Second-Order Weak Approximations of CKLS and CEV Processes by Discrete Random Variables

Abstract

In this paper, we construct second-order weak split-step approximations of the CKLS and CEV processes that use generation of a three−valued random variable at each discretization step without switching to another scheme near zero, unlike other known schemes (Alfonsi, 2010; Mackevičius, 2011). To the best of our knowledge, no second-order weak approximations for the CKLS processes were constructed before. The accuracy of constructed approximations is illustrated by several simulation examples with comparison with schemes of Alfonsi in the particular case of the CIR process and our first-order approximations of the CKLS processes (Lileika– Mackevičius, 2020).