障礙型保本票券評價方法的比較性分析：數值方法的應用

對於標的資產存在設限障礙之保本模型，常因難以導出正確(exact)的封閉解(closed-form solution)而以蒙地卡羅(Monte Carlo)進行數值模擬。在蒙地卡羅模擬法中，Rubinstein and Marcus(1985)與Nelson(1990)發現控制變數蒙地卡羅法是較有效率的方法。而本文重覆多次模擬，並以其平均值和票券的市價計算標準誤(standard error)，檢視控制變數卡羅法於障礙型保本票券的效率性，並比較不同的蒙地卡羅法（普通蒙地卡羅、相對變數蒙地卡羅和準蒙地卡羅）。結果發現，控制變數法之精確度較普通蒙地卡羅法、相對變數蒙地卡羅法和準蒙地卡羅法低，且模擬的時間比普通蒙地卡羅法費時。此外，相對變數蒙地卡羅之精確度是最高的，且模擬的時間並不會很耗時。

關鍵字

障礙型保本票券；相對變數蒙地卡羅法；控制變數蒙地卡羅法；準蒙地卡羅法；精確度

並列摘要

It is difficult for principal-protected and barrier models to derive their exact closed-form solutions. Monte Carlo methods are convenient and efficient to value them. Among Monte Carlo methods, Rubinstein and Marcus (1985) and Nelson (1990) show that control-variate Monte Carlo is more efficient than the others under no jump models. This article examines the performance of control variate Monte Carlo using the path-dependent and principal-protected notes with cap in the sample. A comparison of various Monte Carlo methods is presented such as ordinary Monte Carlo, antithetic variate Monte Carlo, control variate Monte Carlo and quasi Monte Carlo. After repeating simulations and using the market price of the note as a benchmark to compute its standard error, we find that the accuracy of control variate Monte Carlo is not the best among all Monte Carlo methods. Also, it takes much longer time to simulate than ordinary Monte Carlo simulation. In Type I arrangement of random errors of quasi Monte Carlo method, there is the highest accuracy than the others. But one has to spend the largest time to simulate for quasi Monte Carlo method.

並列關鍵字

Barrier Principal-protected Notes ； Antithetic Variate Monte Carlo ； Control Variate Monte Carlo ； Quasi Monte Carlo ； Accuracy

參考文獻

王昭文、張嘉倩(2004)。隨機利率下保本型票券之評價與避險策略。亞太經濟管理評論。7(1)，51-68。

Acworth, P.,M. Broadie,P. Glasserman,P. Hellekalek,H. Niederreiter (ed.)(1997).Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing.New York:Springer.