Evaluating the Interest Rate Derivatives with Historical Simulation Method

[[abstract]]本研究主要目的在於使用歷史模擬法(Historical Simulation Method)求解利率衍生性金融商品不含任何分配限制的一般化定價模型之模型價格。此一般化定價模型與歷史模擬法的設定主要在避免傳統的定價方法常因分配假設錯誤而導致錯誤定價的問題。歷史模擬法不必事先假設利率的分配型式，此方法是先以Esscher轉換(Esscher Transform)方法求得遠期測度，再以利率的歷史資料模擬原始報酬分配並透過Esscher轉換方法測度轉換，藉此模擬出一般化定價模型中在遠期測度下的分配，進而求得利率衍生性金融商品的一般化模型價格。文中並做數值分析，比較這個方法和傳統假設標的資產的波動為常態分配的模型在利率上限契約(Cap)商品上的定價差異。[[abstract]]This thesis uses the historical simulation method to evaluate the price of general pricing models of interest rate derivatives, where the general pricing models are derived without any distribution restrictions. The general pricing models and historical simulation method are set up in order to avoid the mispricing problem that is caused by the mistake of distribution assumption from the traditional pricing methods. The historical simulation method needs not to suppose the distribution type of interest rate in advance. It uses the Esscher transform method to find the forward measure firstly. Then, it changes the probability measure from the original distribution to forward distribution by the Esscher transform method, so as to simulate the distributions of general pricing models that are under the forward measure. Finally, using these simulated distributions, this thesis solves the general model price of interest rate derivatives. The article also provides the numerical analyses on the cap to compare the pricing errors in our method with the pricing errors in the traditional models that assume the volatility of underlying asset return as normal distribution.[[note]]碩