多資產美式彩虹選擇權評價

Abstract

本篇論文將延伸Lin (2016)的兩資產平方逼近法(參考Barone-Adesi, G. and Whaley, R. (1987))簡稱BAW，將其拓展成為可以定價多個資產的方法。在解BAW提早履約貼水時偏微分的部分，將比重做不同的調整，調整過後的比重在定價美式彩虹選擇權時，加上原來Lin (2016)的方法，三個方法去與真實值比較，發現本論文所考慮進去的方法會較為準確。 另外，本篇論文也用BAW法定價五資產之美式彩虹選擇權，並與廣為人知的最小平方法(Least Square Method)去做比較，結果顯示，在精準度上，BAW法擊敗最小平方法。

This paper modifies Lin (2016)’s quadratic approximation method to develop a multi-asset pricing method for American rainbow options. Specifically, I reconsider different weighting schemes for individual underlying assets when solving the partial differential equation of the early exercise premium of the American rainbow option. The proposed weighting schemes are superior to the method used in Lin (2016) in terms of generating accurate option prices for two-asset American rainbow options. Furthermore, I also compare the proposed method with the least-squares Monte-Carlo simulation for pricing five-asset American rainbow options. The results demonstrate that the proposed method is more efficient and accurate than the least-squares Monte-Carlo simulation.