We investigate the performances of the finite element method in solving the Black-Scholes option pricing model. Such an analysis highlights that, if the finite element method is carried out properly, then the solutions obtained are superconvergent at the boundaries of the finite elements. In particular, this is shown to happen for quadratic and cubic finite elements, and for the pricing of European vanilla and barrier options. To the best of our knowledge, lattice-based approximations of the Black-Scholes model that exhibit nodal superconvergence have never been observed so far, and are somehow unexpected, as the solutions of the associated partial differential problems have various kinds of irregularities. © 2012 Elsevier Inc.
Superconvergence of the finite element solutions of the Black-Scholes equation / Golbabai, A.; Ballestra, L.V; Ahmadian, D.. - In: FINANCE RESEARCH LETTERS. - ISSN 1544-6123. - STAMPA. - 10:1(2013), pp. 17-26. [10.1016/j.frl.2012.09.002]
Superconvergence of the finite element solutions of the Black-Scholes equation
BALLESTRA, LUCA VINCENZO;
2013
Abstract
We investigate the performances of the finite element method in solving the Black-Scholes option pricing model. Such an analysis highlights that, if the finite element method is carried out properly, then the solutions obtained are superconvergent at the boundaries of the finite elements. In particular, this is shown to happen for quadratic and cubic finite elements, and for the pricing of European vanilla and barrier options. To the best of our knowledge, lattice-based approximations of the Black-Scholes model that exhibit nodal superconvergence have never been observed so far, and are somehow unexpected, as the solutions of the associated partial differential problems have various kinds of irregularities. © 2012 Elsevier Inc.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
