Stripping the Nominal Zero-Coupon Bond Prices -- C_ Testing the Real Zero-Coupon Bond Price Forward Rate Curve -- V. Estimating the Term Structure Evolution Parameters -- A. Volatility Parameters for the Real Forward Rates -- B. Volatility Parameters for the Nominal Forward Rates -- C. Parameters for the Index Process -- VI. Hedging Analysis -- VII. Pricing Options on the Inflation Index -- VIII. Conclusion -- References -- Part III. Credit Risk -- Introduction -- References -- 17. Pricing Derivatives on Financial Securities Subject to Credit Risk R. Jarrow and S. Turnbull -- ABSTRACT -- I. The Economy -- II. The Two-Period Discrete Trading Economy -- A.1. The Default"Free Term Structure.

A.2. The XYZ Term Structure -- III. The Continuous Trading Economy -- A. The Setup -- B. Arbitrage-Free Restrictions -- C. XYZ Bonds -- D. Options on XYZ Debt -- E. Vulnerable Options -- F. Equity Derivatives -- G. Generalizations and Extensions -- IV. Conclusion -- Appendix -- REFERENCES -- 18. A Markov Model for the Term Structure of Credit Risk Spreads R. Jarrow, D. Lando and S. Turnbull -- 1. The Jarrow-Turnbull Model -- 2. Credit Ratings and Default-Probabilities: The Discrete Time Case -- 2.1 Valuation -- 2.2 Options and hedging -- 2.3 Fitting the credit class zero-curves -- 2.4 Discussion -- 3. Credit Ratings and Default Probabilities: The Continuous Time Case -- 3.1 Valuation -- 3.2 Options and hedging -- 3.3 Examples -- 3.4 Parameter estimation -- 3.4.1 Estimation of default-free parameters. -- 3.4.2 Estimation of the bankruptcy process parameters. -- 3.4.3 Estimating the recovery rate. -- 3.4.4 Estimating the generator matrix A. -- 3.4.5 Estimation of the empirical generator matrix A. -- 3.4.6 Estimation of the risk premium. -- 3.4.7 Survival probabilities and spreads under risk neutrality. -- 3.4.8 An illustrative estimation of the risk premia. -- 4. Conclusion -- Appendix A -- AppendJxB -- References -- 19. Default Risk and Diversification: Theory and Empirical Implications R. Jarrow, D. Lando and F. Yu -- 1. INTRODUCTION -- 2. VARIATIONS IN DEFAULT RISK VERSUS EVENT RISK -- 2.1. Comparisons with Ordinary Term Structure Modeling -- 2.2. Floating Rate Note with Step-Up Provision -- 2.3. Short-Term Bonds -- 3. CONDITIONALLY DIVERSIFIABLE DEFAULT RISK -- 3.l. Default Processes -- 3.2. Valuation of Defaultable Bonds -- 4. INVARIANCE OF THE DEFAULT INTENSITY -- 4.1. The Pricing of Well-Diversified Portfolios -- 4.2. Utility-Based Arguments and Exact Equivalence -- 4.3. Necessary Conditions in a Large Economy and Asymptotic Equivalence.

5. SOME EMPIRICAL IMPLICATIONS OF CONDITIONALLY DIVERSIFIABLE DEFAULT RISK.