Local-stochastic volatility: models and non-models

Lorenzo Bergomi exposes a condition important to the use of LSV models in trading

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Lorenzo Bergomi examines local-stochastic volatility models and derives a simple condition such models must obey so the carry profit and loss of a delta-hedged/vega-hedged position makes sense in a trading context. This article gives examples of admissible and non-admissible models and discusses the issue of the delta position in the hedge portfolio. It ends with a characterisation of the breakeven levels of the local volatility model, which is itself in the

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