摘要
界限選擇權（barrier option）是現在市場上很受歡迎的新奇選擇權（exotic option）之一，跟陽春的選擇權相比，界限選擇權不同處在於它是一種路徑相依的選擇權並非只受期初與期末的股價影響，而必須關注其到期日前標的價格是否曾經大於或小於某一個界限，因此在評價時會遭遇到許多變化與困難。界限選擇權一般大多在幾何布朗運動之下使用反射原理以及標的價格與其極大值（或極小值）的聯合累積機率來定價。雙界限選擇權（double barrier option）和彩虹型界限選擇權（rainbow barrier option）是從界限選擇權衍生出來的新產品，本文所要討論的除了雙界限選擇權或是彩虹型選擇權之外，更推廣去探討彩虹型雙界限選擇權之定價。所謂的彩虹型雙界限選擇權，即在約定時間之內，觀察雙資產其中一資產資產是否曾經跨越界限，如有觸及界限，則該選擇權價失效。在此將利用文獻中所討論的評價雙界限選擇權方法，利用在約定時間內資產沒有觸及界限的分配函數，推導出彩虹型雙界限選擇權評價的封閉解（closed form）。
並列摘要
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. Un-like the plain 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 options is to use the reaction principle to calculate the joint distribution of the maximum (or minimum) and the value at maturity of the underlying stock price 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 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.
延伸閱讀
- Teng, H. W. (2004). 彩虹選擇權之評價 [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU.2004.00259
- Chuang, Y. C. (2016). 跳躍擴散模型下之彩虹選擇權評價 [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU201603455
- Kang, Y. J. (2007). 利用布朗橋快速評價彩虹式障礙選擇權 [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU.2007.01129
- 吳重霖（2017）。多資產美式彩虹選擇權評價〔碩士論文，國立臺灣大學〕。華藝線上圖書館。https://doi.org/10.6342/NTU201702468
- Lin, V. (2006). Pricing Barrier Options in Two Dimensions [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU.2006.00055