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/Levy 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.