TY - JOUR

T1 - A Bismut–Elworthy–Li formula for singular SDEs driven by a fractional Brownian motion and applications to rough volatility modeling

AU - Amine, Oussama

AU - Coffie, Emmanuel

AU - Harang, Fabian

AU - Proske, Frank

PY - 2020/12/11

Y1 - 2020/12/11

N2 - In this paper we derive a Bismut-Elworthy-Li type formula with respect to strong solutions to singular stochastic differential equations (SDE's) with additive noise given by a multidimensional fractional Brownian motion with Hurst parameter H <1/2. "Singular" here means that the drift vector field of such equations is allowed to be merely bounded and integrable. As an application we use this representation formula for the study of the δ price sensitivity of financial claims based on a stock price model with stochastic volatility, whose dynamics is described by means of fractional Brownian motion driven SDE's. Our approach for obtaining these results is based on Malliavin calculus and arguments of a recently developed "local time variational calculus".

AB - In this paper we derive a Bismut-Elworthy-Li type formula with respect to strong solutions to singular stochastic differential equations (SDE's) with additive noise given by a multidimensional fractional Brownian motion with Hurst parameter H <1/2. "Singular" here means that the drift vector field of such equations is allowed to be merely bounded and integrable. As an application we use this representation formula for the study of the δ price sensitivity of financial claims based on a stock price model with stochastic volatility, whose dynamics is described by means of fractional Brownian motion driven SDE's. Our approach for obtaining these results is based on Malliavin calculus and arguments of a recently developed "local time variational calculus".

KW - Bismut-Elworthy-Li formula

KW - singular SDEs

KW - fractional Brownian motion

KW - Malliavin calculus

KW - stochastic flows

KW - stochastic volatility

UR - https://www.intlpress.com/site/pub/pages/journals/items/cms/_home/_main/index.php

U2 - 10.4310/CMS.2020.v18.n7.a3

DO - 10.4310/CMS.2020.v18.n7.a3

M3 - Article

SN - 1539-6746

VL - 18

SP - 1863

EP - 1890

JO - Communications in Mathematical Sciences

JF - Communications in Mathematical Sciences

IS - 7

ER -