DECOMPOSITION FORMULA FOR ROUGH VOLTERRA STOCHASTIC VOLATILITY MODELS

Raúl Merino, Jan Pospíšil, Tomáš Sobotka, Tommi Sottinen and Josep Vives
Additional contact information
Raúl Merino: Universitat de Barcelona, Facultat de Matemàtiques, Gran Via 585, 08007 Barcelona, Spain¶VidaCaixa S.A., Investment Risk Management Department, C/Juan Gris, 2-8, Barcelona 08014, Spain
Jan Pospíšil: #x2020;Department of Mathematics, University of West Bohemia, Univerzitní 2732/8, 301 00 Plzeň, Czech Republic
Tomáš Sobotka: #x2020;Department of Mathematics, University of West Bohemia, Univerzitní 2732/8, 301 00 Plzeň, Czech Republic§Ernst & Young, s.r.o., Na Florenci 2116/15, 110 00 Praha, Czech Republic
Tommi Sottinen: #x2021;Department of Mathematics and Statistics, University of Vaasa, P. O. Box 700, FIN-65101 Vaasa, Finland
Josep Vives: Universitat de Barcelona, Facultat de Matemàtiques, Gran Via 585, 08007 Barcelona, Spain

International Journal of Theoretical and Applied Finance (IJTAF), 2021, vol. 24, issue 02, 1-47

Abstract: The research presented in this paper provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners due to their surprising consistency with financial markets. However, they bring several challenges alongside. Most noticeably, even simple nonlinear financial derivatives as vanilla European options are typically priced by means of Monte–Carlo (MC) simulations which are more computationally demanding than similar MC schemes for standard stochastic volatility models. In this paper, we provide a proof of the prediction law for general Gaussian Volterra processes. The prediction law is then utilized to obtain an adapted projection of the future squared volatility — a cornerstone of the proposed pricing approximation. Firstly, a decomposition formula for European option prices under general Volterra volatility models is introduced. Then we focus on particular models with rough fractional volatility and we derive an explicit semi-closed approximation formula. Numerical properties of the approximation for a popular model — the rBergomi model — are studied and we propose a hybrid calibration scheme which combines the approximation formula alongside MC simulations. This scheme can significantly speed up the calibration to financial markets as illustrated on a set of AAPL options.

Keywords: Volterra stochastic volatility; rough volatility; Bergomi model; option pricing; decomposition formula (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijtafx:v:24:y:2021:i:02:n:s0219024921500084

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DOI: 10.1142/S0219024921500084

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