| Description |
1 online resource (xxii, 303 pages) : illustrations (some color) |
| Contents |
1. Stochastic volatility. 1.1. Introduction. 1.2. Non-stochastic volatilities 1.3. Stochastic volatility. 1.4. Summary -- 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. Lévy-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. 2.11. Mean-reverting stochastic volatility model (continuous-time GARCH model) in energy markets. 2.12. Summary -- 3. Swaps. 3.1. Introduction. 3.2. Definitions of swaps. 3.3. Summary -- 4. Change of time methods. 4.1. Introduction. 4.2. Descriptions of the change of time methods. 4.3. Applications of change of time method. 4.4. Different settings of the change of time method. 4.5. Summary -- 5. Black-Scholes formula by change of time method. 5.1. Introduction. 5.2. Black-Scholes formula by change of time method. 5.3. Black-Scholes formula by change of time method. 5.4. Summary -- 6. Modeling and pricing of swaps for Heston model. 6.1. Introduction. 6.2. Variance and volatility swaps. 6.3. Covariance and correlation swaps for two assets with stochastic volatilities. 6.4. Numerical example: S & P60 Canada index. 6.5. Summary -- 7. Modeling and pricing of variance swaps for stochastic volatilities with delay. 7.1. Introduction. 7.2. Variance swaps. 7.3. Numerical example 1: S & P60 Canada index. 7.4. Numerical example 2: S & P500 index. 7.5. Summary -- 8. Modeling and pricing of variance swaps for multi-factor stochastic volatilities with delay. 8.1. Introduction. 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. 8.5. Numerical example 1: S & P60 Canada index. 8.6. Summary |
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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. 9.4. Delay as a measure of risk. 9.5. Numerical example. 9.6. Summary -- 10. Variance swap for local Lévy-based stochastic volatility with delay. 10.1. Introduction. 10.2. Variance swap for Lévy-based stochastic volatility with delay. 10.3. Examples. 10.4. Parameter estimation. 10.5. Numerical example: S & P500 (2000-01-01 -- 2009-12-31). 10.6. Summary -- 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 -- 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 -- 13. Pricing of variance and volatility swaps with semi-Markov volatilities. 13.1. Introduction. 13.2. Martingale characterization of semi-Markov processes. 13.3. Minimal risk-neutral (Martingale) measure for stock price with semi-Markov stochastic volatility. 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. 13.7. Discussions of some extensions. 13.8. Summary -- 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. 14.4. Covariance and correlation swaps for a two risky assets for financial markets with Markov-modulated stochastic volatilities. 14.5. Example: variance, volatility, covariance and correlation swaps for stochastic volatility driven by two-state continuous Markov chain. 14.6. Numerical example. 14.7. Correlation swaps: first order correction. 14.8. Summary |
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15. Volatility and variance swaps for the COGARCH(1,1) model. 15.1. Introduction. 15.2. Lévy processes. 15.3. The COGARCH process of Klüppelberg et al. 15.4. Pricing variance and volatility swaps under the COGARCH(1,1) model. 15.5. Formula for [symbol] and [symbol]. 15.6. Summary -- 16. Variance and volatility swaps for volatilities driven by fractional Brownian motion. 16.1. Introduction. 16.2. Variance and volatility swaps. 16.3. Fractional Brownian motion and financial markets with long-range dependence. 16.4. Modeling of financial markets with stochastic volatilities driven by fractional Brownian motion (fBm). 16.5. Pricing of variance swaps. 16.6. Pricing of volatility swaps. 16.7. Discussion: asymptotic results for the pricing of variance swaps with zero risk-free rate when the expiration date increases. 16.8. Summary -- 17. Variance and volatility swaps in energy markets. 17.1. Introduction. 17.2. Mean-reverting stochastic volatility model (MRSVM). 17.3. Variance swap for MRSVM. 17.4. Volatility swap for MRSVM. 17.5. Mean-reverting risk-neutral stochastic volatility model. 17.6. Summary -- 18. Explicit option pricing formula for a mean-reverting asset in energy markets. 18.1. Introduction. 18.2. Mean-reverting asset model (MRAM). 18.3. Explicit option pricing formula for european call option for MRAM under physical measure. 18.4. Mean-reverting risk-neutral asset model (MRRNAM). 18.5. Explicit option pricing formula for European call option for MRRNAM. 18.6. Numerical example: AECO Natural GAS Index (1 May 1998 -- 30 April 1999). 18.7. Summary -- 19. Forward and futures in energy markets: multi-factor Lévy models. 19.1. Introduction. 19.2. [symbol]-stable Lévy processes and their properties. 19.3. Stochastic differential equations driven by [symbol]-stable Lévy processes. 19.4. Change of time method (CTM) for SDEs driven by Lévy processes. 19.5. Applications in energy markets. 19.6. Summary -- 20. Generalization of Black-76 formula: Markov-modulated volatility. 20.1 Introduction. 20.2 Generalization of Black-76 formula with Markov-modulated volatility. 20.3. Numerical results for synthetic data. 20.4. Applications: data from Nordpool. 20.5. Summary |
| Summary |
Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities is devoted to the modeling and pricing of various kinds of swaps, such as those for variance, volatility, covariance, correlation, for financial and energy markets with different stochastic volatilities, which include CIR process, regime-switching, delayed, mean-reverting, multi-factor, fractional, Lévy-based, semi-Markov and COGARCH(1,1). One of the main methods used in this book is change of time method. The book outlines how the change of time method works for different kinds of models and problems arising in financial and energy markets and the associated problems in modeling and pricing of a variety of swaps. The book also contains a study of a new model, the delayed Heston model, which improves the volatility surface fitting as compared with the classical Heston model. The author calculates variance and volatility swaps for this model and provides hedging techniques. The book considers content on the pricing of variance and volatility swaps and option pricing formula for mean-reverting models in energy markets. Some topics such as forward and futures in energy markets priced by multi-factor Lévy models and generalization of Black-76 formula with Markov-modulated volatility are part of the book as well, and it includes many numerical examples such as S & P60 Canada Index, S & P500 Index and AECO Natural Gas Index |
| Bibliography |
Includes bibliographical references and index |
| Subject |
Swaps (Finance) -- Mathematical models
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Finance -- Mathematical models.
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Stochastic processes.
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Stochastic Processes
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BUSINESS & ECONOMICS -- Investments & Securities -- General.
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Finance -- Mathematical models
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Stochastic processes
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Swaps (Finance) -- Mathematical models
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| Form |
Electronic book
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| Author |
World Scientific (Firm)
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| ISBN |
9789814440134 |
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9814440132 |
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