Sensitivity Analysis with respect to a Stock Price Model with Rough Volatility via a Bismut-Elworthy-Li Formula for Singular SDEs

Emmanuel Coffie; Sindre Duedahl; Frank Proske

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arXiv · 2107.06022

Sensitivity Analysis with respect to a Stock Price Model with Rough Volatility via a Bismut-Elworthy-Li Formula for Singular SDEs

Emmanuel Coffie·Sindre Duedahl·Frank Proske

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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<1/2 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 also derive a Bismut-Elworthy-Li formula with respect to our stock price model for certain classes of vector fields.

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Emmanuel Coffie, Sindre Duedahl, Frank Proske. 2021-07-13. Sensitivity Analysis with respect to a Stock Price Model with Rough Volatility via a Bismut-Elworthy-Li Formula for Singular SDEs. https://arxiv.org/abs/2107.06022

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