ROUGH-HESTON LOCAL-VOLATILITY MODEL

DALL’ACQUA Enrico (), Riccardo Longoni () and Andrea Pallavicini
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DALL’ACQUA Enrico: Department of Mathematics, Politecnico Milano, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy
Riccardo Longoni: Financial Engineering, Intesa Sanpaolo Group, Largo Mattioli 3, 2021 Milano, Italy

International Journal of Theoretical and Applied Finance (IJTAF), 2023, vol. 26, issue 06n07, 1-18

Abstract: In industrial applications it is quite common to use stochastic-volatility models driven by semi-martingale Markov volatility processes. However, in order to fit exactly market volatilities, these models are usually extended by adding a local-volatility term. Here, we consider the case of singular Volterra processes, and we extend them by adding a local-volatility term to their Markov lift by preserving the stylized results implied by these models on plain-vanilla options. In particular, we focus on the rough-Heston model, and we analyze the small-time asymptotics of its implied local-volatility function in order to provide a proper extrapolation scheme to be used in calibration.

Keywords: Local volatility; rough volatility; rough Heston; Markovian projection; volatility skew; small-time asymptotics (search for similar items in EconPapers)
Date: 2023
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Working Paper: Rough-Heston Local-Volatility Model (2022)
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DOI: 10.1142/S0219024923500218

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