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 journalArticle

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
JournalApplied Mathematical Finance
DOIs
Publication statusAccepted/In press - 2018 Jan 1

Fingerprint

Mean-variance Hedging
Additive Process
Malliavin Calculus
Closed-form
Malliavin Derivative
Numerical Methods
Exponential Model
Numerical methods
Fast Fourier transform
Jump
Fast Fourier transforms
Numerical Results
Model
Derivatives
Strategy
Mean-variance hedging
Malliavin calculus

Keywords

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

ASJC Scopus subject areas

  • Finance
  • Applied Mathematics

Cite this

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