Affiliations: School of Engineering, New York University, Brooklyn, NY, USA
Correspondence:
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Corresponding author: Andrey Itkin, School of Engineering, New York University, 6 Metro Tech Center, RH 517E, Brooklyn, NY 11201, USA. Tel.: +646 855 3389; Fax: +718 260 3355; E-mail: aitkin@nyu.edu
Abstract: This paper is a further extension of the method proposed in Itkin (2014) as applied to another set of jump-diffusion models: Inverse Normal Gaussian, Hyperbolic and Meixner. To solve the corresponding PIDEs we accomplish few steps. First, a second-order operator splitting on financial processes (diffusion and jumps) is applied to these PIDEs. To solve the diffusion equation we use standard finite-difference methods. For the jump part, we transform the jump integral into a pseudo-differential operator and construct its second order approximation on a grid which supersets the grid used for the diffusion part. The proposed schemes are unconditionally stable in time and preserve positivity of the solution which is computed either via a matrix exponential, or via its Páde approximation. Various numerical experiments are provided to justify these results.
