Intro; Preface; Objectives and Audience; Guide to the Chapters; Acknowledgements; Contents; 1 Cumulant Generating Functions and Steepest Descent Method; 1.1 Characteristic Functions and Cumulant Generating Functions; 1.1.1 Generalized Fourier Transform and Characteristic Functions; 1.1.2 Laplace Transform and Cumulant Generating Functions; 1.2 Steepest Descent Method; 1.2.1 Saddlepoint and Steepest Descent Path; 1.2.2 Asymptotic Expansion of Complex Integrals; 2 Saddlepoint Approximations to Density Functions, Tail Probabilities and Tail Expectations; 2.1 Density Functions

2.1.1 Exponentially Tilted Edgeworth Expansion2.1.2 Extension to the Non-Gaussian Base; 2.2 Tail Probabilities; 2.2.1 Extension to Non-Gaussian Base; 2.2.2 Lattice Variables; 2.3 Tail Expectations; 2.3.1 Change of Measure Approach; 2.3.2 Esscher Exponential Tilting and Edgeworth Expansion; 2.3.3 Laplace Inversion Representation; 3 Extended Saddlepoint Approximation Methods; 3.1 Small Time Expansion; 3.1.1 Pure Diffusion Processes; 3.1.2 Jump-Diffusion Processes; 3.2 Affine Jump-Diffusion Processes; 4 Saddlepoint Approximation Formulas for Pricing Options

4.1 Option Prices as Complementary Probabilities4.1.1 Extension to Stochastic Volatility and Interest Rate; 4.1.2 Non-Gaussian Base; 4.2 VIX Derivatives; 4.2.1 Pricing VIX Futures; 4.2.2 Pricing VIX Options; 4.3 Options on Discrete Realized Variance; 4.3.1 Small Time Approximation; 4.3.2 Sample Calculations; 5 Saddlepoint Approximation for Credit Portfolios; 5.1 Default Correlation Models; 5.1.1 CreditRisk+; 5.1.2 Gaussian Copula Models; 5.2 Risk Measures and Risk Contributions; 5.2.1 Value-at-Risk and Expected Shortfall; 5.2.2 Risk Contributions

5.2.3 Risk Measures Calculations for Default Correlation Models5.3 Pricing of Collateralized Debt Obligations; 5.3.1 Cashflows in Different Tranches; 5.3.2 Fair Spread Rates for Tranches; Appendix References; ; Index