Stochastic Volatility Modeling
Chapman and Hall/CRC Financial Mathematics Series

Packed with insights, Lorenzo Bergomi?s Stochastic Volatility Modeling explains how stochastic volatility is used to address issues arising in the modeling of derivatives, including:

• Which trading issues do we tackle with stochastic volatility?
• How do we design models and assess their relevance?
• How do we tell which models are usable and when does calibration make sense?

This manual covers the practicalities of modeling local volatility, stochastic volatility, local-stochastic volatility, and multi-asset stochastic volatility. In the course of this exploration, the author, Risk?s 2009 Quant of the Year and a leading contributor to volatility modeling, draws on his experience as head quant in Société Générale?s equity derivatives division. Clear and straightforward, the book takes readers through various modeling challenges, all originating in actual trading/hedging issues, with a focus on the practical consequences of modeling choices.

Introduction. Local volatility. Forward-start options. Stochastic volatility: introduction. Variance swaps. An example of one-factor dynamics: the Heston model. Forward variance models. The smile of stochastic volatility models. Linking static and dynamic properties of stochastic volatility models. What causes equity smiles? Multi-asset stochastic volatility. Local-stochastic volatility models.

Lorenzo Bergomi heads the quantitative research group at Société Générale, covering all asset classes. A quant for over 15 years, he is well known for his pioneering work on stochastic volatility modeling, some of which has appeared in the Smile Dynamics series of articles in Risk magazine. He was also the magazine’s 2009 Quant of the Year. Originally trained as an electrical engineer and with a PhD in theoretical physics, he was active as a physicist in the condensed matter theory group at IphT, CEA, before moving to finance.