本研究旨在探討歷史模擬法以及將其考慮GARCH(1,1)模型後，與Monte Carlo模擬方法的比較。本文利用中國市場之指數並藉由模擬選擇權報酬後檢定其與原始價格路徑之選擇權報酬差異來探討三種模擬方法何者之root mean squared pricing error (RMSE)較小。 本文首先以數值模擬之方法模擬出股價之可能路徑，並利用回測方法迭代求算不同選擇權價性與到期日之履約價格比率，進而計算各價格路徑之歐式買權價格，而後估計之。最後再檢定各模擬方法之選擇權報酬估計值與原始價格路徑之選擇權報酬之RMSE。 研究結果顯示各模擬方法之選擇權報酬估計值大多顯著異於原始價格路徑之選擇權報酬，但發現經GARCH(1,1)模型調整過後的歷史模擬法之RMSE顯著小於歷史模擬法以及Monte Carlo模擬方法。 This paper utilized a proposed historical simulation, where the effects of a GARCH (1,1) model on an asset’s price path were considered. The Monte Carlo approach was also used to examine the difference in option payoff values between the simulation approaches and the original path. Furthermore, this paper used the root mean squared pricing error (RMSE) to show which simulation model would have a smaller RMSE by examining the RMSE difference between the approaches. This paper applied the approaches to simulate option payoff values on three security indexes series in China from January 4, 2000 to December 31, 2009, using the common back-testing approach. The results showed that the estimated option values were significantly different from the actual option payoff values for the observed period. Finally, it was found that the RMSE of the adjusted historical simulation was less than that of the other two simulation approaches.
