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Variance Reduction Techniques in Pricing Discrete Barrier Options
Yu- Zong Zhang
Barrier Options, Monte Carlo Method, Variance Reduction
|Issue Date: ||2012-12-11 15:38:29 (UTC+8)|
|Abstract: ||自從2008年金融風暴過後，大家意識到風險規避的重要性，而衍生性商品也成為投資者矚目的商品之一，近年來已有不少學者對選擇權相關議題進行研究。界限選擇權可說是目前市場上被廣泛使用的新奇選擇權，對於連續型界限選擇權而言，已經發展出成熟之評價模型，至於間斷型界限選擇權，則是並不存在封閉解(closed form solution)。然而，市場上交易界限選擇權大多為離散型之檢查點，若以連續模型來估算離散式選擇權，將會導致嚴重的誤差，故仍需依賴數值方法求解。本文利用蒙地卡羅法(MC)，進行間斷界限選擇權價格之計算，但是蒙地卡羅模擬法需要一定次數演練與計算才能達到合理解；因此，為了降低蒙地卡羅法之變異並獲得準確之結果，故亦將配合變異數縮減法中的反向變異(AMC)、條件期望值(CMC)以及濾波法(FMC)等來執行模擬演算，希望能有助於改善間斷界限選擇權的評價效率。研究結果發現：(1)採用蒙地卡羅法可避免發生樹狀模型常見之“Barrier-too-close”之問題、(2)CMC法與FMC法均更有助於改善模擬準確性並降低變異、(3)CMC法在執行速度上明顯優於FMC法，且與MC法或AMC法相近。|
After the 2008 financial crisis, the public has become cognizant of the importance of risk aversion, and derivative financial products have become popular among investors. In recent years, many scholars have researched issues relating to options. Barrier options are exotic options that are currently widely used in the market. Mature assessment models have been developed for continuous barrier options, while closed form solutions do not exist for discrete barrier options. However, barrier options traded on the market tend to have discrete checkpoints. Computation of discrete options using continuous models would result in serious errors, and thus solutions still necessarily rely on numerical methods. This study uses the Monte Carlo method (MC) to compute the prices of discrete barrier options, but the Monte Carlo simulation requires a certain number of repetitions and calculations to arrive at reasonable solutions. Thus, in order to reduce variance of the Monte Carlo method and obtain precise results, it is associated with antithetic variates (AMC), conditional expectation (CMC), and filtered Monte Carlo method (FMC) in variance reduction to simulate computations in hopes of improving the assessment efficiency of discrete barrier options. Research results show that: (1) usage of the Monte Carlo method can avoid the “barrier-too-close” problem common to tree structure models; (2) CMC and FMC methods can both help improve simulation precision and reduce variance, and (3) in terms of execution speed, CMC is significantly better than FMC, and is similar to the MC and AMC methods.
|Appears in Collections:||[金融與風險管理系(所)] 博碩士論文|
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