A numerically efficient closed-form representation of mean-variance hedging for exponential additive processes based on Malliavin calculus. Issue 3 (4th May 2018)

• Record Type: Journal Article
• Authors: Arai, Takuji; Imai, Yuto
• Is Part Of: Applied mathematical finance. Volume 25:Issue 3(2018)
• Page Start: 247
• Page End: 267
• Publication Date: 2018-05-04
• Subjects: Mean-variance hedging -- additive processes -- Malliavin calculus -- fast Fourier transform; Business mathematics -- Periodicals; 650.0151
• DOI: 10.1080/1350486X.2018.1506259
• Languages: English
• ISSNs: 1350-486X

Abstract

ABSTRACT: 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.