利用股價與選擇權的數據來估計GARCH選擇權定價模型

Using Stock and Options Data to Estimate the GARCH Options Pricing Model

鄭宏文(Hung-Wen Cheng)

指導教授 ： 傅承德

共同指導教授 ： 王耀輝(Yaw-Huei Wang)

國立臺灣大學/管理學院/財務金融學研究所/博士(2011年)

https://doi.org/10.6342/NTU.2011.03182

摘要

這個研究推導了當只用股票數據（ST）、只用選擇權數據（OT）及用股票和選擇權數據有含（S+O+E）或沒有含誤差項（S+O）時的GARCH(1,1) 選擇權價格模型估計的漸近特性。在大樣本理論下的漸近變異數說明了只用選擇權數據（OT）會導致潛在地偏誤和無效率性的估計，反之，用股票和選擇權數據有含誤差項（S+O+E）會產生大致上比其他任何一種方法更有效性的無偏估計。這些結果被有限樣本模擬的研究證實了。因此，介於 S+O+E 和ST 的估計誤差是實質性地導致顯著地不同風險管理結果。這些誤差大大影響了所採用方法的風險管理指標(如選擇權的deltas 和gammas 值)高達 80%。由於這GARCH 選擇權模型是相對地限制及不能捕捉實證現像（參考Engle 和Mustafa (1992)），我們引進一個誤差項到這選擇權定價模型，借貸所需的呆滯到這個估計過程，由此產生了最大有效率性的無偏估計。也就是說，數據多是更好的，但是只有當數據是正確的被應用時。

關鍵字

GARCH選擇權模型 ； 漸近行為 ； 估計的有效率性及偏誤 ； 風險管理

並列摘要

This study derives asymptotic characteristics of GARCH(1,1) options price model estimators when using stock data only (ST), using option data only (OT), and using stock and options data with (S+O+E) or without an error term (S+O). The asymptotic variance in large sample theory shows that the OT method results in potentially biased and inefficient estimators, whereas S+O+E generates unbiased estimators which are substantially more efficient than either ST (S+O) or OT. These results are confirmed by finite sample simulation studies. Hence, the difference in estimation between S+O+E and ST is substantial and results in significantly different risk management consequences. These errors substantially impact risk management metrics as options deltas and gammas vary by as much as 80%, depending on the method used. Since the GARCH option models are relative restrictive and cannot capture the empirical phenomena (cf. Engle and Mustafa (1992)), we introduce an error term to the options pricing model, lending needed slack to the estimation process and resulting in unbiased estimates that are maximally efficient. That is, more data is better, but only if the data set is appropriately applied.

並列關鍵字

GARCH option model ； asymptotic behavior ； estimator efficiency and bias ； risk management

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