Stochastic volatility modeling. (2016)

• Record Type: Book
• Further Information: Note: Lorenzo Bergomi.
• Authors: Bergomi, Lorenzo
• Contents: Introduction; Characterizing a usable model: the Black-Scholes equation; How (in)effective is delta hedging?; On the way to stochastic volatility; Chapter’s digest Local Volatility; Introduction: local volatility as a market model; From prices to local volatilities; From implied volatilities to local volatilities; From local volatilities to implied volatilities; The dynamics of the local volatility model; Future skews and volatilities of volatilities; Delta and carry P&L; Digression: using payoff-dependent break-even levels; The vega hedge; Markov-functional models; Appendix A: the uncertain volatility model; Chapter’s digest Forward-Start Options; Pricing and hedging forward-start options; Forward-start options in the local volatility model; Chapter’s digest Stochastic Volatility: Introduction; Modeling vanilla option prices; Modeling the dynamics of the local volatility function; Modeling implied volatilities of power payoffs; Chapter’s digest Variance Swaps; Variance swap forward variances; Relationship of variance swaps to log contracts; Impact of large returns; Impact of strike discreteness; Conclusion; Dividends; Pricing variance swaps with a PDE; Interest-rate volatility; Weighted variance swaps; Appendix A: timer options; Appendix B: perturbation of the lognormal distribution; Chapter’s digest An Example of One-Factor Dynamics: The Heston Model; The Heston model; Forward variances in the Heston model; Drift of Vt in first-generation stochastic volatility models; Term structure of volatilities of volatilities in the Heston model; Smile of volatility of volatility; ATMF skew in the Heston model; Discussion; Chapter’s digest Forward Variance Models; Pricing equation; A Markov representation; N -factor models; A two-factor model; Calibration: the vanilla smile; Options on realized variance; VIX futures and options; Discrete forward variance models; Chapter’s digest The Smile of Stochastic Volatility Models; Introduction; Expansion of the price in volatility of volatility; Expansion of implied volatilities; A representation of European option prices in diffusive models; Short maturities; A family of one-factor models: application to the Heston model; The two-factor model; Conclusion; Forward-start options: future smiles; Impact of the smile of volatility of volatility on the vanilla smile; Appendix A: Monte Carlo algorithms for vanilla smiles; Appendix B: local volatility function of stochastic volatility models; Appendix C: partial resummation of higher orders; Chapter’s digest Linking Static and Dynamic Properties of Stochastic Volatility Models; The ATMF skew; The Skew Stickiness Ratio (SSR); Short-maturity limit of the ATMF skew and the SSR; Model-independent range of the SSR; Scaling of ATMF skew and SSR: a classification of models; Type I models: the Heston model; Type II models; Numerical evaluation of the SSR; The SSR for short maturities; Arbitraging the realized short SSR; Conclusion; Chapter’s digest What Causes Equity Smiles?; The distribution of equity returns; Impact of the distribution of daily returns on derivative prices; Appendix A: jump-diffusion/Lévy models; Chapter’s digest Multi-Asset Stochastic Volatility; The short ATMF basket skew; Parametrizing multi-asset stochastic volatility models; The ATMF basket skew; The correlation swap; Conclusion; Appendix A: bias/standard deviation of the correlation estimator; Chapter’s digest Local-Stochastic Volatility Models; Introduction; Pricing equation and calibration; Usable models; Dynamics of implied volatilities; Numerical examples; Discussion; Conclusion; Appendix A: alternative schemes for the PDE method; Chapter’s digest Epilogue Bibliography Index
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2016
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 332.632220151922; Securities -- Mathematical models; Stochastic models
• Languages: English
• ISBNs: 9781482244076
• Related ISBNs: 9781482244069
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; item not viewed.
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