Numerical Analysis on Quadratic Hedging Strategies for Normal Inverse Gaussian Models

Abstract

The authors aim to develop numerical schemes of the two representative quadratic hedging strategies: locally risk-minimizing and mean-variance hedging strategies, for models whose asset price process is given by the exponential of a normal inverse Gaussian process, using the results of Arai et al. (Int J Theor Appl Financ 19:1650008, 2016) and Arai and Imai (A closed-form representation of mean-variance hedging for additive processes via Malliavin calculus, preprint. Available at https://arxiv.org/abs/1702.07556). Here normal inverse Gaussian process is a framework of Levy processes that frequently appeared in financial literature. In addition, some numerical results are also introduced.