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Full Description
Pricing Models of Volatility Products and Exotic Variance Derivatives summarizes most of the recent research results in pricing models of derivatives on discrete realized variance and VIX. The book begins with the presentation of volatility trading and uses of variance derivatives. It then moves on to discuss the robust replication strategy of variance swaps using portfolio of options, which is one of the major milestones in pricing theory of variance derivatives. The replication procedure provides the theoretical foundation of the construction of VIX. This book provides sound arguments for formulating the pricing models of variance derivatives and establishes formal proofs of various technical results. Illustrative numerical examples are included to show accuracy and effectiveness of analytic and approximation methods.
Features
Useful for practitioners and quants in the financial industry who need to make choices between various pricing models of variance derivatives
Fabulous resource for researchers interested in pricing and hedging issues of variance derivatives and VIX products
Can be used as a university textbook in a topic course on pricing variance derivatives
Contents
1. Volatility Trading and Variance Derivatives. 1.1. Implied Volatility and Local Volatility. 1.2. Volatility Trading using Options. 1.3. Derivatives on Discrete Realized Variance. 1.4. Replication of Variance Swaps. 1.5. Practical Implementation of Replication: Finite Strikes and Discrete Monitoring. Appendix. 2. Lévy Processes and Stochastic Volatility Models. 2.1. Compound Poisson process. 2.2. Jump-diffusion Models. 2.3. Lévy Processes. 2.4. Time-changed Lévy Processes. 2.5. Stochastic Volatility Models with Jumps. 2.6. Affine Jump-diffusion Stochastic Volatility Models. 2.7. 3/2 Stochastic Volatility Model. Appendix. 3. VIX Derivatives Under Consistent Models and direct Models. 3.1. VIX, Variance Swap Rate and VIX Derivatives. 3.2. Pricing VIX Derivatives Under Consistent Models. 3.3. Direct Modeling of VIX. Appendix. 4. Swap products on discrete Variance and Volatility. 4.1. Direct Expectation of Square of Log Return. 4.2. Nested Expectation via Partial Integro-differential Equation. 4.3. Moment Generating Function Methods. 4.4. Variance Swaps Under Time-changed Lévy Processes. Appendix. 5. Options on discrete realized Variance. 5.1. Adjustment for Discretization Effect via Lognormal Approximation. 5.2. Normal Approximation to Conditional Distribution of Discrete Realized Variance. 5.3. Partially Exact and Bounded Approximation for Options on Discrete Realized Variance. 5.4. Small Time Asymptotic Approximation. 6 Timer options. 6.1. Model Formulation. 6.2. Pricing Perpetual Timer Options. 6.3. Finite Maturity Discrete Timer Options. Appendix. Bibliography. Index.
