Volatility and Correlation

Abstract

Why a Second Edition. What This Book Is Not About. The New Sub--Title. I Foundations. 1 Theory and Practice of Option Modelling. 2 Option Replication. 3 The Building Blocks. 4 Variance and Mean Reversion in the Real and the Risk--Adjusted Worlds. 5 Instantaneous and Terminal Correlation. II Smiles -- Equity and FX. 6 Pricing Options in the Presence of Smiles. 7 Empirical Facts about Smiles. 8 General Features of Smile--Modelling Approaches. 9 The Input Data: Fitting an Exogenous Smile Surface. 10 Quadratic Variation and Smiles. 11 Local--Volatility Models: the Derman--and--Kani Approach. 12 Extracting the Local Volatility from Option Prices. 13 Stochastic--Volatility Processes. 14 Jump--Diffusion Processes. 15 Variance--Gamma. 16 Displaced Diffusions and Generalizations. 17 No--Arbitrage Restrictions on the Dynamics of Smile Surfaces. III Interest Rates -- Deterministic Volatilities. 18 Mean Reversion in Interest--Rate Models. 19 Volatility and Correlation in the LIBOR Market Model. 20 Calibration Strategies for the LIBOR Market Model. 21 Specifying the Instantaneous Volatility of Forward Rates. 22 Specifying the Instantaneous Correlation Among Forward Rates. IV Interest Rates -- Smiles. 23 How To Model Interest--Rate Smiles. 24 Constant--Elasticity--of--Variance (CEV) Processes in the Context of the LMM. 25 Stochastic--Volatility Extensions of the LIBOR Market Model. 26 The Dynamics of the Swaption Matrix. 27 Stochastic--Volatility Extension of the LMM: Two--Regime Instantaneous Volatility. Bibliography. Index.

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