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Based on a criterium of mathematical simplicity and consistency withempirical market data, a stochastic volatility model has been obtained with thevolatility process driven by fractional noise. Depending on whether thestochasticity generators of log-price and volatility are independent or are thesame, two versions of the model are obtained with different leverage behavior.Here, the no-arbitrage and incompleteness properties of the model are studied.Some risk measures are also discussed in this framework.

The fractional volatility model: No-arbitrage, leverage and risk measures