Elsevier S & T

Advanced Derivatives Pricing and Risk Management: Theory, Tools, and Hands-On Programming Applications

Albanese, Claudio; Campolieti, Giuseppe

In stock
No reviews
44.000 KD inc. VAT
License
Table of contents
  • Contentsv
  • Prefacexi
  • PART I: Pricing Theory and Risk Management1
  • Chapter 1. Pricing Theory3
  • 1.1 Single-Period Finite Financial Models6
  • 1.2 Continuous State Spaces12
  • 1.3 Multivariate Continuous Distributions: Basic Tools16
  • 1.4 Brownian Motion, Martingales, and Stochastic Integrals23
  • 1.5 Stochastic Differential Equations and Itô’s Formula32
  • 1.6 Geometric Brownian Motion37
  • 1.7 Forwards and European Calls and Puts46
  • 1.8 Static Hedging and Replication of Exotic Pay-Offs52
  • 1.9 Continuous-Time Financial Models59
  • 1.10 Dynamic Hedging and Derivative Asset Pricing in Continuous Time65
  • 1.11 Hedging with Forwards and Futures71
  • 1.12 Pricing Formulas of the Black–Scholes Type77
  • 1.13 Partial Differential Equations for Pricing Functions and Kernels88
  • 1.14 American Options93
  • Chapter 2. Fixed-Income Instruments113
  • 2.1 Bonds, Futures, Forwards, and Swaps113
  • 2.2 Pricing Measures and Black–Scholes Formulas120
  • 2.3 One-Factor Models for the Short Rate127
  • 2.4 Multifactor Models141
  • 2.5 Real-World Interest Rate Models146
  • Chapter 3. Advanced Topics in Pricing Theory: Exotic Options and State-Dependent Models149
  • 3.1 Introduction to Barrier Options151
  • 3.2 Single-Barrier Kernels for the Simplest Model: The Wiener Process152
  • 3.3 Pricing Kernels and European Barrier Option Formulas for Geometric Brownian Motion160
  • 3.4 First-Passage Time168
  • 3.5 Pricing Kernels and Barrier Option Formulas for Linear and Quadratic Volatiltiy Models172
  • 3.6 Green’s Functions Method for Diffusion Kernels189
  • 3.7 Kernels for the Bessel Process199
  • 3.8 New Families of Analytical Pricing Formulas: From x-Space to F-SpaceŽ210
  • 3.9 Appendix A: Proof of Lemma 3.1232
  • 3.10 Appendix B: Alternative ProofŽ of Theorem 3.1233
  • 3.11 Appendix C: Some Properties of Bessel Functions235
  • Chapter 4. Numerical Methods for Value-at-Risk239
  • 4.1 Risk-Factor Models243
  • 4.2 Portfolio Models251
  • 4.3 Statistical Estimations for -Portfolios255
  • 4.4 Numerical Methods for -Portfolios261
  • 4.5 The Fast Convolution Method268
  • 4.6 Examples281
  • 4.7 Risk-Factor Aggregation and Dimension Reduction294
  • 4.8 Perturbation Theory306
  • PART II: Numerical Projects in Pricing and Risk Management313
  • Chapter 5. Project: Arbitrage Theory315
  • 5.1 Basic Terminology and Concepts: Asset Prices, States, Returns, and Pay-Offs315
  • 5.2 Arbitrage Portfolios and the Arbitrage Theorem317
  • 5.3 An Example of Single-Period Asset Pricing: Risk-Neutral Probabilities and Arbitrage318
  • 5.4 Arbitrage Detection and the Formation of Arbitrage Portfolios in the N-Dimensional Case319
  • Chapter 6. Project: The Black–Scholes (Lognormal) Model321
  • 6.1 Black–Scholes Pricing Formula321
  • 6.2 Black–Scholes Sensitivity Analysis325
  • Chapter 7. Project: Quantile-Quantile Plots327
  • 7.1 Log-Returns and Standardization327
  • 7.2 Quantile-Quantile Plots328
  • Chapter 8. Project: Monte Carlo Pricer331
  • 8.1 Scenario Generation331
  • 8.2 Calibration332
  • 8.3 Pricing Equity Basket Options333
  • Chapter 9. Project: The Binomial Lattice Model337
  • 9.1 Building the Lattice337
  • 9.2 Lattice Calibration and Pricing339
  • Chapter 10. Project: The Trinomial Lattice Model341
  • 10.1 Building the Lattice341
  • 10.2 Pricing Procedure344
  • 10.3 Calibration346
  • 10.4 Pricing Barrier Options346
  • 10.5 Put-Call Parity in Trinomial Lattices347
  • 10.6 Computing the Sensitivities348
  • Chapter 11. Project: Crank–Nicolson Option Pricer349
  • 11.1 The Lattice for the Crank–Nicolson Pricer349
  • 11.2 Pricing with Crank–Nicolson350
  • 11.3 Calibration351
  • 11.4 Pricing Barrier Options352
  • Chapter 12. Project: Static Hedging of Barrier Options355
  • 12.1 Analytical Pricing Formulas for Barrier Options355
  • 12.2 Replication of Up-and-Out Barrier Options358
  • 12.3 Replication of Down-and-Out Barrier Options361
  • Chapter 13. Project: Variance Swaps363
  • 13.1 The Logarithmic Pay-Off363
  • 13.2 Static Hedging: Replication of a Logarithmic Pay-Off364
  • Chapter 14. Project: Monte Carlo Value-at-Risk for Delta-Gamma Portfolios369
  • 14.1 Multivariate Normal Distribution369
  • 14.2 Multivariate Student t-Distributions371
  • Chapter 15. Project: Covariance Estimation and Scenario Generation in Value-at-Risk375
  • 15.1 Generating Covariance Matrices of a Given Spectrum375
  • 15.2 Reestimating the Covariance Matrix and the Spectral Shift376
  • Chapter 16. Project: Interest Rate Trees: Calibration379
  • 16.1 Background Theory379
  • 16.2 Binomial Lattice Calibration for Discount Bonds381
  • 16.3 Binomial Pricing of Forward Rate Agreements, Swaps, Caplets, Floorlets, Swaptions, and Other De384
  • 16.4 Trinomial Lattice Calibration and Pricing in the Hull–White Model389
  • 16.5 Calibration and Pricing within the Black–Karasinski Model396
  • Bibliography399
  • Index407
Book details
  • Vendor Elsevier S & T
  • SKU 9780120476824
  • ISBN-13 9780080488097
  • Author Albanese, Claudio; Campolieti, Giuseppe
  • Category Business & Economics
  • Subject Finance

Do you have questions about this book?

Ask an expert!

Description eBook delivery & access Reviews
Written by leading academics and practitioners in the field of financial mathematics, the purpose of this book is to provide a unique combination of some of the most important and relevant theoretical and practical tools from which any advanced undergraduate and graduate student, professional quant and researcher will benefit. This book stands out from all other existing books in quantitative finance from the sheer impressive range of ready-to-use software and accessible theoretical tools that are provided as a complete package. By proceeding from simple to complex, the authors cover core topics in derivative pricing and risk management in a style that is engaging, accessible and self-instructional. The book contains a wide spectrum of problems, worked-out solutions, detailed methodologies and applied mathematical techniques for which anyone planning to make a serious career in quantitative finance must master. In fact, core portions of the book’s material originated and evolved after years of classroom lectures and computer laboratory courses taught in a world-renowned professional Master’s program in mathematical finance. As a bonus to the reader, the book also gives a detailed exposition on new cutting-edge theoretical techniques with many results in pricing theory that are published here for the first time.

*Includes easy-to-implement VB/VBA numerical software libraries
*Proceeds from simple to complex in approaching pricing and risk management problems
*Provides analytical methods to derive cutting-edge pricing formulas for equity derivatives