選擇權隱含波動率偏斜價差交易之應用方法與實證研究－以台指選擇權為例

標的資產價格波動率為選擇權定價與避險的重要影響因素，也是唯一無法直接觀察取得的參數，因而必須使用一有效估計方法以估測其值，目前主要的估計方法為歷史波動率法與隱含波動率法，多數學者認為隱含波動率應是未來波動率的最佳估計值，使得隱含波動率被學術界及實務界廣泛應用於選擇權評價。然而，根據一系列相同標的資產選擇權契約所推算出之隱含波動率往往因買權與賣權或履約價格不同有所差異，而且這些差異有時會呈現特定的偏斜現象。雖然隱含波動率差異形成原因仍待深入探究，不過，波動率差異的出現應即表示選擇權價格出現失衡情況，此時執行與偏斜情況對應的價差交易策略即可能存在獲取交易利潤的機會。本研究即從實證角度探討隱含波動率偏斜價差交易的實用性與獲利性，並分別以週到期與月到期台指選擇權為實證研究對象，實際觀察台指選擇權短天期與長天期契約之隱含波動率偏斜情況，並且分析根據偏斜情況執行波動率偏斜價差交易的獲利狀況。實證結果顯示，在長期交易之下，隱含波動率偏斜價差交易全部都獲致可觀的累計正報酬，且週到期契約之獲利表現遠優於月到期契約，台指賣權之整體獲利表現又優於台指買權，另外，週到期選擇權之各期到期報酬與該期波動率全距存在顯著正向關聯，週到期選擇權搭配波動率全距之中位數與最低轉點篩選準則，將可大幅提升偏斜價差交易的交易利得，由此可知，波動率偏斜價差交易策略應更適用於短天期選擇權。

關鍵字

隱含波動率；選擇權價差交易；波動率偏斜價差交易；台指選擇權

並列摘要

The volatility of underlying asset price is an important influencing factor on options pricing and hedging. It is also only parameter, which cannot directly observe, and hence, its value has to estimate through using an effective evaluation method. Presently, the both of historical volatility and implied volatility are commonly utilized to evaluate the volatility. Most researchers consider that implied volatility, which is reversely solved by bringing the options market price into the pricing model, should be the best estimate of future volatility. Accordingly, implied volatility has been widely applied for the purposes of options pricing and hedging. However, implied volatilities obtained from a series of options, which possess the same underlying asset and duration to maturity, often are difference among a range of exercise prices for call and put options. Sometimes, these different implied volatilities may appear a particular skew pattern. Although the cause for resulting in the different implied volatilities needs to be explored deeper, the existence of various implied volatilities evidently indicates that an imbalance in option prices occurred. In the meantime, there is likely a chance to make profits by means of carrying out a corresponding skew spreads based on the volatility skew pattern. This study thus looks at the practicability and profitability of volatility skew spreads in terms of the empirical study. To this end, the weekly and monthly contracts for Taiwan Index Option (TXO) are taken as the empirical object to actually observe the skew patterns of implied volatility for short -term and long-term TXOs. More importantly, this study also analyzes the resulting profits when performing the volatility skew spreads based on skew patterns. The empirical results show that under long-term trading, the implied volatility skew spreads all yield sizeable cumulative positive returns. Moreover, the profitability of the weekly options is much better than that of the monthly options, and put options overall is superior to call options in making profits. Additionally, there is a significantly positive relationship between the terminal profit and the volatility range for weekly options. Furthermore, weekly options will greatly boost up the gains of the volatility skew spreads in case of coupled with the median of volatility range and the lowest turning point screening criteria. In total, the volatility skew spread tends to be more suitable for applying in short-term options.