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Barrier option is one of the Exotic options which are very popular in the market. In contrast with the simplest option, barrier option is continuous time and path dependent.Unlike the common vanilla option, to price the barrier option one not only need to check the starting and the ending prices of the stock, but also have to pay attention to whether the underlying stock price before maturity T has ever crossed the barrier. In that case more variability and difficulties arise in pricing the option.The most popular technique in pricing barrier option is to uses the reflection principle to calculate the joint distribution of the maximum( or minimum )and the value at maturity of the underlying stock prices based on geometry Brownian motion.
Double barrier option and rainbow barrier option are two new products evolved from the barrier option. In addition to the discussion of these options, we will extend our exploration to double barrier rainbow option .Double barrier rainbow option depends on two assets. If one of the assets has ever been crossed the barrier, this option becomes priceless.We will use the technique of pricing double barrier options proposed by the referred papers, and the distribution of underlying assets in the case that the asset never touches barrier, to deduce a closed form of the price of the double barrier rainbow option.
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