Abstract
The previous chapters provide empirical evidence that models with stochastic volatility outperform their deterministic counterpart. In Chap. 1, the multifractal process competes with GARCH models, whereas the Heston model of Chap. 3 achieves a better likelihood than the Black and Scholes model. On the other hand, models based on fractional Brownian motion (fBm) have emerged in recent years. For instance, in the rough Heston model, the volatility is mean reverting and ruled by an fBm. This model belongs to the class of Volterra processes that are introduced in Chap. 9. Fractional Brownian motion is also a particular type of Gaussian field. These Gaussian fields are developed in Chap. 7. This motivates us to review the main properties of fBm.
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Hainaut, D. (2022). Fractional Brownian Motion. In: Continuous Time Processes for Finance. Bocconi & Springer Series, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-031-06361-9_6
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