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

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.