In recent years, the issuances of equity linked products such as ELD (Equity Linked Deposit) and ELS (Equity Linked Securities) have been rapidly growing in Korea, thanks to low deposit rates and competitions between banking and securities industries. A prototype of these equity-linked products is a bond or deposit combined with barrier type option, for which its final payoff depends on the maxima or minima of underlying securities during its life. One of special features of these embedded options in the equity linked products is that they have much longer maturities than exchange-traded options do. Consequently, the stochastic nature of interest rates may be important in pricing barrier options embedded in ELD and ELS.The purpose of this paper is to derive closed or semi-closed form solutions for various type of barrier options under stochastic interest rates. Specifically, using T-forward measures, we derive not only closed-form solutions for options with fixed barriers, but also semi-closed form solutions for options with discounted barriers. Furthermore, we calibrate the derived solutions with parameters estimated from KOSPI200 Index and interest rates data to see the sensitivity of long-term barrier option premiums with respect to the assumptions and parameters of a stochastic interest rates model
