Elsevier S & T

Handbooks in Operations Research and Management Science: Financial Engineering: Financial Engineering

Birge, John R.; Linetsky, Vadim

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Table of contents
  • Cover
  • Contentsv
  • Part I: Introduction1
  • Introduction to the Handbook of FinancialEngineering3
  • References11
  • Chapter 1. An Introduction to Financial Asset Pricing13
  • 1. Introduction13
  • 2. Introduction to derivatives and arbitrage14
  • 3. The core of the theory21
  • 4. American type derivatives60
  • Acknowledgements67
  • References67
  • Part II: Derivative Securities: Models and Methods71
  • Chapter 2. Jump-Diffusion Models for Asset Pricing in Financial Engineering73
  • 1. Introduction73
  • 2. Empirical stylized facts75
  • 3. Motivation for jump-diffusion models84
  • 4. Equilibrium for general jump-diffusion models89
  • 5. Basic setting for option pricing92
  • 6. Pricing call and put option via Laplace transforms94
  • 7. First passage times96
  • 8. Barrier and lookback options100
  • 9. Analytical approximations for American options103
  • 10. Extension of the jump-diffusion models to multivariate cases108
  • References113
  • Chapter 3. Modeling Financial Security Returns Using Lévy Processes117
  • 1. Introduction117
  • 2. Modeling return innovation distribution using Lévy processes120
  • 3. Generating stochastic volatility by applying stochastic time changes127
  • 4. Modeling financial security returns with time-changed Lévy processes133
  • 5. Option pricing under time-changed Lévy processes144
  • 6. Estimating Lévy processes with and without time changes155
  • 7. Concluding remarks159
  • Acknowledgements159
  • References160
  • Chapter 4. Pricing with Wishart Risk Factors163
  • 1. Introduction163
  • 2. Wishart process167
  • 3. Pricing172
  • 4. Examples175
  • 5. Concluding remarks181
  • References181
  • Chapter 5. Volatility183
  • 1. Introduction183
  • 2. A model of price formation with microstructure effects184
  • 3. The variance of the equilibrium price186
  • 4. Solutions to the inconsistency problem191
  • 5. Equilibrium price variance estimation: directions for future work202
  • 6. The variance of microstructure noise: a consistency result210
  • 7. The benefit of consistency: measuring market quality210
  • 8. Volatility and asset pricing216
  • Acknowledgements217
  • References217
  • Chapter 6. Spectral Methods in Derivatives Pricing223
  • 1. Introduction224
  • 2. Self-adjoint semigroups in Hilbert spaces230
  • 3. One-dimensional diffusions: general results237
  • 4. One-dimensional diffusions: a catalog of analytically tractable models253
  • 5. Symmetric multi-dimensional diffusions285
  • 6. Introducing jumps and stochastic volatility via time changes288
  • 7. Conclusion294
  • References294
  • Chapter 7. Variational Methods in Derivatives Pricing301
  • 1. Introduction302
  • 2. European and barrier options in the Black-Scholes-Merton model305
  • 3. American options in the Black-Scholes-Merton model315
  • 4. General multi-dimensional jump-diffusion models320
  • 5. Examples and applications329
  • 6. Summary339
  • References340
  • Chapter 8. Discrete Barrier and Lookback Options343
  • 1. Introduction343
  • 2. A representation of barrier options via the change of numeraire argument348
  • 3. Convolution, Broadie-Yamamoto method via the fast Gaussian transform, and Feng-Linetsky method vi350
  • 4. Continuity corrections355
  • 5. Perturbation method361
  • 6. A Laplace transform method via Spitzer's identity363
  • 7. Which method to use365
  • Appendix A. Proof of (1)366
  • Appendix B. Calculation of the constant beta368
  • References370
  • Part III: Interest Rate and Credit Risk Models and Derivatives375
  • Chapter 9. Topics in Interest Rate Theory377
  • 1. Introduction377
  • 2. Basics378
  • 3. Forward rate models381
  • 4. Change of numeraire387
  • 5. LIBOR market models390
  • 6. Notes400
  • 7. Geometric interest rate theory400
  • 8. Consistency and invariant manifolds401
  • 9. Existence of nonlinear realizations411
  • 10. Potentials and positive interest419
  • References434
  • Chapter 10. Calculating Portfolio Credit Risk437
  • 1. Introduction437
  • 2. Problem setting439
  • 3. Models of dependence444
  • 4. Conditional loss distributions451
  • 5. Unconditional loss distributions457
  • 6. Importance sampling462
  • 7. Summary467
  • References468
  • Chapter 11. Valuation of Basket Credit Derivatives in the Credit Migrations Environment471
  • 1. Introduction472
  • 2. Notation and preliminary results476
  • 3. Markovian market model481
  • 4. Changes of measures and Markovian numeraires485
  • 5. Valuation of single name credit derivatives492
  • 6. Valuation of basket credit derivatives497
  • 7. Model implementation500
  • References507
  • Part IV: Incomplete Markets509
  • Chapter 12. Incomplete Markets511
  • 1. Introduction511
  • 2. The over-the-counter market513
  • 3. Causes of incompleteness516
  • 4. Pricing and optimization518
  • 5. Issues in pricing and expected utility examples528
  • 6. Quadratics533
  • 7. Entropy and exponential utility536
  • 8. Loss, quantiles, and prediction537
  • 9. Pricing kernel restrictions540
  • 10. Ambiguity and robustness544
  • 11. Calibration550
  • 12. Conclusion551
  • Acknowledgements554
  • Appendix A. Definition of incompleteness and fundamental theorems554
  • Appendix B. Financial perspectives on incompleteness556
  • References558
  • Chapter 13. Option Pricing: Real and Risk-Neutral Distributions565
  • 1. Introduction566
  • 2. Implications of the absence of arbitrage567
  • 3. Additional restrictions implied by utility maximization570
  • 4. Special case: one period without transaction costs574
  • 5. Special case: one period with transaction costs and general payoffs578
  • 6. Special case: two periods without transaction costs and general payoffs579
  • 7. Special case: two periods with transaction costs and general payoffs580
  • 8. Multiple periods without transaction costs and with convex payoffs581
  • 9. Multiple periods with transaction costs and with convex payoffs583
  • 10. Empirical results585
  • 11. Concluding remarks588
  • Acknowledgements589
  • References589
  • Chapter 14. Total Risk Minimization Using Monte Carlo Simulations593
  • 1. Introduction593
  • 2. Discrete hedging criteria599
  • 3. Total risk minimization in the Black-Scholes framework603
  • 4. Total risk minimization in a stochastic volatility framework618
  • 5. Shortfall risk minimization625
  • 6. Conclusions632
  • References634
  • Chapter 15. Queuing Theoretic Approaches to Financial Price Fluctuations637
  • 1. Introduction638
  • 2. Agent-based models of financial markets639
  • 3. Microstructure models with inert investors649
  • 4. Outlook and conclusion671
  • Acknowledgements674
  • References674
  • Part V: Risk Management679
  • Chapter 16. Economic Credit Capital Allocation and Risk Contributions681
  • 1. Introduction682
  • 2. Credit portfolio models and general framework684
  • 3. Capital allocation and risk contributions688
  • 4. Credit risk contributions in analytical models693
  • 5. Numerical methods to compute risk contributions701
  • 6. Case studies706
  • 7. Summary and further research717
  • Appendix A721
  • References724
  • Chapter 17. Liquidity Risk and Option Pricing Theory727
  • 1. Introduction727
  • 2. The model729
  • 3. The extended first fundamental theorem733
  • 4. The extended second fundamental theorem735
  • 5. Example (extended Black-Scholes economy)741
  • 6. Economies with supply curves for derivatives743
  • 7. Transaction costs745
  • 8. Examples of supply curves747
  • 9. Conclusion751
  • Acknowledgement751
  • Appendix A751
  • References761
  • Chapter 18. Financial Engineering: Applications in Insurance763
  • 1. Introduction763
  • 2. Insurance products and markets765
  • 3. Premium principles and risk measures768
  • 4. Risk management for life insurance770
  • 5. Variable annuities775
  • 6. Guaranteed annuity options781
  • 7. Conclusions784
  • Acknowledgements784
  • References785
  • Part VI: Portfolio Optimization787
  • Chapter 19. Dynamic Portfolio Choice and Risk Aversion789
  • 1. Introduction789
  • 2. Optimality and state pricing793
  • 3. Recursive utility804
  • 4. Modeling risk aversion814
  • 5. Scale-invariant solutions821
  • 6. Extensions833
  • Acknowledgements839
  • References839
  • Chapter 20. Optimization Methods in Dynamic Portfolio Management845
  • 1. Introduction845
  • 2. Formulation846
  • 3. Approximation methods849
  • 4. Solution methods857
  • 5. Extensions and conclusions860
  • Acknowledgements861
  • References861
  • Chapter 21. Simulation Methods for Optimal Portfolios867
  • 1. Introduction867
  • 2. The consumption-portfolio choice problem869
  • 3. Simulation methods for portfolio computation878
  • 4. Asymptotic properties of portfolio estimators887
  • 5. Performance evaluation: a numerical study903
  • 6. Conclusion907
  • Acknowledgement909
  • Appendix A. An introduction to Malliavin calculus909
  • Appendix B. Proofs915
  • References922
  • Chapter 22. Duality Theory and Approximate Dynamic Programming for Pricing American Options and Port925
  • 1. Introduction925
  • 2. Pricing American options927
  • 3. Portfolio optimization937
  • References947
  • Chapter 23. Asset Allocation with Multivariate Non-Gaussian Returns949
  • 1. Introduction949
  • 2. Non-Gaussian investment951
  • 3. Modeling distributions953
  • 4. Exponential utility and investment in zero cost VG cash flows955
  • 5. Identifying the joint distribution of returns958
  • 6. Non-Gaussian and Gaussian investment compared960
  • 7. Conclusion962
  • Appendix A. Formal analysis of skewness preference and kurtosis aversion963
  • Appendix B. Proof of Theorem 4.1964
  • Appendix C. Proof of Theorem 4.2966
  • References968
  • Chapter 24. Large Deviation Techniques and Financial Applications971
  • 1. Introduction971
  • 2. Large deviation techniques972
  • 3. Applications to portfolio management979
  • 4. Tail risk of portfolios986
  • 5. Application to simulation987
  • 6. Incomplete markets992
  • 7. Conclusions and potential topics for future research997
  • Acknowledgements998
  • References998
  • Subject Index1001
Book details
  • Vendor Elsevier S & T
  • SKU 9780444517814
  • ISBN-13 9780080553252
  • Author Birge, John R.; Linetsky, Vadim
  • Category Business & Economics
  • Subject Operations Research

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The remarkable growth of financial markets over the past decades has been accompanied by an equally remarkable explosion in financial engineering, the interdisciplinary field focusing on applications of mathematical and statistical modeling and computational technology to problems in the financial services industry. The goals of financial engineering research are to develop empirically realistic stochastic models describing dynamics of financial risk variables, such as asset prices, foreign exchange rates, and interest rates, and to develop analytical, computational and statistical methods and tools to implement the models and employ them to design and evaluate financial products and processes to manage risk and to meet financial goals. This handbook describes the latest developments in this rapidly evolving field in the areas of modeling and pricing financial derivatives, building models of interest rates and credit risk, pricing and hedging in incomplete markets, risk management, and portfolio optimization. Leading researchers in each of these areas provide their perspective on the state of the art in terms of analysis, computation, and practical relevance. The authors describe essential results to date, fundamental methods and tools, as well as new views of the existing literature, opportunities, and challenges for future research.