TY - JOUR

T1 - A numerically efficient closed-form representation of mean-variance hedging for exponential additive processes based on Malliavin calculus

AU - Arai, Takuji

AU - Imai, Yuto

N1 - Funding Information:
This work was supported by the Japan Society for the Promotion of Science [Grant number KAKENHI 15K04936].

PY - 2018/5/4

Y1 - 2018/5/4

N2 - We focus on mean-variance hedging problem for models whose asset price follows an exponential additive process. Some representations of mean-variance hedging strategies for jump-type models have already been suggested, but none is suited to develop numerical methods of the values of strategies for any given time up to the maturity. In this paper, we aim to derive a new explicit closed-form representation, which enables us to develop an efficient numerical method using the fast Fourier transforms. Note that our representation is described in terms of Malliavin derivatives. In addition, we illustrate numerical results for exponential Lévy models.

AB - We focus on mean-variance hedging problem for models whose asset price follows an exponential additive process. Some representations of mean-variance hedging strategies for jump-type models have already been suggested, but none is suited to develop numerical methods of the values of strategies for any given time up to the maturity. In this paper, we aim to derive a new explicit closed-form representation, which enables us to develop an efficient numerical method using the fast Fourier transforms. Note that our representation is described in terms of Malliavin derivatives. In addition, we illustrate numerical results for exponential Lévy models.

KW - Malliavin calculus

KW - Mean-variance hedging

KW - additive processes

KW - fast Fourier transform

UR - http://www.scopus.com/inward/record.url?scp=85052568588&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85052568588&partnerID=8YFLogxK

U2 - 10.1080/1350486X.2018.1506259

DO - 10.1080/1350486X.2018.1506259

M3 - Article

AN - SCOPUS:85052568588

VL - 25

SP - 247

EP - 267

JO - Applied Mathematical Finance

JF - Applied Mathematical Finance

SN - 1350-486X

IS - 3

ER -