The Analytic Valuation Of Three New Barirer Options

In this paper, we give the valuation of the down-and-out asian rainbow exponential bar-rier call options, the down-and-out exchange barrier options and the down-and-out multi-assetsbarrier call options with rainbow feature. The asian rainbow barrier option is an extension torainbow barrier option which is only knocked in or knocked out if a second asset touches theconstant barrier prior to expiration. We go beyond the scope of Peter Carr’s formulas by al-lowing the barrier level to be exponential. At the same time, this new kind of option also hasthe feature of asian options, which means the payoff depends on the average asset price andthe average value of the barrier variable. Exchange barrier option is an extension to exchangeoptions and barrier options, which gives the holder the right but not the obligation to exchangeone risky asset for another, and it will be knocked out or knocked in if the barrier asset touchesthe constant barrier prior to expiration. Multi-assets barrier options with rainbow feature alsocan help the investor to have a better result. The method of reflection is used to derive theclosed form valuation formula which can also be extended to price other kinds of these threenew barrier options.