Sensitivity analysis with respect to a stochastic stock price model with rough volatility via a Bismut–Elworthy–Li formula for singular SDEs

Emmanuel Coffie, Sindre Duedahl and Frank Proske

Stochastic Processes and their Applications, 2023, vol. 156, issue C, 156-195

Abstract: In this paper, we show the existence of unique Malliavin differentiable solutions to SDE‘s driven by a fractional Brownian motion with Hurst parameter H<12 and singular, unbounded drift vector fields, for which we also prove a stability result. Further, using the latter results, we propose a stock price model with rough and correlated volatility, which also allows for capturing regime switching effects. Finally, we derive a Bismut–Elworthy–Li formula with respect to our stock price model for certain classes of vector fields.

Keywords: Bismut–Elworthy–Li formula; Singular SDEs; Fractional Brownian motion; Malliavin calculus; Stochastic flows; Stochastic volatility (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:156:y:2023:i:c:p:156-195

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DOI: 10.1016/j.spa.2022.11.001

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