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Volatility and correlation in the pricing of equity, FX, and interest-rate options

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Stochastic processes and financial applications Financial Markets and Investment Strategies Financial Risk and Volatility Modeling

Abstract

FOUNDATIONS. Volatility: Fundamental Concepts and Definitions. Variance and Mean Reversion in the Real and the Risk-Adjusted Worlds. Instantaneous and Terminal Correlations. DEALING WITH SMILES. Pricing Options in the Presence of Smiles. Tree Methodologies for Smiley Option Prices. Efficient Extraction of the Future Local Volatility from Plain-Vanilla Option Prices. Closed-Form Solutions for Smiley Option Prices via Direct Modelling of the Density. Explaining Smiles by Means of Mixed Jump-Diffusion Processes. INTEREST RATES. The Role of Mean Reversion in Interest-Rate Models. Optimal Calibration of the Brace-Gatarek-Musiela Model. Specifying the Instantaneous Volatility of Forward Rates. References. Index.

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