InhaltsangabeChapter 1 Mathematical Preliminaries. Complex Numbers. Finding Roots of Functions. OLS and WLS. NelderMead Algorithm. Maximum Likelihood Estimation. Cubic Spline Interpolation. Exercises and Solutions. Chapter 2 Numerical Integration. NewtonCoates Formulas. Implementing Newton-Coates Formulas in VBA. Gaussian Quadratures. Exercises and Solutions. Chapter 3 Tree-Based Methods. CRR Binomial Tree. LeisenReimer Binomial Tree. Edgeworth Binomial Tree. Flexible Binomial Tree. Trinomial Tree. Adaptive Mesh Method. Comparing Trees. Implied Volatility Trees. Allowing for Dividends and the Cost of Carry. Exercises and Solutions. Chapter 4 The Black-Scholes, Practitioner Black-Scholes, and Gram-Charlier Models. BlackScholes Model. Implied Volatility and the DVF. Practitioner Black-Scholes Model. GramCharlier Model. Exercises and Solutions. Chapter 5 The Heston Stochastic Volatility Model. Heston (1993) Model. Increasing Integration Accuracy. The Fundamental Tranform. Sensitivity Analysis. Exercises and Solutions. Chapter 6 The Heston and Nandi GARCH Model. Persistent Volatility in Asset Returns. GARCH Variance Modeling. Heston and Nandi (2000) Model. Exercises and Solutions. Chapter 7 The Greeks. BlackScholes Greeks. Greeks From the Trees. Greeks From the Gram-Charlier Model. Greeks From the Heston (1993) Model. Greeks From the Heston and Nandi (2000) Model. Greeks by Finite Differences. Exercises and Solutions. Chapter 8 Exotic Options. SingleBarrier Options. Digital Options. Asian Options. FloatingStrike Lookback Options. Exercises and Solutions. Chapter 9 Parameter Estimation. Unconditional Moments. Maximum Likelihood for GARCH Models. Estimation by Loss Functions. Exercises and Solutions. Chapter 10 Implied Volatility. Obtaining Implied Volatility. Explaining Smiles and Smirks Fitting the Smile with the Heston (1993) Model. Exercises and Solutions. Chapter 11 Model-Free Implied Volatility. Theoretical Foundation. Implementation. Interpolation-Extrapolation Method. ModelFree Implied Forward Volatility. The VIX Index. Exercises and Solutions. Chapter 12 Model-Free Higher Moments. Theoretical Foundation. Implementation. Verifying Implied Moments. GramCharlier Implied Moments. Exercises and Solutions. Chapter 13 Volatility Returns. Straddle Returns. DeltaHedged Gains. Volatility Exposure. Variance Swaps. Exercises and Solutions. Appendix VBA Primer.

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InhaltsangabeChapter 1 Mathematical Preliminaries. Complex Numbers. Finding Roots of Functions. OLS and WLS. NelderMead Algorithm. Maximum Likelihood Estimation. Cubic Spline Interpolation. Exercises and Solutions. Chapter 2 Numerical Integration. NewtonCoates Formulas. Implementing Newton-Coates Formulas in VBA. Gaussian Quadratures. Exercises and Solutions. Chapter 3 Tree-Based Methods. CRR Binomial Tree. LeisenReimer Binomial Tree. Edgeworth Binomial Tree. Flexible Binomial Tree. Trinomial Tree. Adaptive Mesh Method. Comparing Trees. Implied Volatility Trees. Allowing for Dividends and the Cost of Carry. Exercises and Solutions. Chapter 4 The Black-Scholes, Practitioner Black-Scholes, and Gram-Charlier Models. BlackScholes Model. Implied Volatility and the DVF. Practitioner Black-Scholes Model. GramCharlier Model. Exercises and Solutions. Chapter 5 The Heston Stochastic Volatility Model. Heston (1993) Model. Increasing Integration Accuracy. The Fundamental Tranform. Sensitivity Analysis. Exercises and Solutions. Chapter 6 The Heston and Nandi GARCH Model. Persistent Volatility in Asset Returns. GARCH Variance Modeling. Heston and Nandi (2000) Model. Exercises and Solutions. Chapter 7 The Greeks. BlackScholes Greeks. Greeks From the Trees. Greeks From the Gram-Charlier Model. Greeks From the Heston (1993) Model. Greeks From the Heston and Nandi (2000) Model. Greeks by Finite Differences. Exercises and Solutions. Chapter 8 Exotic Options. SingleBarrier Options. Digital Options. Asian Options. FloatingStrike Lookback Options. Exercises and Solutions. Chapter 9 Parameter Estimation. Unconditional Moments. Maximum Likelihood for GARCH Models. Estimation by Loss Functions. Exercises and Solutions. Chapter 10 Implied Volatility. Obtaining Implied Volatility. Explaining Smiles and Smirks Fitting the Smile with the Heston (1993) Model. Exercises and Solutions. Chapter 11 Model-Free Implied Volatility. Theoretical Foundation. Implementation. Interpolation-Extrapolation Method. ModelFree Implied Forward Volatility. The VIX Index. Exercises and Solutions. Chapter 12 Model-Free Higher Moments. Theoretical Foundation. Implementation. Verifying Implied Moments. GramCharlier Implied Moments. Exercises and Solutions. Chapter 13 Volatility Returns. Straddle Returns. DeltaHedged Gains. Volatility Exposure. Variance Swaps. Exercises and Solutions. Appendix VBA Primer.

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