Chapman–Kolmogorov equations for multi-period equity-linked note with conditional coupons

Abstract

An equity-linked note with complex payoff and a path dependent variable maturity is analyzed analytically and numerically. This note pays up to one coupon, the size of which depends on the period count in which it is paid and with initial investment partially protected. Valuation of this instrument is achieved in closed form in terms of multivariate normal distribution function, but simple, fast and accurate numerical solution in terms of Chapman–Kolmogorov equations is preferred. The note has a number of unique features, some of which expose the investors to types of risk not usually encountered in either equity or fixed income world.