呂育道Lyuu, Yuh-Dauh臺灣大學:財務金融學研究所范育誠Fan, Yu-ChenYu-ChenFan2010-05-112018-07-092010-05-112018-07-092009U0001-1607200914071600http://ntur.lib.ntu.edu.tw//handle/246246/182798　　離散型亞式選擇權有固定履約價(fixed-strike)、浮動履約價(floating-strike)兩種型態，此二類離散型亞式選擇權有對稱的性質，因此我們只需探討前者，而後者可透過此關係間接求得。接著利用平移對數常態分配(shifted log-normal distribution)動差擬合(moment matching)觀察期間的平均價格，求出選擇權價格及避險係數(Greeks)的封閉解。在我們的認知中，之前的文獻是用數值方法去找出該近似分配的參數，但我們發現有封閉解，所以執行起來更方便。最後以蒙地卡羅模擬(Monte Carlo simulation)所得價格當作基準，和以平移對數常態分配、對數常態分配(log-normal distribution)、反伽馬分配(reciprocal gamma distribution)做動差擬合所求出的價格做比較。數值結果顯示我們的評價方法非常接近模擬價格。There are two types of discrete Asian options, fixed-strike and floating-strike. We focus on the fixed-strike type because the floating-strike type can be calculated through the symmetric property. To derive the closed-form solution to the option price and Greeks, we use the shifted log-normal distribution to match the moments of the arithmetic average value. Furthermore, we find a closed-form solution to the parameters which is new in the literature so that pricing and hedging are faster to execute than before. In the end, we compare three moment matching methods (based on shifted log-normal, log-normal and reciprocal gamma distribution) and Monte Carlo simulation as benchmark. Numerical results show our approach gives results very close to those by Monte Carlo simulation.1簡介 1亞式選擇權的特性 4.1模型簡介 4.2買權與賣權的平價關係 5.3固定履約價和浮動履約價的對稱性 6評價公式及避險係數的封閉解 10.1平移對數常態分配 10.2其它分配 13.3圖形比較 14.4避險係數的封閉解 17數值結果 18結論 22錄 23錄1 23錄2 24錄3 28錄4 29考文獻 33application/pdf459323 bytesapplication/pdfen-US離散型亞式選擇權平移對數常態分配動差擬合避險係數封閉解discrete Asian optionsshifted log-normal distributionGreeksmoment matchingclosed-form solutionthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/182798/1/ntu-98-R96723063-1.pdf