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

• Main Authors: Hung-Wen Cheng, 鄭宏文
• Other Authors: Cheng-Der Fuh
• Format: Others
• Language: en_US
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/35989769453159655149

博士 === 國立臺灣大學 === 財務金融學研究所 === 99 === 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.