On the paper “ Is Itô calculus oversold ? ” by A . Izmailov and B . Shay

The main message of the paper “Is Itô calculus oversold?” by A. Izmailov and B. Shay is, we quote: “However, when applied to the nonlinear interest rate models such as CoxIngersoll-Ross, Itô calculus only gives approximate results (...)” This surprising claim is first supported in the introduction by few words on the “diffusion approximation,” in which the authors seem to suggest that the Stratonovich integral gives a more exact approximation than the Itô integral. We are, of course, aware about the difference in both kinds of integrals, however, it is unclear to us to what extent this is related to the main topic of the paper. Also, since the authors only mention vaguely the diffusion approximation, without clarifying this important issue, a serious discussion with their statements in this regard is not possible. Let us only mention that the Cox-Ingersoll-Ross (CIR) diffusion-type model is well known to be a good diffusion approximation for several branching processes. Since many other authors’ statements are vague and frequently confusing, we shall comment on the purely mathematical aspects of the paper only.