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標題: 測量誤差與選擇權價格:兩個實證研究
Ignorace Is Bliss? Measurement Errors and Option Prices: Two Empirical Studies
作者: 葉宗穎
關鍵字: 管理科學;基礎研究
這個計畫試圖探討選擇權價格中的測量誤差如何影響選擇權定價模型的參數估計。這個問題在實證文獻上是很重要的,因為在選擇權合約的樣本資料中具有許多雜訊,而這些交易雜訊與市場微結構議題息息相關。除外,許多選擇權合約過於複雜而造成選擇權價格沒有封閉解,這時就必須使用數值方法來計算選擇權價格。數值估價所引起的數值誤差以及交易雜訊都將會顯著地影響參數估計的精確度。然而這個問題在文獻上還沒有被廣泛研究。這個計畫就是試圖想填補文獻上的這一塊空白。這個研究計畫包含兩個主題。第一個主題集中在Monte Carlo模擬的誤差。在標準的GARCH選擇權定價模型裡,我們需要使用Monte Carlo模擬來計算選擇權的價格。在實證研究中,因為我們需要使用Monte Carlo模擬計算每個選擇權合約的價格,這會造成在巨大的數值計算負擔。因此許多實證文獻研究都減少模擬路徑以減輕計算負擔。但是這種作法會引起巨大的Monte Carlo模擬的誤差。所以我提出一個實證方法來處理這個Monte Carlo模擬誤差的問題。在第二個主題裡,我專注在樣本數據的測量誤差。我延伸Duan and Yeh (2010) 的方法使用Chicago Board Options Exchange (CBOE) 的VIX來估計隨機波動跳躍模型,其中VIX 包含測量誤差。原因是VIX的編算會產生離散誤差、截斷誤差和內插錯誤。再者,長天期的選擇權合約流動性通常會比較低,交易雜訊較大,而VIX是一種選擇權價格的線性組合。所以若我們使用在模型中使用VIX來估計,這些測量誤差都會影響模型參數估計的精密度。因此在第二個主題中,我提出了一個particle filtering的方法來處理這個問題。

This project attempts to investigate how measurement errors in the option prices affect the parameter estimation for option pricing models. This issue is particularly importance in empirical finance literature because data samples for option contracts are noisy due to the trading noises caused by market microstructure issues. In addition, many option contracts are too complicated to have closed-form expressions for option prices so that numerical valuation is needed. The numerical errors due to numerical valuation, in conjunction with trading noises, will significantly affect the precision of parameter estimation. However, this issue has not been widely investigated in the empirical option pricing literature. This project attempts to fill this gap in the literature. This research project comprises two topics.The first topic focuses on the Monte Carlo simulation errors. In the standard GARCH option pricing model, we need to use Monte Carlo simulation to compute option prices. The computation burden becomes unmanageable when we conduct empirical implementation with a large data sample. This is because we need to perform option pricing for every option contracts. Many empirical studies reduce the simulation sample paths to ease the concern of computation burden. However, it may give rise to considerably Monte Carlo errors in option pricing and affect the precision of parameter estimation. In the first topic, I propose an empirical method to tackle this Monte Carlo errors issue. Based on this proposed method, we can obtain more accurate parameter estimates with too many simulation sample paths.In the second topic, I focus on the measurement errors embodied in data samples. I extend the approach of Duan and Yeh (2010) to estimate the stochastic volatility model with jumps using VIX, the volatility index constructed by Chicago Board Options Exchange (CBOE), in which VIX involves measurement errors. This is because the VIX construction, in fact, involves discretization errors, truncation errors, and interpolation errors. In addition, VIX is synthesized by a particular linear combination of option prices and the liquidity for option contracts with longer maturity tends to be low, causing considerably trading noises. So these measurement errors are expected to affect the precision of model parameter estimates if we use VIX in the model implementation. In the second topic, I propose a particle filtering approach to deal with this issue.
其他識別: NSC100-2410-H005-014-MY2
Appears in Collections:財務金融學系所

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