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

Takuji Arai, Yuto Imai

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)247-267
Number of pages21
JournalApplied Mathematical Finance
Volume25
Issue number3
DOIs
Publication statusPublished - 2018 May 4

Keywords

  • Malliavin calculus
  • Mean-variance hedging
  • additive processes
  • fast Fourier transform

ASJC Scopus subject areas

  • Finance
  • Applied Mathematics

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