衍生性商品數值評價─樹狀圖法

Abstract

這篇論文將介紹 Black 和 Scholes 於1973年提出的歐式選擇權價格模型, 同時介紹以二項式、 三項式、 有限差分及 Implied Tree …等數值方法逼近 Black-Scholes 的解析解, 並且近一步計算美式選擇權的合理價格。 最後, 我們以這些方法計算往後看選擇權 (Lookback Option) 的合理價格, 並且以 Root Mean Square Error (RMSE) 探討不同數值方法及參數之間對精確度的差異性。

In this paper, we will introduce the European option pricing model developed by Black and Scholes in 1973. At the same time, it can approximate the Black-Scholes formula by many numerical methods, like binomial, trinomial, finite difference, implied tree, etc. We will compute the reasonable price of American option furthermore. Finally, we compute the Lookback option price by these numerical methods and use root mean square error (RMSE) to investigate the accuracies between different numerical methods with parameters.