DG method for pricing European options under Merton jump-diffusion model

Abstract

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz 64 (2019)

Option valuation under the VG process by a DG method

“…Following the standard techniques as in [20], we proceed in the same way as in the variational formulation, with the only difference that we apply the integration by parts to convection terms as well, cf. (2.63), and include discontinuities across partition nodes with the aid of operators (3.2).…”

“…Further, to introduce the semidiscrete variant of (2.63), we recall three slightly modified bilinear forms from [20] defined on S p h × S p h , that is,…”

“…As in [20], we introduce the linear form ℓ ε h to enforce the fulfillment of the boundary conditions and to encompass the remainders from the large jumps, specifically…”

“…The presented work is the follow up to the results from [20] where a jump process of a finite activity is assumed. In a similar way we transform the original governing equation to the initial-boundary value problem that reflects the properties of the VG process.…”

“…All the above attributes make this method a suitable candidate for solving the problem of option pricing under the VG process. Apart from our recent results [18], [19] and [20], let us mention some of the few other applications of the DG approach in option pricing problems, e.g., [24] and [32].…”