Front Cover -- Advanced Derivatives Pricing and Risk Management -- Copyright Page -- Contents -- Preface -- PART I: Pricing Theory and Risk Management -- Chapter 1. Pricing Theory -- 1.1 Single-Period Finite Financial Models -- 1.2 Continuous State Spaces -- 1.3 Multivariate Continuous Distributions: Basic Tools -- 1.4 Brownian Motion, Martingales, and Stochastic Integrals -- 1.5 Stochastic Differential Equations and Itô's Formula -- 1.6 Geometric Brownian Motion -- 1.7 Forwards and European Calls and Puts -- 1.8 Static Hedging and Replication of Exotic Pay-Offs -- 1.9 Continuous-Time Financial Models -- 1.10 Dynamic Hedging and Derivative Asset Pricing in Continuous Time -- 1.11 Hedging with Forwards and Futures -- 1.12 Pricing Formulas of the Black-Scholes Type -- 1.13 Partial Differential Equations for Pricing Functions and Kernels -- 1.14 American Options -- Chapter 2. Fixed-Income Instruments -- 2.1 Bonds, Futures, Forwards, and Swaps -- 2.2 Pricing Measures and Black-Scholes Formulas -- 2.3 One-Factor Models for the Short Rate -- 2.4 Multifactor Models -- 2.5 Real-World Interest Rate Models -- Chapter 3. Advanced Topics in Pricing Theory: Exotic Options and State-Dependent Models -- 3.1 Introduction to Barrier Options -- 3.2 Single-Barrier Kernels for the Simplest Model: The Wiener Process -- 3.3 Pricing Kernels and European Barrier Option Formulas for Geometric Brownian Motion -- 3.4 First-Passage Time -- 3.5 Pricing Kernels and Barrier Option Formulas for Linear and Quadratic Volatiltiy Models -- 3.6 Green's Functions Method for Diffusion Kernels -- 3.7 Kernels for the Bessel Process -- 3.8 New Families of Analytical Pricing Formulas: "From x-Space to F-Space" -- 3.9 Appendix A: Proof of Lemma 3.1 -- 3.10 Appendix B: Alternative "Proof" of Theorem 3.1 -- 3.11 Appendix C: Some Properties of Bessel Functions.

Chapter 4. Numerical Methods for Value-at-Risk -- 4.1 Risk-Factor Models -- 4.2 Portfolio Models -- 4.3 Statistical Estimations for -Portfolios -- 4.4 Numerical Methods for -Portfolios -- 4.5 The Fast Convolution Method -- 4.6 Examples -- 4.7 Risk-Factor Aggregation and Dimension Reduction -- 4.8 Perturbation Theory -- PART II: Numerical Projects in Pricing and Risk Management -- Chapter 5. Project: Arbitrage Theory -- 5.1 Basic Terminology and Concepts: Asset Prices, States, Returns, and Pay-Offs -- 5.2 Arbitrage Portfolios and the Arbitrage Theorem -- 5.3 An Example of Single-Period Asset Pricing: Risk-Neutral Probabilities and Arbitrage -- 5.4 Arbitrage Detection and the Formation of Arbitrage Portfolios in the N-Dimensional Case -- Chapter 6. Project: The Black-Scholes (Lognormal) Model -- 6.1 Black-Scholes Pricing Formula -- 6.2 Black-Scholes Sensitivity Analysis -- Chapter 7. Project: Quantile-Quantile Plots -- 7.1 Log-Returns and Standardization -- 7.2 Quantile-Quantile Plots -- Chapter 8. Project: Monte Carlo Pricer -- 8.1 Scenario Generation -- 8.2 Calibration -- 8.3 Pricing Equity Basket Options -- Chapter 9. Project: The Binomial Lattice Model -- 9.1 Building the Lattice -- 9.2 Lattice Calibration and Pricing -- Chapter 10. Project: The Trinomial Lattice Model -- 10.1 Building the Lattice -- 10.2 Pricing Procedure -- 10.3 Calibration -- 10.4 Pricing Barrier Options -- 10.5 Put-Call Parity in Trinomial Lattices -- 10.6 Computing the Sensitivities -- Chapter 11. Project: Crank-Nicolson Option Pricer -- 11.1 The Lattice for the Crank-Nicolson Pricer -- 11.2 Pricing with Crank-Nicolson -- 11.3 Calibration -- 11.4 Pricing Barrier Options -- Chapter 12. Project: Static Hedging of Barrier Options -- 12.1 Analytical Pricing Formulas for Barrier Options -- 12.2 Replication of Up-and-Out Barrier Options.

12.3 Replication of Down-and-Out Barrier Options -- Chapter 13. Project: Variance Swaps -- 13.1 The Logarithmic Pay-Off -- 13.2 Static Hedging: Replication of a Logarithmic Pay-Off -- Chapter 14. Project: Monte Carlo Value-at-Risk for Delta-Gamma Portfolios -- 14.1 Multivariate Normal Distribution -- 14.2 Multivariate Student t-Distributions -- Chapter 15. Project: Covariance Estimation and Scenario Generation in Value-at-Risk -- 15.1 Generating Covariance Matrices of a Given Spectrum -- 15.2 Reestimating the Covariance Matrix and the Spectral Shift -- Chapter 16. Project: Interest Rate Trees: Calibration and Pricing -- 16.1 Background Theory -- 16.2 Binomial Lattice Calibration for Discount Bonds -- 16.3 Binomial Pricing of Forward Rate Agreements, Swaps, Caplets, Floorlets, Swaptions, and Other Derivatives -- 16.4 Trinomial Lattice Calibration and Pricing in the Hull-White Model -- 16.5 Calibration and Pricing within the Black-Karasinski Model -- Bibliography -- Index.