Local-Stochastic Volatility: Models and Non-Models

9 Pages Posted: 21 Jan 2017 Last revised: 20 Jul 2017

Date Written: January 1, 2017

Abstract

We examine local-stochastic volatility models and derive a simple condition such models need to obey so that the carry P&L of a delta-hedged/vega-hedged position makes sense in a trading context.

We give examples of admissible and non-admissible models and discuss the issue of the delta position in the hedge portfolio.

We end with a characterization of the break-even levels of the local volatility model - itself in the admissible class.

Keywords: Local volatility, Stochastic volatility

JEL Classification: G13

Suggested Citation

Bergomi, Lorenzo, Local-Stochastic Volatility: Models and Non-Models (January 1, 2017). Available at SSRN: https://ssrn.com/abstract=2902130 or http://dx.doi.org/10.2139/ssrn.2902130

Lorenzo Bergomi (Contact Author)

Societe Generale ( email )

Paris-La Défense, Paris 92987
France

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