Pricing ADR-Linked Bonds Driven By Lévy Processes

This article prices a kind of bull high-yield notes, Fubon Commercial Bank TSM ADR-linked bonds in the Lévy financial market. The high-yield notes composed of zero-coupon bonds and selling the underlying asset options is a kind of structured notes. It belongs to new financial instruments with characteristics such as high yield,high risk, diversity, variety, etc. and it can be divided into four types: bull HYNs,bear HYNs, bear spread HYNs and strangle HYNs according to the different views of investors. Lévy process is a random process constructed by Brownian motion and pure jump process. We use Lévy process as a basic module to establish a mathematical model by assuming the logarithm of underlying asset price, TSM ADR, is a Lévy process. The incompleteness of the market leads to not only one equivalent martingale measure, so the key issue is choosing a good equivalent martingale measure. We get the equivalent martingale measure by Esscher transform and then further deduce the pricing formula by differential method and density function method. Finally, we calculate the pricing results of two examples each method using numerical simulation and Monte Carlo algorithm in Matlab.