Contents -- Preface -- Acknowledgments -- 1. Stochastic Volatility -- 1.1 Introduction -- 1.2 Non-Stochastic Volatilities -- 1.2.1 Historical Volatility -- 1.2.2 Implied Volatility -- 1.2.3 Level-Dependent Volatility and Local Volatility -- 1.3 Stochastic Volatility -- 1.3.1 Approaches to Introduce Stochastic Volatility -- 1.3.2 Discrete Models for Stochastic Volatility -- 1.3.3 Jump-Diffusion Volatility -- 1.3.4 Multi-Factor Models for Stochastic Volatility -- 1.4 Summary -- Bibliography -- 2. Stochastic Volatility Models -- 2.1 Introduction -- 2.2 Heston Stochastic Volatility Model -- 2.3 Stochastic Volatility with Delay -- 2.4 Multi-Factor Stochastic Volatility Models -- 2.5 Stochastic Volatility Models with Delay and Jumps -- 2.6 Levy-Based Stochastic Volatility with Delay -- 2.7 Delayed Heston Model -- 2.8 Semi-Markov-Modulated Stochastic Volatility -- 2.9 COGARCH(1,1) Stochastic Volatility Model -- 2.10 Stochastic Volatility Driven by Fractional Brownian Motion -- 2.10.1 Stochastic Volatility Driven by Fractional Ornstein-Uhlenbeck Process -- 2.10.2 Stochastic Volatility Driven by Fractional Vasicek Process -- 2.10.3 Markets with Stochastic Volatility Driven by Geometric Fractional Brownian Motion -- 2.10.4 Stochastic Volatility Driven by Fractional Continuous- Time GARCH Process -- 2.11 Mean-Reverting Stochastic Volatility Model (Continuous-Time GARCH Model) in Energy Markets -- 2.12 Summary -- Bibliography -- 3. Swaps -- 3.1 Introduction -- 3.2 Definitions of Swaps -- 3.2.1 Variance and Volatility Swaps -- 3.2.2 Covariance and Correlation Swaps -- 3.2.3 Pseudo-Swaps -- 3.3 Summary -- Bibliography -- 4. Change of Time Methods -- 4.1 Introduction -- 4.2 Descriptions of the Change of Time Methods -- 4.2.1 The General Theory of Time Changes -- 4.2.1.1 Martingale and Semimartingale Settings of Change of Time.

4.2.1.2 Stochastic Differential Equations Setting of Change of Time -- 4.2.2 Subordinators as Time Changes -- 4.2.2.1 Subordinators -- 4.2.2.2 Subordinators and Stochastic Volatility -- 4.3 Applications of Change of Time Method -- 4.3.1 Black-Scholes by Change of Time Method -- 4.3.2 An Option Pricing Formula for a Mean-Reverting Asset Model Using a Change of Time Method -- 4.3.3 Swaps by Change of Time Method in Classical Heston Model -- 4.3.4 Swaps by Change of Time Method in Delayed Heston Model -- 4.4 Different Settings of the Change of Time Method -- 4.4.0.1 Change of Time Method in Martingale Setting -- 4.4.0.2 Change of Time Method in Stochastic Differential Equation Setting -- 4.4.0.3 Examples: Solutions of Some SDEs17 -- 4.5 Summary -- Bibliography -- 5. Black-Scholes Formula by Change of Time Method -- 5.1 Introduction -- 5.2 Black-Scholes Formula by Change of Time Method -- 5.2.1 Black-Scholes Formula -- 5.2.2 Solution of SDE for Geometric Brownian Motion using Change of Time Method -- 5.2.3 Properties of the Process W ( t-1) -- 5.3 Black-Scholes Formula by Change of Time Method -- 5.4 Summary -- Bibliography -- 6. Modeling and Pricing of Swaps for Heston Model -- 6.1 Introduction -- 6.2 Variance and Volatility Swaps -- 6.2.1 Variance and Volatility Swaps for Heston Model -- 6.2.1.1 Stochastic Volatility Model -- 6.2.1.2 Explicit Expression for t2 -- 6.2.1.3 Properties of Processes w2( t-1) and t2 -- 6.2.1.4 Valuing Variance and Volatility Swaps -- 6.2.1.5 Calculation of E{V} in Discrete Case -- 6.3 Covariance and Correlation Swaps for Two Assets with Stochastic Volatilities -- 6.3.1 Definitions of Covariance and Correlation Swaps -- 6.3.2 Valuing of Covariance and Correlation Swaps -- 6.3.3 Variance Swaps for Levy-Based Heston Model -- 6.4 Numerical Example: S&P60 Canada Index -- 6.5 Summary -- Bibliography.

7. Modeling and Pricing of Variance Swaps for Stochastic Volatilities with Delay -- 7.1 Introduction -- 7.2 Variance Swaps -- 7.2.1 Modeling of Financial Markets with Stochastic Volatility with Delay -- 7.2.1.1 Model of Financial Markets with Delay -- 7.2.1.2 Continuous-time GARCH model for Stochastic Volatility with Delay -- 7.2.2 Variance Swaps for Stochastic Volatility with Delay -- 7.2.2.1 Key Features of Stochastic Volatility Model with Delay -- 7.2.2.2 Valuing of Variance Swaps with Delay in Stationary Regime under Risk-Neutral Measure -- 7.2.2.3 Valuing of Variance Swaps with Delay in General Case -- 7.2.3 Delay as A Measure of Risk -- 7.2.4 Comparison of Stochastic Volatility in Heston Model and Stochastic Volatility with Delay -- 7.3 Numerical Example 1: S&P60 Canada Index -- 7.4 Numerical Example 2: S&P500 Index -- 7.5 Summary -- Bibliography -- 8. Modeling and Pricing of Variance Swaps for Multi-Factor Stochastic Volatilities with Delay -- 8.1 Introduction -- 8.1.1 Variance Swaps -- 8.1.2 Volatility -- 8.2 Multi-Factor Models -- 8.3 Multi-Factor Stochastic Volatility Models with Delay -- 8.4 Pricing of Variance Swaps for Multi-Factor Stochastic Volatility Models with Delay -- 8.4.1 Pricing of Variance Swap for Two-Factor Stochastic Volatility Model with Delay and with Geometric Brownian Motion Mean-Reversion -- 8.4.2 Pricing of Variance Swap for Two-Factor Stochastic Volatility Model with Delay and with Ornstein-Uhlenbeck Mean-Reversion -- 8.4.3 Pricing of Variance Swap for Two-Factor Stochastic Volatility Model with Delay and with Pilipovic One-Factor Mean-Reversion -- 8.4.4 Variance Swap for Three-Factor Stochastic Volatility Model with Delay and with Pilipovic Mean-Reversion -- 8.5 Numerical Example 1: S&P60 Canada Index -- 8.6 Summary -- Bibliography -- 9. Pricing Variance Swaps for Stochastic Volatilities with Delay and Jumps.

9.1 Introduction -- 9.2 Stochastic Volatility with Delay -- 9.3 Pricing Model of Variance Swaps for Stochastic Volatility with Delay and Jumps -- 9.3.1 Simple Poisson Process Case -- 9.3.2 Compound Poisson Process Case -- 9.3.3 More General Case -- 9.4 Delay as a Measure of Risk -- 9.5 Numerical Example -- 9.6 Summary -- Bibliography -- 10. Variance Swap for Local Levy-Based Stochastic Volatility with Delay -- 10.1 Introduction -- 10.2 Variance Swap for Levy-Based Stochastic Volatility with Delay -- 10.3 Examples -- 10.3.1 Example 1 (Variance Gamma) -- 10.3.2 Example 2 (Tempered Stable) -- 10.3.3 Example 3 (Jump-Diffusion) -- 10.3.4 Example 4 (Kou's Jump-Diffusion) -- 10.4 Parameter Estimation -- 10.5 Numerical Example: S&P500 (2000-01-01{2009-12-31) -- 10.6 Summary -- Bibliography -- 11. Delayed Heston Model: Improvement of the Volatility Surface Fitting -- 11.1 Introduction -- 11.2 Modeling of Delayed Heston Stochastic Volatility -- 11.3 Model Calibration -- 11.4 Numerical Results -- 11.5 Summary -- Bibliography -- 12. Pricing and Hedging of Volatility Swap in the Delayed Heston Model -- 12.1 Introduction -- 12.2 Modeling of Delayed Heston Stochastic Volatility: Recap -- 12.3 Pricing Variance and Volatility Swaps -- 12.4 Volatility Swap Hedging -- 12.5 Numerical Results -- 12.6 Summary -- Bibliography -- 13. Pricing of Variance and Volatility Swaps with Semi-Markov Volatilities -- 13.1 Introduction -- 13.2 Martingale Characterization of Semi-Markov Processes -- 13.2.1 Markov Renewal and Semi-Markov Processes -- 13.2.2 Jump Measure for Semi-Markov Process -- 13.2.3 Martingale Characterization of Semi-Markov Processes -- 13.3 Minimal Risk-Neutral (Martingale) Measure for Stock Price with Semi-Markov Stochastic Volatility -- 13.3.1 Current Life Stochastic Volatility Driven by Semi-Markov Process (Current Life Semi-Markov Volatility).

13.3.2 Minimal Martingale Measure -- 13.4 Pricing of Variance Swaps for Stochastic Volatility Driven by a Semi-Markov Process -- 13.5 Example of Variance Swap for Stochastic Volatility Driven by Two- State Continuous-Time Markov Chain -- 13.6 Pricing of Volatility Swaps for Stochastic Volatility Driven by a Semi-Markov Process -- 13.6.1 Volatility Swap -- 13.6.2 Pricing of Volatility Swap -- 13.7 Discussions of Some Extensions -- 13.7.1 Local Current Stochastic Volatility Driven by a Semi- Markov Process (Local Current Semi-Markov Volatility) -- 13.7.2 Local Stochastic Volatility Driven by a Semi-Markov Process (Local Semi-Markov Volatility) -- 13.7.3 Dupire Formula for Semi-Markov Local Volatility -- 13.7.4 Risk-Minimizing Strategies (or Portfolios) and Residual Risk -- 13.8 Summary -- Bibliography -- 14. Covariance and Correlation Swaps for Markov-Modulated Volatilities -- 14.1 Introduction -- 14.2 Martingale Representation of Markov Processes -- 14.3 Variance and Volatility Swaps for Financial Markets with Markov- Modulated Stochastic Volatilities -- 14.3.1 Pricing Variance Swaps -- 14.3.2 Pricing Volatility Swaps -- 14.4 Covariance and Correlation Swaps for a Two Risky Assets for Financial Markets with Markov-Modulated Stochastic Volatilities -- 14.4.1 Pricing Covariance Swaps -- 14.4.2 Pricing Correlation Swaps -- 14.4.3 Correlation Swap Made Simple -- 14.5 Example: Variance, Volatility, Covariance and Correlation Swaps for Stochastic Volatility Driven by Two-State Continuous Markov Chain -- 14.6 Numerical Example -- 14.6.1 S&P500: Variance and Volatility Swaps -- 14.6.2 S&P500 and NASDAQ-100: Covariance and Correlation Swaps -- 14.7 Correlation Swaps: First Order Correction -- 14.8 Summary -- Bibliography -- 15. Volatility and Variance Swaps for the COGARCH(1,1) Model -- 15.1 Introduction -- 15.2 Levy Processes.

15.3 The COGARCH Process of Kluppelberg et al.