Valuation of step-down knock-in in one stock linked security using numerical and Monte Carlo integration

This paper shows a new methodology for evaluating the value and sensitivity of autocall knock-in type equity-linked securities. While the existing evaluation methods, Monte Carlo simulation and finite difference method, have limitations in underestimating the knock-in effect, which is one of the important characteristics of this type, this paper presents a precise joint probability formula for multiple autocall chances and knock-in events. Based on this, the calculation results obtained by utilizing numerical and Monte Carlo integration are presented and compared with those of existing models. The results of the proposed model show notable improvements in terms of accuracy and calculation time.